Research ArticleCollision-Free Path-Planning for Six-DOF Serial HarvestingRobot Based on Energy Optimal and Artificial Potential Field
Lufeng Luo 1 Hanjin Wen1 Qinghua Lu 1 Haojie Huang1 Weilin Chen1
Xiangjun Zou2 and Chenglin Wang3
1College of Mechanical and Electrical Engineering Foshan University 18 Jiangwan Road Foshan 528000 China2Key Laboratory of Key Technology on Agricultural Machine and Equipment Ministry of EducationSouth China Agricultural University 483 Wushan Road Guangzhou 510642 China3College of Mechanical and Electrical Engineering Chongqing University of Arts and Sciences 319 Honghe RoadYongchuan Chongqing 402160 China
Correspondence should be addressed to Lufeng Luo luolufengfosueducn and Qinghua Lu qhlufosueducn
Received 7 August 2018 Revised 6 October 2018 Accepted 18 October 2018 Published 1 November 2018
Guest Editor Zhaojie Ju
Copyright copy 2018 Lufeng Luo et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Collision-free autonomous path planning under a dynamic and uncertainty vineyard environment is the most important issuewhich needs to be resolved firstly in the process of improving robotic harvesting manipulator intelligence We present and applyenergy optimal and artificial potential field to develop a path planning method for six degree of freedom (DOF) serial harvestingrobot under dynamic uncertain environment Firstly the kinematical model of Six-DOF serial manipulator was constructed byusing the Denavit-Hartenberg (D-H) method The model of obstacles was defined by axis-aligned bounding box and then theconfiguration space of harvesting robot was described by combining the obstacles and arm space of robot Secondly the harvestingsequence in path planning was computed by energy optimal method and the anticollision path points were automatically generatedbased on the artificial potential field and sampling searching method Finally to verify and test the proposed path planningalgorithm a virtual test system based on virtual reality was developed After obtaining the space coordinates of grape pickingpoint and anticollision bounding volume the path points were drew out by the proposed method 10 times picking tests for grapeanticollision path planning were implemented on the developed simulation system and the success rate was up to 90The resultsshowed that the proposed path planning method can be used to the harvesting robot
1 Introduction
Planning optimal paths is an important branch in the researchfield of intelligent robot and an ideal path planning methodis very important for improving the performance of robots[1 2] In agricultural production fruit harvesting is a time-consuming and labour-intensive procedure and the studyon timely harvesting of fruits using robotics manipulatoris becoming a significant challenge for researchers [3] Toaccomplish the task of fruit harvesting successfully automaticobstacle-avoidance path planning of harvesting manipulatoris one of the key technical problems of fruit harvesting robot[4] In the process of solving the path planning problemif the environment information is completely knowable thetime global planning can be used to obtain an optimal path
to reach the target state from the initial state [5] Howeverthe harvesting robot usually operates in a nonstructuraland complex natural environment and its work space ofteninvolves various uncertainties which robots must evade suchas branches and immature fruits which distributed aroundripe fruits (harvesting target) So the dynamic uncertaintyof the obstacle and the location of the picking target makethe path planning a difficult problem In such case it canonly be based on the real-time detection of the environmentalinformation and reprogramming to get themoving path fromthe current state to the target state
In recent years scholars from different parts of theworld have proposed many methods and strategies forsolving anticollision path for automatic robot in uncertainenvironment and dynamic obstacle environment [6] These
HindawiComplexityVolume 2018 Article ID 3563846 12 pageshttpsdoiorg10115520183563846
2 Complexity
studies can be divided into four primary categories [7] grid-based approaches potential field approaches sample-basedapproaches and discrete optimization approaches In [7] areal-time dynamic path planning method for autonomousdriving that avoids both static and moving obstacles waspresented In [8] two efficient sampling-based approachescombining two RRT variants were developed to solve acomplex path planning problem and a path planningmethodwhich uses mutual information was proposed for the multi-AUV (AutonomousUnderwaterVehicle) systemCui et al [9]presented an adaptive path planning algorithm for multipleAUVs to estimate the scalar field over a region of interestTomake the manipulator avoid collisions with the plant stemin sweet-pepper harvesting Bac et al [10] presented a stemlocalization of sweet-pepper plants using the supportwire as avisual cueThe objectives of this study were to find the obsta-cles so that the robot can plan a collision-avoidance path Toconduct an undamaged robotic grape-harvesting Luo et al[11] focused their works on locating the spatial coordinatesof the cutting points on a peduncle of grape clusters for theend-effector and determining the bounding volume of thegrape clusters for the motion planner of the manipulator Athree-dimensional CAD model used in [12] has solved theproblem of collision between the cucumber picking robotand the stem but the amount of collision calculation is verylarge To decrease the movement uncertainty of industrialrobots Gao et al [13] presented a parameter identificationmethod based on the D-H model in where the redundantparameters are particularly addressed Experimental studiesbased on a 6 DOF industrial robot show the proposedmethod can improve themovement accuracy of the industrialrobot significantly To make the robotic manipulator workefficiently and safely in a dynamic unstructured environmentWei et al [14] proposed an autonomous obstacle avoidancedynamic path-planning method for a robotic manipulatorbased on an improved RRT algorithm For solving serialmanipulators path-planning when grabbing target in obstacleworkspace Dai et al [15] presented a solution based on screwtheory and ant colony algorithm In [16] a new approachto time-optimal path parameterization (TOPP) based onreachability analysis was proposed
Through the above analysis we can see that the pathplanning strategies applied in unstructured environments inrecent years focused on autonomous driving autonomousunderwater vehicle and industry robots Although somedomestic and foreign scholars have carried out some researchon the path planning of fruit and vegetable picking robotthe research on collision-free autonomous path planningfor the grape harvesting robot under a dynamic vineyardenvironment is still in the initial stage
To conduct an undamaged robotic grape-harvesting inan unstructured vineyard a collision-free autonomous pathplanning method based on minimum energy and artificialpotential field for grape harvesting robot was developed inthis study Firstly the kinematical model of six-DOF serialharvesting manipulator was constructed by using the D-Hmethod the model of obstacles was defined by the axis-aligned bounding box and then the configuration space ofharvesting robot was described by combining the obstacles
and arm space of robot Secondly the harvesting sequencein path planning was computed by energy optimal methodand the anticollision path points were generated based onthe artificial potential field and sampling searching methodFinally to verify and test the proposed path planning algo-rithm a virtual test system based on virtual reality wasdeveloped The innovation of this study is the developmentof the energy optimal harvesting sequence planning methodand the anticollision path points generating method basedon the configuration space of six-DOF serial harvestingmanipulator
The paper is organized as follows Section 2 shows severalbasic models for harvesting robot that will be used in the pathplanning strategies Section 3 describes the plan planningmethod that was designed based on energy minimum andartificial potential field Section 4 performed an experimentto validate the performance of the developed plan planningmethod Section 5 summarizes and discusses the experimentresults The paper ends with the conclusions and future work
2 Basic Models Building for Harvesting Robot
The task of obstacle avoidance path planning of the six degreeof freedommanipulator is to search for a series of continuousjoint angle values under the condition of the given obstaclethe starting and target position of themanipulator which candrive the manipulator to move from the starting position tothe target position safely without collision To elaborate theprinciple and process of the path planning method proposedin this paper in detail it is necessary to establish the robotcoordinate system kinematic model obstacle model and theconfiguration space model which are the design basis of thepath planning algorithm
21 Kinematical Modelling for Six-DOF Serial Robot Theshape of the six degree of freedom series harvesting robotis as shown in Figure 1(a) which is made up of six rotatingjoints They are responsible for adjusting the end-effectorto the appropriate picking position so that the actuator canclamp the grapes and cut the peduncles The end-effectoris composed of three functional parts clamper pallet andscissor The harvesting manipulator is made up of rigid linkand rigid joint and its motion is realized by controlling thejoints of the manipulator
211 Establishing D-H Coordinate System for Harvesting ArmTo establish the forward and reverse kinematics models ofthe harvesting robot the Denavit- Hartenberg (D-H)method[17] was adopted in this study The D-H table (see Table 1) isbuilt on the basis of the structure and parameters of the robotAnd then the coordinate system of the picking robot is set upin which the reference coordinate system is O0 and the localcoordinate system of each joint is Oi (i = 1 2 6) and theend-effector coordinate system is Oh The coordinate systemof each joint of the picking robot is shown by Figure 1(b)
212 Forward and Inverse Kinematic Modeling The motionof the harvesting robot is driven by the forward kinematics
Complexity 3
ClamperScissors
Pallet
(a) Harvesting robot shape
O2
O0
O3
O4O5 O6
x6
y6
z6z5
x5
x4
z4
y4
x3
y3
z0x0y0
y5
O1
xh
yh zh
Oh
a3
d4
x1
z1
y1
z2
x2
y2
z3a2
a 1
1
2
3
54
6
(b) Origin coordinate and joints coordinate systems ofharvesting robot
Figure 1 Harvesting robot shape and its joints coordinate systems Note that 1198740 is the base coordinate of harvesting robot 119874119894 is the localcoordinate system of the 119894th(119894 = 1 2 6) linkages 119874ℎ is the coordinate system of end effector 120572119894-1 is twist angle 120572119894-1 is length of linkages120579119894 is joint angle and 119889119894 is offset of linkages
model which is to calculate the position and attitude ofthe end-effector coordinate system Oh relative to the basecoordinate system O0 by a given set of joint values Thetransformation matrix between two adjacent connecting rodscan be calculated by the D-H parameters in Formula (1) andthe Table 1
119894minus1119894119879
=[[[[[[[
119888119894 minus119904119894 0 119886119894minus1119904119894 cos 120572119894minus1 119888119894 cos 120572119894minus1 minus sin 120572119894minus1 minus119889119894 sin 120572119894minus1119904119894 sin 120572119894minus1 119888119894 sin 120572119894minus1 cos120572119894minus1 119889119894 cos 120572119894minus1
0 0 0 1
]]]]]]]
(1)
where 119904119894 indicates sin 120579119894 119888119894 indicates cos 120579119894 (119894 = 1 2 3 6)120572119894-1 is the twist angle 120572119894-1 is the length of linkages and 119889119894 isthe offset of linkages
The transformation matrix of the manipulator 06119879 canbe obtained by multiplying continuously the transformationmatrix of each connecting rod 119894minus1119894119879 (i = 1 2 6) which is afunction with the six joint variables (1205791 1205792 1205793 1205794 1205795 1205796) andcan be described by Formula (2) It represents the positionrelationships between the end-effector attitude (119899 119900 119886 119901) andthe basic coordinate system [18]
119899119909 = c1 [11988823 (119888411988851198886 minus 11990441199046) minus 1199042311990451198886]+ 1199041 (119904411988851198886 + 11988841199046)
119899119910 = 1199041 [11988823 (119888411988851198886 minus 11990441199046) minus 1199042311990451198886]minus 1198881 (119904411988851198886 + 11988841199046)
119899119911 = minus11990423 (119888411988851198886 minus 11990441199046) minus 1198882311990451198886119900119909 = minus1198881 [11988823 (119888411988851199046 + 11990441198886) minus 1199042311990451199046]
minus 1199041 (119904411988851199046 minus 11988841198886)119900119910 = minus1199041 [11988823 (119888411988851199046 + 11990441198886) minus 1199042311990451199046]
+ 1198881 (119904411988851199046 minus 11988841198886)119900119911 = 11990423 (119888411988851199046 + 11990441198886) + 1198882311990451199046119886119909 = 1198881 (minus1198882311988841199045 minus 119904231198885) minus 119904111990441199045119886119910 = 1199041 (minus1198882311988841199045 minus 119904231198885) + 119888111990441199045119886119911 = 1199042311988841199045 minus 119888231198885
119901119909 = 1198881 (119886311988823 minus 119889411990423 + 1198861 + 11988621198882)119901119910 = 1199041 (119886311988823 minus 119889411990423 + 1198861 + 11988621198882)119901119911 = minus119886311990423 minus 119889411988823 minus 1198862119904211988823 = cos (1205792 + 1205793)11990423 = sin (1205792 + 1205793)
(3)
In the robotics grape harvesting the three-dimensionalcoordinates of the cutting point on the peduncle of grapecluster are obtained by the visual system of robot and thetarget position of the end-effector coordinate system Oh canbe calculated by the cutting point position The attitude ofthe end-effector (119899 119900 119886 119901) can be derived by combining withthe growth posture of grape clusters In the case of knowingthe relative position between the target position of the end-effector and the current position the inverse kinematicsmodel is responsible for calculating the satisfied joint variableof the manipulator which can control the manipulator movefrom the current position to the target position To constructthe inverse kinematics model the inverse transformationmethod [19] was used in this study and the calculationformulas of these joint variable (1205791 1205792 1205793 1205794 1205795 1205796) are asshown Formula (4) So the relation between the position ofthe terminal connecting rod and the joint variable of themanipulator can be established
1205791 = arctan119901119910119901119909
1205792 = arctan(11988621199043 minus 1198894) (1198881119901119909 + 1199041119901119910 minus 1198861) minus (1198863 + 11988621198883) 119901119911(1198863 + 11988621198883) (1198881119901119909 + 1199041119901119910 minus 1198861) minus (1198894 minus 11988621199043) 119901119911 minus 1205793
1205793 = arctan11988631198894 minus arctan 119896
radic11988632 + 11988942 minus 11989621205794 = arctan
minus1198861199091199041 + 1198861199101198881minus119886119909119888111988823 minus 119886119910119904111988823 + 11988611991111990423
1205795 = arctanminus119886119909 (1198881119888411988823 + 11990411199044) minus 119886119910 (1199041119888411988823 minus 11988811199044) + 119886119911 (119904231198884)
minus119899119909 (1198881119904411988823 minus 11990411198884) minus 119899119910 (1199041119904411988823 + 11988811198884) + 119899119911 (119904411990423)119899119909 [1198885 (1198881119888411988823 + 11990411199044) minus 1198881119904511990423] + 119899119910 [1198885 (1199041119888411988823 minus 11988811199044) minus 1199041119904511990423] minus 119899119911 (1198884119888511990423 + 119904511988823)
(4)
where 119896 = (1199011199092 + 1199011199102 + 1199011199112 + 11988612 minus 21198861(1198881119901119909 + 1199041119901119910) minus 11988632 minus11988622 minus 11988942)21198862To verify the correctness of the kinematics model the
values of a set of joint variables (1205791 = 1205873 1205792 = -1205873 1205793 =1205873 1205794 = 1205876 1205795 = 1205872 1205796 = 1205874) is artificially allocatedand then these values were input to the forward kinematicmodel (Formula (2)) to solve the terminal pose matrix 06119879
The following 06119879 was calculated by using Matlab
Figure 2 The bounding volume of obstacles such as cylinder andsphere
Then the obtained 06119879 seen as known conditions wasinput to the inverse kinematic model (Formula (4)) to solvethe angle values of the robot joints and the joint values(1205791 = 600000 1205792 = -600000 1205793 = 600000 1205794 = 2999931205795 = 900000 and 1205796 = 450022) were calculated It can beseen that the result is basically consistent with the variablevalues allocated by manual which shows the correctness ofthe kinematics model of the robot
22 Obstacles Modeling In the collision detection thebounding volume is a simple geometric space which containsobjects of complex shape The purpose of adding a boundingvolume to an object is to quickly carry out collision detectionor to filter the exact collision detection The bounding bodytypes include sphere axis aligned bounding box (AABB)directed bounding box (OBB) 8-DOP and convex hull Theobstacles in the actual picking environment are usually notregular geometry so it is difficult to describe them witha precise model [20] To facilitate the collision avoidancepath-planning the axis-aligned bounding box (AABB) wasadopted to establish the obstacles model approximately inthis study Although this modeling method expands theobstacle domain to a certain extent it greatly decreases thecalculation amount of the interference detection between themanipulator and the obstacles and effectively improves theefficiency of the path planning and also makes the plannedpath more secure
The axis-aligned minimum bounding box for a givenpoint set is its minimum bounding box subject to the con-straint that the edges of the box are parallel to the coordinateaxes It is simply the Cartesian product of 119873 intervals eachof which is defined by the minimal and maximal value ofthe corresponding coordinate for the points in 119878 In theobstacles modeling the farthest and nearest points in X Yand Z directions from the vertex collection of the obstacleare obtained firstly and then the AABB box was built byusing these points The AABB box is a simple hexahedronand each of whose side is parallel to a coordinate plane Itslength width and height can be different from each other InFigure 2 two simple 3D objects and their AABB are drawnSome important properties of the AABB can be described asfollows Firstly the points (119909 119910 119911) in the AABB box satisfythe following conditions 119909min le 119909 le 119909max 119910min le 119910 le 119910maxand 119911min le 119911 le 119911max and the points Pmin = [119909min 119910min 119911min]
and Pmax = [119909max 119910max 119911max] were two important pointsof the AABB box The center point c can be calculated bythe equation (c = (Pmin + Pmax)2) A bounding box of theobstacle can clearly be represented by using the two pointsPmin and Pmax
23 Configuration Space Modelling for Harvesting Robot Tosolve a collision avoidance path for the harvesting robot it isvery importance to determine the configuration space of themanipulator For a manipulator with 119899 degrees of freedomsetting 119864(12 n) as a set of active joint values of itin which i is the rotation angle of the 119894-th active joint ofthe manipulator If the point 119875 represents a point on themanipulator then the relative position relationship betweenthe point and the obstacle can be expressed as follows [21]
Γ (119875 (119864)) = 1 the point 119875 is inside the obstacle
0 the rest(6)
where D(119875(119864)) is relative position relationship betweenthe point 119875 and the obstacle when the manipulator is drivenwith the joint value and 119875(119864) is the position coordinate of thepoint 119875 on the manipulator in the basic coordinate systemwhen the joint value is 119864 If the rods of the manipulatorare uniformly dispersed into 119898 points according to the stepsize 119889min (mm)119898 discrete points constitute a point set 119875link The relative positional relation between the whole arm drivenwith the joint value 119864 and the obstacle can be expressed asfollows
Γ (Ε) = 119898sum119894=1
Γ (119875119894 (119864)) (7)
in which D(119864) is the relative positional relationship betweenthe driven manipulator and the obstacle when the joint valueis E
It can be known from formula (6) and formula (7) thatthe manipulator does not interfere with the obstacle only ifD(119864) = 0 The joint configuration spaceΩ is established withthe joint values of themanipulators of n degrees of freedom Ifthe set of the joint value E of themanipulator is represented byH then any point in the joint configuration spaceΩ uniquelycorresponds to one of the elements in the setH and vice versaIn other words the joint configuration spaceΩ and the set Hare bijective
Therefore the relative positional relationship between thedriven manipulator and the obstacle with the joint valueE can be expressed by the following formula in the jointconfiguration space
Ω(119864) = 1 Γ (119864) = 10 Γ (119864) = 0 (8)
where Ω(119864) is the value of the point in the joint con-figuration space Ω with the element in the joint value 119864of the manipulator as the coordinate and represents therelative positional relationship with the obstacle when the
6 Complexity
manipulator is in the position corresponding to 119864 If themanipulator interferes with the obstacle Ω(119864) is equal to 1otherwise Ω(119864) is equal to 0 So the set 119867part (1198641 1198642 119864119889)can represent a set of continuously varying poses of themanipulator the set represents a set of discrete points inthe joint configuration space Ω If a set of discrete points isconnected a path can be obtained where 119889 is the numberof the path control points Only when the following formulais satisfied does the driven manipulator not collide with theobstacle when the joint value set is119867part
where Ψ is the relative positional relationship between themanipulator the obstacle when the joint value set is119867part
Therefore the obstacle path planning is performed on themanipulator that is a set 119867part of joint values is searched inthe joint configuration space Ω so that the set is connectedto the initial configuration joint value 119864s and the targetjoint value 119864g of the manipulator Meanwhile it satisfies thecollision-free condition on the path as shown in (9)
To calculate the configuration space of the joint arm ofthe harvesting robot a simulation model of the robot wasestablished by using two functions of ldquolinkrdquo and ldquodrivebotrdquothat were provided byMatlab Robotics Toolbox Toolbox [22]And then the motion range of the harvesting manipulator inthe actual working environment is calculated and analyzedto carry better out the path-planning of picking operationAccording to the structure of the robot the motion space ofthe robot is mainly determined by the first three joints (1 to 3linkages) and the latter three joints (4 to 6 linkages) have noeffect on the motion space The first three joints determinethe position of the end-effector and the last three jointsdetermine the posture of the end-effector At present thereare mainly three methods for solving the motion space of therobots analytic methods numerical methods and graphicmethods The analytic method is to use algebraic method toobtain the equation about the structure parameters of therobot The advantage of this method is that it can accuratelydescribe the relationship between the structure parameters ofthe robot and the space of the robot but its computation islarge In this study we used analytic method and take Matlabto solve the robotrsquos motion space and the motion space of theharvesting robot can be shown as Figure 3
3 Path-Planning Based on Energy Optimaland Artificial Potential Field
The work process of the grape harvesting robot is as followsFirstly the picking robot acquires the information on numberof fruits in the field of view and the position of each fruitthrough the visual system Secondly the picking sequence isplanned The picking order of all fruits is sorted accordingto certain principles Thirdly controller has robot arm moveto the picking point of first bunch of grape rapidly andthe end effector performs the picking action Fourthly thesecond bunch of fruit is picked according to the above same
procedure until all the fruit is harvested Fifth the robot armreturns to the initial posture and the picking robot controlsthe mobile platform tomove forward and then starts the nextstage of picking Therefore the path planning of the pickingrobot work process is divided into two stages The first stageis to plan the picking sequence and the second stage is to planthe path point for each bunch of fruit picking The schematicdiagram for the path planning of the grape harvesting robotcan be shown as Figure 4
31 Harvesting Sequence Planning Based onMinimumEnergyAs the requirement of multiobjectives harvesting with theaim to get the minimum sum of weighted rotating jointangles in joint space the objective function on six-degree-of-freedom harvesting robot arm task planning based on mini-mum energy principle is proposed By calculating the value ofobjective function the picking sequence with the minimumenergy consumption can be obtained In this paper anobjective function to determine the harvesting sequence ofgrape bunches is proposed The optimal harvesting sequenceis finally determined by calculating the function value thussolves the problem of harvesting task planning
The harvesting sequence can be described in mathe-matically as assuming that the current manipulator is inthe initial position of the harvesting (1199090 1199100 1199110) there are 119899bunches of fruits in the visual area to be picked and the spaceposition coordinates are (119909i 119910i 119911i) and the correspondingspace variables of themanipulator are (1205791i 1205792i 1205793i 1205794i 1205795i 1205796i)in which 119894 = 1 2 119899 Manipulator is required to search foran optimal harvesting sequence from the initial position Allthe fruits are picked sequentially and then returned to theoriginal position It is assumed that the motion parameters(including angular velocity and angular acceleration) of alljoints of a manipulator are the same In order to minimizethe energy in the process of motion when a joint of thearm carry out harvesting task it selects the proper sequenceof harvesting to minimize the total angle of rotation whichindicates that the operating time and energy consumption ofthe joint under this sequence to complete the harvesting taskare minimal The optimization objective of single joint is
119875 = 119899sum119895=1
10038161003816100381610038161003816120579119895 minus 120579119895+110038161003816100381610038161003816 (10)
in which 119875 is the function of optimization objective 120579 is themotion angle of joint and 119899 is the number of the space pointsthat end effector need to move through
However there are multiple joints for the harvestingmanipulator in this study if the minimum sum of the singlejoint angle changes was took as the optimization objectiveand then each joint would have an optimal objective Atthis time the problem of the harvesting sequence of themanipulator is transformed into a multiobjective optimiza-tion problem Considering the angle changes of each jointof the manipulator may not reach the minimum at the sametime in the same harvesting sequence so it is necessary tocoordinate the sub objective functions of each joint to achievethe optimal objective function and the optimum of each jointwhen determine the optimal objective function of the whole
Complexity 7
10001000
500Y axis (mm)
0
X axis (mm)0
minus500minus1000 minus1000
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(a) Motion space in X Y and Z coordinates
minus1000
minus500
0
500
1000
Y ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(b) Motion space in X and Y coordinates
minus1000
minus500
0
500
1000
Z ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(c) Motion space in X and Z coordinates
0 500 1000minus500minus1000Y axis (mm)
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(d) Motion space in Y and Z coordinates
Figure 3 The motion space of the harvesting robot
destination
path point
cutting point①
②
③④
⑤
Figure 4 Schematic diagram for the path planning of the grapeharvesting robot
manipulator Moreover the power of each joint motor isdifferent according to the value of the power of each jointmotor of the manipulator different weights should be givento each joint angle and different weights should also be givento the sub targets of each joint of the manipulator So thesequence planning of the six degree of freedom harvestingmanipulator based on the principle of minimum energy canbe described by the following
1198751015840 = 119898sum119894=1
120596119894119869119894 =119898sum119894=1
119899sum119895=1
120596119894 10038161003816100381610038161003816120579119894119895 minus 120579119894119895+110038161003816100381610038161003816 (11)
where 1198751015840 indicates the objective function of the manipulatorthat can embody the energy consumption of the manipulatormotion 119898 is the number of the joints 120596i is the weight of theobjective function of the 119894th joints and 120579ij indicates the anglevalue of the 119894th joint when the manipulator is locating the 119895thspace point
32 Harvesting Path Generating Based on Artificial PotentialField eory In the process of grape harvesting collision-free path planning under a vineyard environment is themost important issue which need be resolved firstly to avoiddamage the fruits At present there are two main pathplanning methods [23] model-based global path planningand sensor-based local path planning In this study the localpath planning method based on artificial potential field wasadopted
321 Principle of Artificial Potential Field The path planningmethod based on artificial potential field is a virtual forcemethod proposed by Khatib [24] Its basic idea is to designthe motion of the robot in the surrounding environment intoan abstract artificial gravitational fieldThe artificial potentialfield includes the gravitational field and the repulsion field inwhich the object produces the gravitational attraction to theobject and guides the object to move toward it The obstaclesrepel other objects to avoid collisions with it The resultant
8 Complexity
Input the current point coordinates of the end-effector (1199090 1199100 1199110) the terminal coordinates(119909t 119910t 119911t) (the cutting point on the peduncles of grape cluster) the bounding box model ofobstacles 119877(119874s 119874e)Output the path points (119909i 119910i 119911i)
1 Find all collision-free sampling points2 for each sampling points p do
(a) calculate the probability that the current point is the candidate path points(b) find the point whose probability is maximum(c) consider the points as a candidate path point
end3 Repeat the above process until the terminal coordinates is reached
Algorithm 1 Sampling-based path point generating method
force of every point on a path is equal to the sum of allrepulsive forces and gravitational forces on this point
The basic idea of the proposed path planning in thisstudy is that the harvesting point is attractive to the motionof the harvesting manipulator by the virtual force fieldthe anticollision bounding body of grape cluster and otherobstacles are repulsive to it and the path planning is carriedout through the interaction of attraction and repulsion forceThe artificial potential field 119880sum(119883) can be defined by thefollowing [24]
in which119880att(119883) indicates the gravitational field generated bythe target 119880rep(119883) indicates the repulsion field generated bythe obstacles119883 = (119909 119910 119911)119879 is the position of the end-effectorin the workspace Setting the position of the target as119883g andthe gravitational field119880att(119883) can be defined by the following
119880att (119883) = 12119896 (119883 minus 119883119892)2 (13)
where 119896 is a constant about the gravitational field and then thegravitation 119865att(119883) can be solved by calculating the negativegradient value of the gravitational field which is described asFormula (14)
To define the mathematical expression about the repul-sive force field the following two conditions need firstly beconformed [25] (1) the artificial potential field119880sum(119883)mustbe a continuous-differential function and when119883 is equal to119883g the value of119880sum(119883) is 0 (minimum value) (2) Under theeffect of the artificial potential field 119880sum(119883) the system canbe stable Setting 1198830 as the space position of the obstacle therepulsive force field 119880rep(119883) can be defined by the following
119880rep (119883) =12120578(
1119883 minus 1198830 minus
1120588)2 (119883 minus 1198830) lt 120588
0 (119883 minus 1198830) ge 120588 (15)
where 120578 is a constant about the repulsive force field and 120588 isthe maximum range of the impact of the obstacle When the
distance between the obstacle and the end-effector is largerthan120588 the repulsive fieldwould no longer to affect themotionof harvesting robotThe repulsive force 119865rep(119883) can be solvedby calculating the negative gradient value of the repulsiveforce field 119880rep(119883) which is described as the following
120597 (119883 minus 1198830)120597119883 (119883 minus 1198830) lt 1205880 (119883 minus 1198830) ge 120588
(16)
322 Sampling-Based Path Points Generating Method Thearray of the path point sets (119909i 119910i 119911i) are firstly establishedand then the terminal pose of the end-effector is determinedbased on the current pose of the robot and the pose of grapecluster The current point coordinates of the end-effector(1199090 1199100 1199110) the terminal coordinates (119909t 119910t 119911t) (the cuttingpoint on the peduncles of grape cluster) and the boundingbox model of obstacles 119877(119874s 119874e) are given respectivelyAccording to the artificial potential field method new sam-pling points are generated randomly in the neighbourhoodand collision detection is performed on the sampling pointsThe probability that all collision-free sampling points areselected as the candidate path points is calculated and thesampling point with the highest probability is added to thepath array as the following path point Repeat the aboveprocess until the terminal coordinates is reachedThe pseudocode of sampling-based path point generating method is asshown in Algorithm 1
4 Experiments and Results
To validate the performance of the proposed anticollisionpath planning algorithm in a complex orchard a virtualharvesting robot simulation system was developed based onthe virtual reality software platform and then the perfor-mance of path planning method was investigated based onthe developed simulation system
41 Virtual Harvesting Robot Testing System The virtual sim-ulation systemwas implemented on theWindows 7 operatingsystem by using the software tools such as Visual studio 2013
Complexity 9
Figure 5 Schematic diagram for the path planning of the grapeharvesting robot
EON Studio 3Dmax and Solidworks In this study the virtualharvesting robot is constructed according to the actual sizeand workspace of the 6-DOF robot prototype Firstly the 3Dmodel of orchard scene and harvesting robotrsquos body structureis constructed and the kinematics model of the manipulatoris set by D-H parameter methodThen the virtual grape clus-ters and their anticollision space bounding body are drawnunder the virtual environment The collision avoidance pathpoints are computed by the proposed algorithm Finallythe path is simulated by a three-dimensional visualizationmethod The end-effector on the harvesting robot is consistsof three functional parts clamping finger pallet and scissorThe clamping mechanism is mainly responsible for clampingthe peduncle of grape cluster The pallet holds the grapecluster from behind and underneath carrying part of grapegravity to prevent the grape from shaking and slippingWhenthe fingers and pallets lock up the grape cluster the peduncleis cut by the scissors mechanism The software interface isshown as Figure 5
After the collision-free path is planned the joint variablesparameters of the manipulator are calculated by the inversekinematics model and then the forward kinematics methodis used to control the robotrsquos end-effector to the targetposition In the virtual simulation system the collision nodein the EON platform was used to detect collision in thisresearch The node can detect the collision events betweendifferent geometric objects in the virtual environment whichcan monitor the collision between the harvesting robot andthe obstacle in real-time To control the motion behaviorof virtual harvesting robot the modular programming androuting communication mechanism in EON platform wereadoptedThemainmodules involved aremovement rotationposition sensor angle sensor time sensor switch node rout-ing and so on The movement module is mainly used for theclamping behavior control of the end-effector The rotationmodule is used to control the rotation of the six joints of themanipulator and the rotary cutting motion of the actuatorscissors The position and angle sensors are used to perceivethe real-time travel and position of the joint motionThe timesensor is used to control the motion speed and acceleration ofthe joints of the manipulator and the switch nodes are usedto connect the communication between the modules Thecommunications among several functionmodules are carried
out through routing mechanism in the virtual environmentThe routing mechanism is responsible to mainly passesand monitors the running state of each module throughevents and then broadcast the state parameters to otherfunctional modules in real time the coordination of themultifunctional modules is finally realized Events are thedata information transmitted between two domains whichinclude two types Input and Output The Input event is theinformation generated by other sending nodes to change thestate of the receiving node and the Output event is a statethat the state of the node itself changes and outputs theinformation When one of the behavior modules sends thecommand the receiving node gets the instructions throughthe route transfers the nodes through the event driven andrealizes the message driven mechanism
42 Path-Planning Testing and Analysis The path planningtests on multiple harvesting objectives were implementedbase on the developed virtual simulation The cluster numberof the tested grape was set from 2 to 5 and their positionswere randomly given in the configuration space of themanipulator The harvesting sequence was firstly calculatedby the energy optimal and the path points were generatedby artificial potential field The simulation test platformare as follows a laptop (Lenovo T430) with 4G RAM andIntel(R)Core(TM)i5-3230 M CPU260 GHz a Windows7 operating system and a Visual C++ 2008 platform Thestatistics and analysis are made on the path length thenumber of sampling points the collision situation and theaverage time of path planning in each harvesting The resultsof the tests are shown as Table 2 The relationship betweenpath length 119871 and key point 119875i can be described by Formula(17)
119871 = sum1le119894le119870
radic(119909119894 minus 119909119894minus1)2 + (119910119894 minus 119910119894minus1)2 + (119911119894 minus 119911119894minus1)2 (17)
where119870 indicates the number of sampling points of the pathand (119909i 119910i 119911i) is the coordinates of the 119894-th sampling points
From the Table 2 we can see that there are 9 times issuccessful and 1 times failure in the 10 grape harvesting testsThe success rate was 90 the path lengthwas between 44867cm and 147265 cm the number of sampling points wasbetween 90 and 206 and the average time of path planningwas between 98ms and 273 ms It can be seen that the reasonfor the failure of the test was the collision between the endeffector and the anticollision space bounding body of thegrape cluster If the distance between the end effector andgrape cluster is too small the end effector will be easy tocollide with the upper part of the grape cluster when theend effector move closely to the fruit peduncle for harvestingoperationHarvesting path-planning can be optimized by set-ting and adjusting the minimum safety margin between thecutting point and the anticollision space bounding volumeMoreover the average time of path planning increases withthe number of objective and the number of sampling pointsFigure 6 shows a successful grape harvesting path planningThewhite dots are the path points swept by the clamper centerof the end effector during the harvesting
10 Complexity
Table 2 Statistical results of the virtual tests for grape harvesting path-planning
Number ofobjectives Harvesting optimal sequence Length of
path (Lcm)
Number ofsamplingpoints (K)
Collision(YN)
Average timeof planning
(ms)3 B 997888rarrC 997888rarrA 63578 108 N 1522 B 997888rarrA 44867 72 N 1084 C 997888rarrD 997888rarrA 997888rarrB 98523 172 N 2155 B 997888rarrD 997888rarrC 997888rarrA 997888rarr E 136245 206 N 2613 A 997888rarrC 997888rarrB 72333 102 N 1634 B 997888rarrC 997888rarrD 997888rarrA 106158 170 N 2035 E 997888rarrC 997888rarrA 997888rarrB 997888rarr D 147265 216 Y 2742 A 997888rarrB 46365 91 N 983 B 997888rarrC 997888rarrA 75687 127 N 1514 C 997888rarrB 997888rarrD 997888rarrA 104526 162 N 199
(a) (b)
(c)
Figure 6 The path points drew by the proposed path-planning method
5 Discussion
Traditional path planning methods (such as skeleton celldecomposition and subgoal graph etc) are very effective forlower degree of freedom robot (2 to 3 DOF) With theincrease in the degree of freedom of robots these algorithms
will be out of work A collision-free autonomous path plan-ning methodolgy for six-DOF serial harvesting manipulatorunder a dynamic vineyard environment was presented inthis study The kinematical modelling of Six-DOF serialmanipulator the model of obstacles and the configurationspace of harvesting robot was firstly introduced in detail
Complexity 11
And then the harvesting sequence and the anticollision pathpoints were calculated by using the energy optimal and theartificial potential field The virtual tests based on virtualreality were performed to validate the performance of theproposed algorithm Through the virtual simulation test ofthe harvesting path planning the three-dimensional spacepath points of the end-effector of the harvesting manipulatorwere calculated in real time in virtual environment andthe collision detection is analyzed The success rate wasup to 90 It can be known that the simulation systemdesigned in this study has a good practical value to helptest and improve the intelligent behavior algorithm of therobot
To obtain an optimal harvesting path taking the sumof the joint angle of the weighted rotation as the goalthe harvesting sequence planning objective function of thesix-DOF harvesting manipulator is established by usingthe minimum energy principle and the minimum energyconsumption sequence can be obtained by calculating thevalue of the target function In addition the mapping modelof obstacles in the joint configuration space is built on thebasis of sampling method and the artificial potential fieldis used to search the obstacle avoidance path in the jointconfiguration space which improves the generality of thealgorithm However due to the proposed algorithm adoptsrandom sampling strategy the sampling points may collidewith the obstacles so it is necessary to resample If thenumber of maximum sampling point is too small the failureprobability of the path planning increases And if the numberofmaximumsampling point value is too large it will cause thepath to not exist or be difficult to find or the planning time istoo long So the parameters need test repeatedly
6 Conclusion
To conduct an undamaged robotic grape-harvesting in anunstructured vineyard a path planning strategies based onminimum energy and artificial potential field for grapeharvesting robot was developed in this studyThe kinematicalmodel of Six-DOF serial manipulator was firstly constructedby using the D-H method the model of obstacles wasdefined by the axis-aligned bounding box and then theconfiguration space of harvesting robot was described bycombining the obstacles and robot Then the harvestingsequence in path planning was computed by energy optimalmethod and the anticollision path points were generatedbased on the artificial potential field and sampling searchingmethod Finally to verify and test the proposed path planningalgorithm a virtual test system based on virtual reality wasdeveloped 10 times harvesting tests for grape anticollisionpath planning were implemented on the developed sim-ulation system and the success rate was up to 90 Inconclusion the developed approach can effectively plan acollision-free path for the grape harvesting robot in the com-plex vineyard environment However when facing multipleoverlapped and adjoining grape clusters the path planning isstill an issue that needs to be solved and will require furtherresearch
Data Availability
The grape harvesting robot data used to support the findingsof this study are available from the corresponding authorupon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
This work was supported by grants from the National Nat-ural Science Foundation of China (no 51705365) and theNational Key Research and Development Program of China(2017YFD0700100)
References
[1] M A Hossain and I Ferdous ldquoAutonomous robot pathplanning in dynamic environment using a new optimizationtechnique inspired by bacterial foraging techniquerdquo Roboticsand Autonomous Systems vol 64 pp 137ndash141 2015
[2] V San JuanM Santos and JM Andujar ldquoIntelligentUAVMapGeneration and Discrete Path Planning for Search and RescueOperationsrdquoComplexity vol 2018 Article ID 6879419 17 pages2018
[3] L Luo Y Tang Q Lu X Chen P Zhang and X Zou ldquoA visionmethodology for harvesting robot to detect cutting points onpeduncles of double overlapping grape clusters in a vineyardrdquoComputers in Industry vol 99 pp 130ndash139 2018
[4] P Li S-H Lee and H-Y Hsu ldquoReview on fruit harvestingmethod for potential use of automatic fruit harvesting systemsrdquoin Proceedings of the 2011 International Conference on PowerElectronics and EngineeringApplication PEEA 2011 pp 351ndash366China December 2011
[5] W Wei D-T Ouyang S Lu and Y-X Feng ldquoMultiobjectivepath planning under dynamic uncertain environmentrdquo JisuanjiXuebaoChinese Journal of Computers vol 34 no 5 pp 836ndash845 2011
[6] M G Mohanan andA Salgoankar ldquoA survey of roboticmotionplanning in dynamic environmentsrdquo Robotics and AutonomousSystems vol 100 pp 171ndash185 2018
[7] X Hu L Chen B Tang D Cao and H He ldquoDynamicpath planning for autonomous driving on various roads withavoidance of static and moving obstaclesrdquo Mechanical Systemsand Signal Processing vol 100 pp 482ndash500 2018
[8] DDevaurs T Simeon and J Cortes ldquoOptimal Path Planning inComplex Cost Spaces with Sampling-Based Algorithmsrdquo IEEETransactions on Automation Science and Engineering vol 13 no2 pp 415ndash424 2016
[9] R Cui Y Li and W Yan ldquoMutual information-based multi-AUV path planning for scalar field sampling using multi-dimensional RRTrdquo IEEE Transactions on Systems Man andCybernetics Systems vol 46 no 7 pp 993ndash1004 2016
[10] CW Bac J Hemming and E J VanHenten ldquoStem localizationof sweet-pepper plants using the support wire as a visual cuerdquoComputers and Electronics in Agriculture vol 105 pp 111ndash1202014
12 Complexity
[11] L Luo Y Tang X ZouM YeW Feng andG Li ldquoVision-basedextraction of spatial information in grape clusters for harvestingrobotsrdquo Biosystems Engineering vol 151 pp 90ndash104 2016
[12] E J VanHenten J Hemming B A J VanTuijl J G Kornet andJ Bontsema ldquoCollision-free Motion Planning for a CucumberPicking Robotrdquo Biosystems Engineering vol 86 no 2 pp 135ndash144 2003
[13] G Gao G Sun J Na Y Guo and XWu ldquoStructural parameteridentification for 6 DOF industrial robotsrdquoMechanical Systemsand Signal Processing vol 113 pp 145ndash155 2018
[14] K Wei and B Ren ldquoA Method on Dynamic Path Planning forRobotic Manipulator Autonomous Obstacle Avoidance Basedon an Improved RRT Algorithmrdquo Sensors vol 18 no 2 p 5712018
[15] Y Dai and M Zhao ldquoManipulator path-planning avoidingobstacle based on screw theory and ant colony algorithmrdquoJournal of Computational and eoretical Nanoscience vol 13no 1 pp 922ndash927 2016
[16] H Pham and Q Pham ldquoTime-Optimal Path Tracking viaReachability Analysisrdquo in Proceedings of the 2018 IEEE Inter-national Conference on Robotics and Automation (ICRA) pp3007ndash3012 Brisbane QLD May 2018
[17] G Legnani F Casalo P Righettini and B Zappa ldquoA homo-geneous matrix approach to 3D kinematics and dynamics - IIApplications to chains of rigid bodies and serial manipulatorsrdquoMechanism and Machine eory vol 31 no 5 pp 589ndash6051996
[18] J Craig Introduction to Robotics Mechanics and Control 3rdedition 2015
[19] R P Paul B Shimano and G E Mayer ldquoKinematic controlequations for simple manipulatorsrdquo IEEE Transactions on Sys-tems Man and Cybernetics vol 11 no 6 pp 449ndash455 1981
[20] G Zachmann ldquoRapid collision detection by dynamicallyaligned DOP-treesrdquo in Proceedings of the 1998 IEEE VirtualReality Annual International Symposium VRAIS pp 90ndash97March 1998
[21] H Yang L Li and Z Gao ldquoObstacle avoidance path planningof hybrid harvesting manipulator based on joint configurationspacerdquoNongyeGongcheng Xuebao vol 33 no 4 pp 55ndash62 2017
[22] C Peter Robotics Vision amp Control Springer 2nd edition 2017[23] Z Daqi and Y Mingzhong ldquoSurvey on technology of mobile
robot path planningrdquo Control and Decision vol 25 no 7 pp961ndash967 2010
[24] O Khatib ldquoReal-time obstacle avoida nce for manipulators andmobile robotsrdquo International Journal of Robotics Research vol5 no 1 pp 90ndash98 1986
[25] M Fakoor A Kosari and M Jafarzadeh ldquoRevision on fuzzyartificial potential field for humanoid robot path planningin unknown environmentrdquo International Journal of AdvancedMechatronic Systems vol 6 no 4 pp 174ndash183 2015
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2 Complexity
studies can be divided into four primary categories [7] grid-based approaches potential field approaches sample-basedapproaches and discrete optimization approaches In [7] areal-time dynamic path planning method for autonomousdriving that avoids both static and moving obstacles waspresented In [8] two efficient sampling-based approachescombining two RRT variants were developed to solve acomplex path planning problem and a path planningmethodwhich uses mutual information was proposed for the multi-AUV (AutonomousUnderwaterVehicle) systemCui et al [9]presented an adaptive path planning algorithm for multipleAUVs to estimate the scalar field over a region of interestTomake the manipulator avoid collisions with the plant stemin sweet-pepper harvesting Bac et al [10] presented a stemlocalization of sweet-pepper plants using the supportwire as avisual cueThe objectives of this study were to find the obsta-cles so that the robot can plan a collision-avoidance path Toconduct an undamaged robotic grape-harvesting Luo et al[11] focused their works on locating the spatial coordinatesof the cutting points on a peduncle of grape clusters for theend-effector and determining the bounding volume of thegrape clusters for the motion planner of the manipulator Athree-dimensional CAD model used in [12] has solved theproblem of collision between the cucumber picking robotand the stem but the amount of collision calculation is verylarge To decrease the movement uncertainty of industrialrobots Gao et al [13] presented a parameter identificationmethod based on the D-H model in where the redundantparameters are particularly addressed Experimental studiesbased on a 6 DOF industrial robot show the proposedmethod can improve themovement accuracy of the industrialrobot significantly To make the robotic manipulator workefficiently and safely in a dynamic unstructured environmentWei et al [14] proposed an autonomous obstacle avoidancedynamic path-planning method for a robotic manipulatorbased on an improved RRT algorithm For solving serialmanipulators path-planning when grabbing target in obstacleworkspace Dai et al [15] presented a solution based on screwtheory and ant colony algorithm In [16] a new approachto time-optimal path parameterization (TOPP) based onreachability analysis was proposed
Through the above analysis we can see that the pathplanning strategies applied in unstructured environments inrecent years focused on autonomous driving autonomousunderwater vehicle and industry robots Although somedomestic and foreign scholars have carried out some researchon the path planning of fruit and vegetable picking robotthe research on collision-free autonomous path planningfor the grape harvesting robot under a dynamic vineyardenvironment is still in the initial stage
To conduct an undamaged robotic grape-harvesting inan unstructured vineyard a collision-free autonomous pathplanning method based on minimum energy and artificialpotential field for grape harvesting robot was developed inthis study Firstly the kinematical model of six-DOF serialharvesting manipulator was constructed by using the D-Hmethod the model of obstacles was defined by the axis-aligned bounding box and then the configuration space ofharvesting robot was described by combining the obstacles
and arm space of robot Secondly the harvesting sequencein path planning was computed by energy optimal methodand the anticollision path points were generated based onthe artificial potential field and sampling searching methodFinally to verify and test the proposed path planning algo-rithm a virtual test system based on virtual reality wasdeveloped The innovation of this study is the developmentof the energy optimal harvesting sequence planning methodand the anticollision path points generating method basedon the configuration space of six-DOF serial harvestingmanipulator
The paper is organized as follows Section 2 shows severalbasic models for harvesting robot that will be used in the pathplanning strategies Section 3 describes the plan planningmethod that was designed based on energy minimum andartificial potential field Section 4 performed an experimentto validate the performance of the developed plan planningmethod Section 5 summarizes and discusses the experimentresults The paper ends with the conclusions and future work
2 Basic Models Building for Harvesting Robot
The task of obstacle avoidance path planning of the six degreeof freedommanipulator is to search for a series of continuousjoint angle values under the condition of the given obstaclethe starting and target position of themanipulator which candrive the manipulator to move from the starting position tothe target position safely without collision To elaborate theprinciple and process of the path planning method proposedin this paper in detail it is necessary to establish the robotcoordinate system kinematic model obstacle model and theconfiguration space model which are the design basis of thepath planning algorithm
21 Kinematical Modelling for Six-DOF Serial Robot Theshape of the six degree of freedom series harvesting robotis as shown in Figure 1(a) which is made up of six rotatingjoints They are responsible for adjusting the end-effectorto the appropriate picking position so that the actuator canclamp the grapes and cut the peduncles The end-effectoris composed of three functional parts clamper pallet andscissor The harvesting manipulator is made up of rigid linkand rigid joint and its motion is realized by controlling thejoints of the manipulator
211 Establishing D-H Coordinate System for Harvesting ArmTo establish the forward and reverse kinematics models ofthe harvesting robot the Denavit- Hartenberg (D-H)method[17] was adopted in this study The D-H table (see Table 1) isbuilt on the basis of the structure and parameters of the robotAnd then the coordinate system of the picking robot is set upin which the reference coordinate system is O0 and the localcoordinate system of each joint is Oi (i = 1 2 6) and theend-effector coordinate system is Oh The coordinate systemof each joint of the picking robot is shown by Figure 1(b)
212 Forward and Inverse Kinematic Modeling The motionof the harvesting robot is driven by the forward kinematics
Complexity 3
ClamperScissors
Pallet
(a) Harvesting robot shape
O2
O0
O3
O4O5 O6
x6
y6
z6z5
x5
x4
z4
y4
x3
y3
z0x0y0
y5
O1
xh
yh zh
Oh
a3
d4
x1
z1
y1
z2
x2
y2
z3a2
a 1
1
2
3
54
6
(b) Origin coordinate and joints coordinate systems ofharvesting robot
Figure 1 Harvesting robot shape and its joints coordinate systems Note that 1198740 is the base coordinate of harvesting robot 119874119894 is the localcoordinate system of the 119894th(119894 = 1 2 6) linkages 119874ℎ is the coordinate system of end effector 120572119894-1 is twist angle 120572119894-1 is length of linkages120579119894 is joint angle and 119889119894 is offset of linkages
model which is to calculate the position and attitude ofthe end-effector coordinate system Oh relative to the basecoordinate system O0 by a given set of joint values Thetransformation matrix between two adjacent connecting rodscan be calculated by the D-H parameters in Formula (1) andthe Table 1
119894minus1119894119879
=[[[[[[[
119888119894 minus119904119894 0 119886119894minus1119904119894 cos 120572119894minus1 119888119894 cos 120572119894minus1 minus sin 120572119894minus1 minus119889119894 sin 120572119894minus1119904119894 sin 120572119894minus1 119888119894 sin 120572119894minus1 cos120572119894minus1 119889119894 cos 120572119894minus1
0 0 0 1
]]]]]]]
(1)
where 119904119894 indicates sin 120579119894 119888119894 indicates cos 120579119894 (119894 = 1 2 3 6)120572119894-1 is the twist angle 120572119894-1 is the length of linkages and 119889119894 isthe offset of linkages
The transformation matrix of the manipulator 06119879 canbe obtained by multiplying continuously the transformationmatrix of each connecting rod 119894minus1119894119879 (i = 1 2 6) which is afunction with the six joint variables (1205791 1205792 1205793 1205794 1205795 1205796) andcan be described by Formula (2) It represents the positionrelationships between the end-effector attitude (119899 119900 119886 119901) andthe basic coordinate system [18]
119899119909 = c1 [11988823 (119888411988851198886 minus 11990441199046) minus 1199042311990451198886]+ 1199041 (119904411988851198886 + 11988841199046)
119899119910 = 1199041 [11988823 (119888411988851198886 minus 11990441199046) minus 1199042311990451198886]minus 1198881 (119904411988851198886 + 11988841199046)
119899119911 = minus11990423 (119888411988851198886 minus 11990441199046) minus 1198882311990451198886119900119909 = minus1198881 [11988823 (119888411988851199046 + 11990441198886) minus 1199042311990451199046]
minus 1199041 (119904411988851199046 minus 11988841198886)119900119910 = minus1199041 [11988823 (119888411988851199046 + 11990441198886) minus 1199042311990451199046]
+ 1198881 (119904411988851199046 minus 11988841198886)119900119911 = 11990423 (119888411988851199046 + 11990441198886) + 1198882311990451199046119886119909 = 1198881 (minus1198882311988841199045 minus 119904231198885) minus 119904111990441199045119886119910 = 1199041 (minus1198882311988841199045 minus 119904231198885) + 119888111990441199045119886119911 = 1199042311988841199045 minus 119888231198885
119901119909 = 1198881 (119886311988823 minus 119889411990423 + 1198861 + 11988621198882)119901119910 = 1199041 (119886311988823 minus 119889411990423 + 1198861 + 11988621198882)119901119911 = minus119886311990423 minus 119889411988823 minus 1198862119904211988823 = cos (1205792 + 1205793)11990423 = sin (1205792 + 1205793)
(3)
In the robotics grape harvesting the three-dimensionalcoordinates of the cutting point on the peduncle of grapecluster are obtained by the visual system of robot and thetarget position of the end-effector coordinate system Oh canbe calculated by the cutting point position The attitude ofthe end-effector (119899 119900 119886 119901) can be derived by combining withthe growth posture of grape clusters In the case of knowingthe relative position between the target position of the end-effector and the current position the inverse kinematicsmodel is responsible for calculating the satisfied joint variableof the manipulator which can control the manipulator movefrom the current position to the target position To constructthe inverse kinematics model the inverse transformationmethod [19] was used in this study and the calculationformulas of these joint variable (1205791 1205792 1205793 1205794 1205795 1205796) are asshown Formula (4) So the relation between the position ofthe terminal connecting rod and the joint variable of themanipulator can be established
1205791 = arctan119901119910119901119909
1205792 = arctan(11988621199043 minus 1198894) (1198881119901119909 + 1199041119901119910 minus 1198861) minus (1198863 + 11988621198883) 119901119911(1198863 + 11988621198883) (1198881119901119909 + 1199041119901119910 minus 1198861) minus (1198894 minus 11988621199043) 119901119911 minus 1205793
1205793 = arctan11988631198894 minus arctan 119896
radic11988632 + 11988942 minus 11989621205794 = arctan
minus1198861199091199041 + 1198861199101198881minus119886119909119888111988823 minus 119886119910119904111988823 + 11988611991111990423
1205795 = arctanminus119886119909 (1198881119888411988823 + 11990411199044) minus 119886119910 (1199041119888411988823 minus 11988811199044) + 119886119911 (119904231198884)
minus119899119909 (1198881119904411988823 minus 11990411198884) minus 119899119910 (1199041119904411988823 + 11988811198884) + 119899119911 (119904411990423)119899119909 [1198885 (1198881119888411988823 + 11990411199044) minus 1198881119904511990423] + 119899119910 [1198885 (1199041119888411988823 minus 11988811199044) minus 1199041119904511990423] minus 119899119911 (1198884119888511990423 + 119904511988823)
(4)
where 119896 = (1199011199092 + 1199011199102 + 1199011199112 + 11988612 minus 21198861(1198881119901119909 + 1199041119901119910) minus 11988632 minus11988622 minus 11988942)21198862To verify the correctness of the kinematics model the
values of a set of joint variables (1205791 = 1205873 1205792 = -1205873 1205793 =1205873 1205794 = 1205876 1205795 = 1205872 1205796 = 1205874) is artificially allocatedand then these values were input to the forward kinematicmodel (Formula (2)) to solve the terminal pose matrix 06119879
The following 06119879 was calculated by using Matlab
Figure 2 The bounding volume of obstacles such as cylinder andsphere
Then the obtained 06119879 seen as known conditions wasinput to the inverse kinematic model (Formula (4)) to solvethe angle values of the robot joints and the joint values(1205791 = 600000 1205792 = -600000 1205793 = 600000 1205794 = 2999931205795 = 900000 and 1205796 = 450022) were calculated It can beseen that the result is basically consistent with the variablevalues allocated by manual which shows the correctness ofthe kinematics model of the robot
22 Obstacles Modeling In the collision detection thebounding volume is a simple geometric space which containsobjects of complex shape The purpose of adding a boundingvolume to an object is to quickly carry out collision detectionor to filter the exact collision detection The bounding bodytypes include sphere axis aligned bounding box (AABB)directed bounding box (OBB) 8-DOP and convex hull Theobstacles in the actual picking environment are usually notregular geometry so it is difficult to describe them witha precise model [20] To facilitate the collision avoidancepath-planning the axis-aligned bounding box (AABB) wasadopted to establish the obstacles model approximately inthis study Although this modeling method expands theobstacle domain to a certain extent it greatly decreases thecalculation amount of the interference detection between themanipulator and the obstacles and effectively improves theefficiency of the path planning and also makes the plannedpath more secure
The axis-aligned minimum bounding box for a givenpoint set is its minimum bounding box subject to the con-straint that the edges of the box are parallel to the coordinateaxes It is simply the Cartesian product of 119873 intervals eachof which is defined by the minimal and maximal value ofthe corresponding coordinate for the points in 119878 In theobstacles modeling the farthest and nearest points in X Yand Z directions from the vertex collection of the obstacleare obtained firstly and then the AABB box was built byusing these points The AABB box is a simple hexahedronand each of whose side is parallel to a coordinate plane Itslength width and height can be different from each other InFigure 2 two simple 3D objects and their AABB are drawnSome important properties of the AABB can be described asfollows Firstly the points (119909 119910 119911) in the AABB box satisfythe following conditions 119909min le 119909 le 119909max 119910min le 119910 le 119910maxand 119911min le 119911 le 119911max and the points Pmin = [119909min 119910min 119911min]
and Pmax = [119909max 119910max 119911max] were two important pointsof the AABB box The center point c can be calculated bythe equation (c = (Pmin + Pmax)2) A bounding box of theobstacle can clearly be represented by using the two pointsPmin and Pmax
23 Configuration Space Modelling for Harvesting Robot Tosolve a collision avoidance path for the harvesting robot it isvery importance to determine the configuration space of themanipulator For a manipulator with 119899 degrees of freedomsetting 119864(12 n) as a set of active joint values of itin which i is the rotation angle of the 119894-th active joint ofthe manipulator If the point 119875 represents a point on themanipulator then the relative position relationship betweenthe point and the obstacle can be expressed as follows [21]
Γ (119875 (119864)) = 1 the point 119875 is inside the obstacle
0 the rest(6)
where D(119875(119864)) is relative position relationship betweenthe point 119875 and the obstacle when the manipulator is drivenwith the joint value and 119875(119864) is the position coordinate of thepoint 119875 on the manipulator in the basic coordinate systemwhen the joint value is 119864 If the rods of the manipulatorare uniformly dispersed into 119898 points according to the stepsize 119889min (mm)119898 discrete points constitute a point set 119875link The relative positional relation between the whole arm drivenwith the joint value 119864 and the obstacle can be expressed asfollows
Γ (Ε) = 119898sum119894=1
Γ (119875119894 (119864)) (7)
in which D(119864) is the relative positional relationship betweenthe driven manipulator and the obstacle when the joint valueis E
It can be known from formula (6) and formula (7) thatthe manipulator does not interfere with the obstacle only ifD(119864) = 0 The joint configuration spaceΩ is established withthe joint values of themanipulators of n degrees of freedom Ifthe set of the joint value E of themanipulator is represented byH then any point in the joint configuration spaceΩ uniquelycorresponds to one of the elements in the setH and vice versaIn other words the joint configuration spaceΩ and the set Hare bijective
Therefore the relative positional relationship between thedriven manipulator and the obstacle with the joint valueE can be expressed by the following formula in the jointconfiguration space
Ω(119864) = 1 Γ (119864) = 10 Γ (119864) = 0 (8)
where Ω(119864) is the value of the point in the joint con-figuration space Ω with the element in the joint value 119864of the manipulator as the coordinate and represents therelative positional relationship with the obstacle when the
6 Complexity
manipulator is in the position corresponding to 119864 If themanipulator interferes with the obstacle Ω(119864) is equal to 1otherwise Ω(119864) is equal to 0 So the set 119867part (1198641 1198642 119864119889)can represent a set of continuously varying poses of themanipulator the set represents a set of discrete points inthe joint configuration space Ω If a set of discrete points isconnected a path can be obtained where 119889 is the numberof the path control points Only when the following formulais satisfied does the driven manipulator not collide with theobstacle when the joint value set is119867part
where Ψ is the relative positional relationship between themanipulator the obstacle when the joint value set is119867part
Therefore the obstacle path planning is performed on themanipulator that is a set 119867part of joint values is searched inthe joint configuration space Ω so that the set is connectedto the initial configuration joint value 119864s and the targetjoint value 119864g of the manipulator Meanwhile it satisfies thecollision-free condition on the path as shown in (9)
To calculate the configuration space of the joint arm ofthe harvesting robot a simulation model of the robot wasestablished by using two functions of ldquolinkrdquo and ldquodrivebotrdquothat were provided byMatlab Robotics Toolbox Toolbox [22]And then the motion range of the harvesting manipulator inthe actual working environment is calculated and analyzedto carry better out the path-planning of picking operationAccording to the structure of the robot the motion space ofthe robot is mainly determined by the first three joints (1 to 3linkages) and the latter three joints (4 to 6 linkages) have noeffect on the motion space The first three joints determinethe position of the end-effector and the last three jointsdetermine the posture of the end-effector At present thereare mainly three methods for solving the motion space of therobots analytic methods numerical methods and graphicmethods The analytic method is to use algebraic method toobtain the equation about the structure parameters of therobot The advantage of this method is that it can accuratelydescribe the relationship between the structure parameters ofthe robot and the space of the robot but its computation islarge In this study we used analytic method and take Matlabto solve the robotrsquos motion space and the motion space of theharvesting robot can be shown as Figure 3
3 Path-Planning Based on Energy Optimaland Artificial Potential Field
The work process of the grape harvesting robot is as followsFirstly the picking robot acquires the information on numberof fruits in the field of view and the position of each fruitthrough the visual system Secondly the picking sequence isplanned The picking order of all fruits is sorted accordingto certain principles Thirdly controller has robot arm moveto the picking point of first bunch of grape rapidly andthe end effector performs the picking action Fourthly thesecond bunch of fruit is picked according to the above same
procedure until all the fruit is harvested Fifth the robot armreturns to the initial posture and the picking robot controlsthe mobile platform tomove forward and then starts the nextstage of picking Therefore the path planning of the pickingrobot work process is divided into two stages The first stageis to plan the picking sequence and the second stage is to planthe path point for each bunch of fruit picking The schematicdiagram for the path planning of the grape harvesting robotcan be shown as Figure 4
31 Harvesting Sequence Planning Based onMinimumEnergyAs the requirement of multiobjectives harvesting with theaim to get the minimum sum of weighted rotating jointangles in joint space the objective function on six-degree-of-freedom harvesting robot arm task planning based on mini-mum energy principle is proposed By calculating the value ofobjective function the picking sequence with the minimumenergy consumption can be obtained In this paper anobjective function to determine the harvesting sequence ofgrape bunches is proposed The optimal harvesting sequenceis finally determined by calculating the function value thussolves the problem of harvesting task planning
The harvesting sequence can be described in mathe-matically as assuming that the current manipulator is inthe initial position of the harvesting (1199090 1199100 1199110) there are 119899bunches of fruits in the visual area to be picked and the spaceposition coordinates are (119909i 119910i 119911i) and the correspondingspace variables of themanipulator are (1205791i 1205792i 1205793i 1205794i 1205795i 1205796i)in which 119894 = 1 2 119899 Manipulator is required to search foran optimal harvesting sequence from the initial position Allthe fruits are picked sequentially and then returned to theoriginal position It is assumed that the motion parameters(including angular velocity and angular acceleration) of alljoints of a manipulator are the same In order to minimizethe energy in the process of motion when a joint of thearm carry out harvesting task it selects the proper sequenceof harvesting to minimize the total angle of rotation whichindicates that the operating time and energy consumption ofthe joint under this sequence to complete the harvesting taskare minimal The optimization objective of single joint is
119875 = 119899sum119895=1
10038161003816100381610038161003816120579119895 minus 120579119895+110038161003816100381610038161003816 (10)
in which 119875 is the function of optimization objective 120579 is themotion angle of joint and 119899 is the number of the space pointsthat end effector need to move through
However there are multiple joints for the harvestingmanipulator in this study if the minimum sum of the singlejoint angle changes was took as the optimization objectiveand then each joint would have an optimal objective Atthis time the problem of the harvesting sequence of themanipulator is transformed into a multiobjective optimiza-tion problem Considering the angle changes of each jointof the manipulator may not reach the minimum at the sametime in the same harvesting sequence so it is necessary tocoordinate the sub objective functions of each joint to achievethe optimal objective function and the optimum of each jointwhen determine the optimal objective function of the whole
Complexity 7
10001000
500Y axis (mm)
0
X axis (mm)0
minus500minus1000 minus1000
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(a) Motion space in X Y and Z coordinates
minus1000
minus500
0
500
1000
Y ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(b) Motion space in X and Y coordinates
minus1000
minus500
0
500
1000
Z ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(c) Motion space in X and Z coordinates
0 500 1000minus500minus1000Y axis (mm)
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(d) Motion space in Y and Z coordinates
Figure 3 The motion space of the harvesting robot
destination
path point
cutting point①
②
③④
⑤
Figure 4 Schematic diagram for the path planning of the grapeharvesting robot
manipulator Moreover the power of each joint motor isdifferent according to the value of the power of each jointmotor of the manipulator different weights should be givento each joint angle and different weights should also be givento the sub targets of each joint of the manipulator So thesequence planning of the six degree of freedom harvestingmanipulator based on the principle of minimum energy canbe described by the following
1198751015840 = 119898sum119894=1
120596119894119869119894 =119898sum119894=1
119899sum119895=1
120596119894 10038161003816100381610038161003816120579119894119895 minus 120579119894119895+110038161003816100381610038161003816 (11)
where 1198751015840 indicates the objective function of the manipulatorthat can embody the energy consumption of the manipulatormotion 119898 is the number of the joints 120596i is the weight of theobjective function of the 119894th joints and 120579ij indicates the anglevalue of the 119894th joint when the manipulator is locating the 119895thspace point
32 Harvesting Path Generating Based on Artificial PotentialField eory In the process of grape harvesting collision-free path planning under a vineyard environment is themost important issue which need be resolved firstly to avoiddamage the fruits At present there are two main pathplanning methods [23] model-based global path planningand sensor-based local path planning In this study the localpath planning method based on artificial potential field wasadopted
321 Principle of Artificial Potential Field The path planningmethod based on artificial potential field is a virtual forcemethod proposed by Khatib [24] Its basic idea is to designthe motion of the robot in the surrounding environment intoan abstract artificial gravitational fieldThe artificial potentialfield includes the gravitational field and the repulsion field inwhich the object produces the gravitational attraction to theobject and guides the object to move toward it The obstaclesrepel other objects to avoid collisions with it The resultant
8 Complexity
Input the current point coordinates of the end-effector (1199090 1199100 1199110) the terminal coordinates(119909t 119910t 119911t) (the cutting point on the peduncles of grape cluster) the bounding box model ofobstacles 119877(119874s 119874e)Output the path points (119909i 119910i 119911i)
1 Find all collision-free sampling points2 for each sampling points p do
(a) calculate the probability that the current point is the candidate path points(b) find the point whose probability is maximum(c) consider the points as a candidate path point
end3 Repeat the above process until the terminal coordinates is reached
Algorithm 1 Sampling-based path point generating method
force of every point on a path is equal to the sum of allrepulsive forces and gravitational forces on this point
The basic idea of the proposed path planning in thisstudy is that the harvesting point is attractive to the motionof the harvesting manipulator by the virtual force fieldthe anticollision bounding body of grape cluster and otherobstacles are repulsive to it and the path planning is carriedout through the interaction of attraction and repulsion forceThe artificial potential field 119880sum(119883) can be defined by thefollowing [24]
in which119880att(119883) indicates the gravitational field generated bythe target 119880rep(119883) indicates the repulsion field generated bythe obstacles119883 = (119909 119910 119911)119879 is the position of the end-effectorin the workspace Setting the position of the target as119883g andthe gravitational field119880att(119883) can be defined by the following
119880att (119883) = 12119896 (119883 minus 119883119892)2 (13)
where 119896 is a constant about the gravitational field and then thegravitation 119865att(119883) can be solved by calculating the negativegradient value of the gravitational field which is described asFormula (14)
To define the mathematical expression about the repul-sive force field the following two conditions need firstly beconformed [25] (1) the artificial potential field119880sum(119883)mustbe a continuous-differential function and when119883 is equal to119883g the value of119880sum(119883) is 0 (minimum value) (2) Under theeffect of the artificial potential field 119880sum(119883) the system canbe stable Setting 1198830 as the space position of the obstacle therepulsive force field 119880rep(119883) can be defined by the following
119880rep (119883) =12120578(
1119883 minus 1198830 minus
1120588)2 (119883 minus 1198830) lt 120588
0 (119883 minus 1198830) ge 120588 (15)
where 120578 is a constant about the repulsive force field and 120588 isthe maximum range of the impact of the obstacle When the
distance between the obstacle and the end-effector is largerthan120588 the repulsive fieldwould no longer to affect themotionof harvesting robotThe repulsive force 119865rep(119883) can be solvedby calculating the negative gradient value of the repulsiveforce field 119880rep(119883) which is described as the following
120597 (119883 minus 1198830)120597119883 (119883 minus 1198830) lt 1205880 (119883 minus 1198830) ge 120588
(16)
322 Sampling-Based Path Points Generating Method Thearray of the path point sets (119909i 119910i 119911i) are firstly establishedand then the terminal pose of the end-effector is determinedbased on the current pose of the robot and the pose of grapecluster The current point coordinates of the end-effector(1199090 1199100 1199110) the terminal coordinates (119909t 119910t 119911t) (the cuttingpoint on the peduncles of grape cluster) and the boundingbox model of obstacles 119877(119874s 119874e) are given respectivelyAccording to the artificial potential field method new sam-pling points are generated randomly in the neighbourhoodand collision detection is performed on the sampling pointsThe probability that all collision-free sampling points areselected as the candidate path points is calculated and thesampling point with the highest probability is added to thepath array as the following path point Repeat the aboveprocess until the terminal coordinates is reachedThe pseudocode of sampling-based path point generating method is asshown in Algorithm 1
4 Experiments and Results
To validate the performance of the proposed anticollisionpath planning algorithm in a complex orchard a virtualharvesting robot simulation system was developed based onthe virtual reality software platform and then the perfor-mance of path planning method was investigated based onthe developed simulation system
41 Virtual Harvesting Robot Testing System The virtual sim-ulation systemwas implemented on theWindows 7 operatingsystem by using the software tools such as Visual studio 2013
Complexity 9
Figure 5 Schematic diagram for the path planning of the grapeharvesting robot
EON Studio 3Dmax and Solidworks In this study the virtualharvesting robot is constructed according to the actual sizeand workspace of the 6-DOF robot prototype Firstly the 3Dmodel of orchard scene and harvesting robotrsquos body structureis constructed and the kinematics model of the manipulatoris set by D-H parameter methodThen the virtual grape clus-ters and their anticollision space bounding body are drawnunder the virtual environment The collision avoidance pathpoints are computed by the proposed algorithm Finallythe path is simulated by a three-dimensional visualizationmethod The end-effector on the harvesting robot is consistsof three functional parts clamping finger pallet and scissorThe clamping mechanism is mainly responsible for clampingthe peduncle of grape cluster The pallet holds the grapecluster from behind and underneath carrying part of grapegravity to prevent the grape from shaking and slippingWhenthe fingers and pallets lock up the grape cluster the peduncleis cut by the scissors mechanism The software interface isshown as Figure 5
After the collision-free path is planned the joint variablesparameters of the manipulator are calculated by the inversekinematics model and then the forward kinematics methodis used to control the robotrsquos end-effector to the targetposition In the virtual simulation system the collision nodein the EON platform was used to detect collision in thisresearch The node can detect the collision events betweendifferent geometric objects in the virtual environment whichcan monitor the collision between the harvesting robot andthe obstacle in real-time To control the motion behaviorof virtual harvesting robot the modular programming androuting communication mechanism in EON platform wereadoptedThemainmodules involved aremovement rotationposition sensor angle sensor time sensor switch node rout-ing and so on The movement module is mainly used for theclamping behavior control of the end-effector The rotationmodule is used to control the rotation of the six joints of themanipulator and the rotary cutting motion of the actuatorscissors The position and angle sensors are used to perceivethe real-time travel and position of the joint motionThe timesensor is used to control the motion speed and acceleration ofthe joints of the manipulator and the switch nodes are usedto connect the communication between the modules Thecommunications among several functionmodules are carried
out through routing mechanism in the virtual environmentThe routing mechanism is responsible to mainly passesand monitors the running state of each module throughevents and then broadcast the state parameters to otherfunctional modules in real time the coordination of themultifunctional modules is finally realized Events are thedata information transmitted between two domains whichinclude two types Input and Output The Input event is theinformation generated by other sending nodes to change thestate of the receiving node and the Output event is a statethat the state of the node itself changes and outputs theinformation When one of the behavior modules sends thecommand the receiving node gets the instructions throughthe route transfers the nodes through the event driven andrealizes the message driven mechanism
42 Path-Planning Testing and Analysis The path planningtests on multiple harvesting objectives were implementedbase on the developed virtual simulation The cluster numberof the tested grape was set from 2 to 5 and their positionswere randomly given in the configuration space of themanipulator The harvesting sequence was firstly calculatedby the energy optimal and the path points were generatedby artificial potential field The simulation test platformare as follows a laptop (Lenovo T430) with 4G RAM andIntel(R)Core(TM)i5-3230 M CPU260 GHz a Windows7 operating system and a Visual C++ 2008 platform Thestatistics and analysis are made on the path length thenumber of sampling points the collision situation and theaverage time of path planning in each harvesting The resultsof the tests are shown as Table 2 The relationship betweenpath length 119871 and key point 119875i can be described by Formula(17)
119871 = sum1le119894le119870
radic(119909119894 minus 119909119894minus1)2 + (119910119894 minus 119910119894minus1)2 + (119911119894 minus 119911119894minus1)2 (17)
where119870 indicates the number of sampling points of the pathand (119909i 119910i 119911i) is the coordinates of the 119894-th sampling points
From the Table 2 we can see that there are 9 times issuccessful and 1 times failure in the 10 grape harvesting testsThe success rate was 90 the path lengthwas between 44867cm and 147265 cm the number of sampling points wasbetween 90 and 206 and the average time of path planningwas between 98ms and 273 ms It can be seen that the reasonfor the failure of the test was the collision between the endeffector and the anticollision space bounding body of thegrape cluster If the distance between the end effector andgrape cluster is too small the end effector will be easy tocollide with the upper part of the grape cluster when theend effector move closely to the fruit peduncle for harvestingoperationHarvesting path-planning can be optimized by set-ting and adjusting the minimum safety margin between thecutting point and the anticollision space bounding volumeMoreover the average time of path planning increases withthe number of objective and the number of sampling pointsFigure 6 shows a successful grape harvesting path planningThewhite dots are the path points swept by the clamper centerof the end effector during the harvesting
10 Complexity
Table 2 Statistical results of the virtual tests for grape harvesting path-planning
Number ofobjectives Harvesting optimal sequence Length of
path (Lcm)
Number ofsamplingpoints (K)
Collision(YN)
Average timeof planning
(ms)3 B 997888rarrC 997888rarrA 63578 108 N 1522 B 997888rarrA 44867 72 N 1084 C 997888rarrD 997888rarrA 997888rarrB 98523 172 N 2155 B 997888rarrD 997888rarrC 997888rarrA 997888rarr E 136245 206 N 2613 A 997888rarrC 997888rarrB 72333 102 N 1634 B 997888rarrC 997888rarrD 997888rarrA 106158 170 N 2035 E 997888rarrC 997888rarrA 997888rarrB 997888rarr D 147265 216 Y 2742 A 997888rarrB 46365 91 N 983 B 997888rarrC 997888rarrA 75687 127 N 1514 C 997888rarrB 997888rarrD 997888rarrA 104526 162 N 199
(a) (b)
(c)
Figure 6 The path points drew by the proposed path-planning method
5 Discussion
Traditional path planning methods (such as skeleton celldecomposition and subgoal graph etc) are very effective forlower degree of freedom robot (2 to 3 DOF) With theincrease in the degree of freedom of robots these algorithms
will be out of work A collision-free autonomous path plan-ning methodolgy for six-DOF serial harvesting manipulatorunder a dynamic vineyard environment was presented inthis study The kinematical modelling of Six-DOF serialmanipulator the model of obstacles and the configurationspace of harvesting robot was firstly introduced in detail
Complexity 11
And then the harvesting sequence and the anticollision pathpoints were calculated by using the energy optimal and theartificial potential field The virtual tests based on virtualreality were performed to validate the performance of theproposed algorithm Through the virtual simulation test ofthe harvesting path planning the three-dimensional spacepath points of the end-effector of the harvesting manipulatorwere calculated in real time in virtual environment andthe collision detection is analyzed The success rate wasup to 90 It can be known that the simulation systemdesigned in this study has a good practical value to helptest and improve the intelligent behavior algorithm of therobot
To obtain an optimal harvesting path taking the sumof the joint angle of the weighted rotation as the goalthe harvesting sequence planning objective function of thesix-DOF harvesting manipulator is established by usingthe minimum energy principle and the minimum energyconsumption sequence can be obtained by calculating thevalue of the target function In addition the mapping modelof obstacles in the joint configuration space is built on thebasis of sampling method and the artificial potential fieldis used to search the obstacle avoidance path in the jointconfiguration space which improves the generality of thealgorithm However due to the proposed algorithm adoptsrandom sampling strategy the sampling points may collidewith the obstacles so it is necessary to resample If thenumber of maximum sampling point is too small the failureprobability of the path planning increases And if the numberofmaximumsampling point value is too large it will cause thepath to not exist or be difficult to find or the planning time istoo long So the parameters need test repeatedly
6 Conclusion
To conduct an undamaged robotic grape-harvesting in anunstructured vineyard a path planning strategies based onminimum energy and artificial potential field for grapeharvesting robot was developed in this studyThe kinematicalmodel of Six-DOF serial manipulator was firstly constructedby using the D-H method the model of obstacles wasdefined by the axis-aligned bounding box and then theconfiguration space of harvesting robot was described bycombining the obstacles and robot Then the harvestingsequence in path planning was computed by energy optimalmethod and the anticollision path points were generatedbased on the artificial potential field and sampling searchingmethod Finally to verify and test the proposed path planningalgorithm a virtual test system based on virtual reality wasdeveloped 10 times harvesting tests for grape anticollisionpath planning were implemented on the developed sim-ulation system and the success rate was up to 90 Inconclusion the developed approach can effectively plan acollision-free path for the grape harvesting robot in the com-plex vineyard environment However when facing multipleoverlapped and adjoining grape clusters the path planning isstill an issue that needs to be solved and will require furtherresearch
Data Availability
The grape harvesting robot data used to support the findingsof this study are available from the corresponding authorupon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
This work was supported by grants from the National Nat-ural Science Foundation of China (no 51705365) and theNational Key Research and Development Program of China(2017YFD0700100)
References
[1] M A Hossain and I Ferdous ldquoAutonomous robot pathplanning in dynamic environment using a new optimizationtechnique inspired by bacterial foraging techniquerdquo Roboticsand Autonomous Systems vol 64 pp 137ndash141 2015
[2] V San JuanM Santos and JM Andujar ldquoIntelligentUAVMapGeneration and Discrete Path Planning for Search and RescueOperationsrdquoComplexity vol 2018 Article ID 6879419 17 pages2018
[3] L Luo Y Tang Q Lu X Chen P Zhang and X Zou ldquoA visionmethodology for harvesting robot to detect cutting points onpeduncles of double overlapping grape clusters in a vineyardrdquoComputers in Industry vol 99 pp 130ndash139 2018
[4] P Li S-H Lee and H-Y Hsu ldquoReview on fruit harvestingmethod for potential use of automatic fruit harvesting systemsrdquoin Proceedings of the 2011 International Conference on PowerElectronics and EngineeringApplication PEEA 2011 pp 351ndash366China December 2011
[5] W Wei D-T Ouyang S Lu and Y-X Feng ldquoMultiobjectivepath planning under dynamic uncertain environmentrdquo JisuanjiXuebaoChinese Journal of Computers vol 34 no 5 pp 836ndash845 2011
[6] M G Mohanan andA Salgoankar ldquoA survey of roboticmotionplanning in dynamic environmentsrdquo Robotics and AutonomousSystems vol 100 pp 171ndash185 2018
[7] X Hu L Chen B Tang D Cao and H He ldquoDynamicpath planning for autonomous driving on various roads withavoidance of static and moving obstaclesrdquo Mechanical Systemsand Signal Processing vol 100 pp 482ndash500 2018
[8] DDevaurs T Simeon and J Cortes ldquoOptimal Path Planning inComplex Cost Spaces with Sampling-Based Algorithmsrdquo IEEETransactions on Automation Science and Engineering vol 13 no2 pp 415ndash424 2016
[9] R Cui Y Li and W Yan ldquoMutual information-based multi-AUV path planning for scalar field sampling using multi-dimensional RRTrdquo IEEE Transactions on Systems Man andCybernetics Systems vol 46 no 7 pp 993ndash1004 2016
[10] CW Bac J Hemming and E J VanHenten ldquoStem localizationof sweet-pepper plants using the support wire as a visual cuerdquoComputers and Electronics in Agriculture vol 105 pp 111ndash1202014
12 Complexity
[11] L Luo Y Tang X ZouM YeW Feng andG Li ldquoVision-basedextraction of spatial information in grape clusters for harvestingrobotsrdquo Biosystems Engineering vol 151 pp 90ndash104 2016
[12] E J VanHenten J Hemming B A J VanTuijl J G Kornet andJ Bontsema ldquoCollision-free Motion Planning for a CucumberPicking Robotrdquo Biosystems Engineering vol 86 no 2 pp 135ndash144 2003
[13] G Gao G Sun J Na Y Guo and XWu ldquoStructural parameteridentification for 6 DOF industrial robotsrdquoMechanical Systemsand Signal Processing vol 113 pp 145ndash155 2018
[14] K Wei and B Ren ldquoA Method on Dynamic Path Planning forRobotic Manipulator Autonomous Obstacle Avoidance Basedon an Improved RRT Algorithmrdquo Sensors vol 18 no 2 p 5712018
[15] Y Dai and M Zhao ldquoManipulator path-planning avoidingobstacle based on screw theory and ant colony algorithmrdquoJournal of Computational and eoretical Nanoscience vol 13no 1 pp 922ndash927 2016
[16] H Pham and Q Pham ldquoTime-Optimal Path Tracking viaReachability Analysisrdquo in Proceedings of the 2018 IEEE Inter-national Conference on Robotics and Automation (ICRA) pp3007ndash3012 Brisbane QLD May 2018
[17] G Legnani F Casalo P Righettini and B Zappa ldquoA homo-geneous matrix approach to 3D kinematics and dynamics - IIApplications to chains of rigid bodies and serial manipulatorsrdquoMechanism and Machine eory vol 31 no 5 pp 589ndash6051996
[18] J Craig Introduction to Robotics Mechanics and Control 3rdedition 2015
[19] R P Paul B Shimano and G E Mayer ldquoKinematic controlequations for simple manipulatorsrdquo IEEE Transactions on Sys-tems Man and Cybernetics vol 11 no 6 pp 449ndash455 1981
[20] G Zachmann ldquoRapid collision detection by dynamicallyaligned DOP-treesrdquo in Proceedings of the 1998 IEEE VirtualReality Annual International Symposium VRAIS pp 90ndash97March 1998
[21] H Yang L Li and Z Gao ldquoObstacle avoidance path planningof hybrid harvesting manipulator based on joint configurationspacerdquoNongyeGongcheng Xuebao vol 33 no 4 pp 55ndash62 2017
[22] C Peter Robotics Vision amp Control Springer 2nd edition 2017[23] Z Daqi and Y Mingzhong ldquoSurvey on technology of mobile
robot path planningrdquo Control and Decision vol 25 no 7 pp961ndash967 2010
[24] O Khatib ldquoReal-time obstacle avoida nce for manipulators andmobile robotsrdquo International Journal of Robotics Research vol5 no 1 pp 90ndash98 1986
[25] M Fakoor A Kosari and M Jafarzadeh ldquoRevision on fuzzyartificial potential field for humanoid robot path planningin unknown environmentrdquo International Journal of AdvancedMechatronic Systems vol 6 no 4 pp 174ndash183 2015
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
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Complexity 3
ClamperScissors
Pallet
(a) Harvesting robot shape
O2
O0
O3
O4O5 O6
x6
y6
z6z5
x5
x4
z4
y4
x3
y3
z0x0y0
y5
O1
xh
yh zh
Oh
a3
d4
x1
z1
y1
z2
x2
y2
z3a2
a 1
1
2
3
54
6
(b) Origin coordinate and joints coordinate systems ofharvesting robot
Figure 1 Harvesting robot shape and its joints coordinate systems Note that 1198740 is the base coordinate of harvesting robot 119874119894 is the localcoordinate system of the 119894th(119894 = 1 2 6) linkages 119874ℎ is the coordinate system of end effector 120572119894-1 is twist angle 120572119894-1 is length of linkages120579119894 is joint angle and 119889119894 is offset of linkages
model which is to calculate the position and attitude ofthe end-effector coordinate system Oh relative to the basecoordinate system O0 by a given set of joint values Thetransformation matrix between two adjacent connecting rodscan be calculated by the D-H parameters in Formula (1) andthe Table 1
119894minus1119894119879
=[[[[[[[
119888119894 minus119904119894 0 119886119894minus1119904119894 cos 120572119894minus1 119888119894 cos 120572119894minus1 minus sin 120572119894minus1 minus119889119894 sin 120572119894minus1119904119894 sin 120572119894minus1 119888119894 sin 120572119894minus1 cos120572119894minus1 119889119894 cos 120572119894minus1
0 0 0 1
]]]]]]]
(1)
where 119904119894 indicates sin 120579119894 119888119894 indicates cos 120579119894 (119894 = 1 2 3 6)120572119894-1 is the twist angle 120572119894-1 is the length of linkages and 119889119894 isthe offset of linkages
The transformation matrix of the manipulator 06119879 canbe obtained by multiplying continuously the transformationmatrix of each connecting rod 119894minus1119894119879 (i = 1 2 6) which is afunction with the six joint variables (1205791 1205792 1205793 1205794 1205795 1205796) andcan be described by Formula (2) It represents the positionrelationships between the end-effector attitude (119899 119900 119886 119901) andthe basic coordinate system [18]
119899119909 = c1 [11988823 (119888411988851198886 minus 11990441199046) minus 1199042311990451198886]+ 1199041 (119904411988851198886 + 11988841199046)
119899119910 = 1199041 [11988823 (119888411988851198886 minus 11990441199046) minus 1199042311990451198886]minus 1198881 (119904411988851198886 + 11988841199046)
119899119911 = minus11990423 (119888411988851198886 minus 11990441199046) minus 1198882311990451198886119900119909 = minus1198881 [11988823 (119888411988851199046 + 11990441198886) minus 1199042311990451199046]
minus 1199041 (119904411988851199046 minus 11988841198886)119900119910 = minus1199041 [11988823 (119888411988851199046 + 11990441198886) minus 1199042311990451199046]
+ 1198881 (119904411988851199046 minus 11988841198886)119900119911 = 11990423 (119888411988851199046 + 11990441198886) + 1198882311990451199046119886119909 = 1198881 (minus1198882311988841199045 minus 119904231198885) minus 119904111990441199045119886119910 = 1199041 (minus1198882311988841199045 minus 119904231198885) + 119888111990441199045119886119911 = 1199042311988841199045 minus 119888231198885
119901119909 = 1198881 (119886311988823 minus 119889411990423 + 1198861 + 11988621198882)119901119910 = 1199041 (119886311988823 minus 119889411990423 + 1198861 + 11988621198882)119901119911 = minus119886311990423 minus 119889411988823 minus 1198862119904211988823 = cos (1205792 + 1205793)11990423 = sin (1205792 + 1205793)
(3)
In the robotics grape harvesting the three-dimensionalcoordinates of the cutting point on the peduncle of grapecluster are obtained by the visual system of robot and thetarget position of the end-effector coordinate system Oh canbe calculated by the cutting point position The attitude ofthe end-effector (119899 119900 119886 119901) can be derived by combining withthe growth posture of grape clusters In the case of knowingthe relative position between the target position of the end-effector and the current position the inverse kinematicsmodel is responsible for calculating the satisfied joint variableof the manipulator which can control the manipulator movefrom the current position to the target position To constructthe inverse kinematics model the inverse transformationmethod [19] was used in this study and the calculationformulas of these joint variable (1205791 1205792 1205793 1205794 1205795 1205796) are asshown Formula (4) So the relation between the position ofthe terminal connecting rod and the joint variable of themanipulator can be established
1205791 = arctan119901119910119901119909
1205792 = arctan(11988621199043 minus 1198894) (1198881119901119909 + 1199041119901119910 minus 1198861) minus (1198863 + 11988621198883) 119901119911(1198863 + 11988621198883) (1198881119901119909 + 1199041119901119910 minus 1198861) minus (1198894 minus 11988621199043) 119901119911 minus 1205793
1205793 = arctan11988631198894 minus arctan 119896
radic11988632 + 11988942 minus 11989621205794 = arctan
minus1198861199091199041 + 1198861199101198881minus119886119909119888111988823 minus 119886119910119904111988823 + 11988611991111990423
1205795 = arctanminus119886119909 (1198881119888411988823 + 11990411199044) minus 119886119910 (1199041119888411988823 minus 11988811199044) + 119886119911 (119904231198884)
minus119899119909 (1198881119904411988823 minus 11990411198884) minus 119899119910 (1199041119904411988823 + 11988811198884) + 119899119911 (119904411990423)119899119909 [1198885 (1198881119888411988823 + 11990411199044) minus 1198881119904511990423] + 119899119910 [1198885 (1199041119888411988823 minus 11988811199044) minus 1199041119904511990423] minus 119899119911 (1198884119888511990423 + 119904511988823)
(4)
where 119896 = (1199011199092 + 1199011199102 + 1199011199112 + 11988612 minus 21198861(1198881119901119909 + 1199041119901119910) minus 11988632 minus11988622 minus 11988942)21198862To verify the correctness of the kinematics model the
values of a set of joint variables (1205791 = 1205873 1205792 = -1205873 1205793 =1205873 1205794 = 1205876 1205795 = 1205872 1205796 = 1205874) is artificially allocatedand then these values were input to the forward kinematicmodel (Formula (2)) to solve the terminal pose matrix 06119879
The following 06119879 was calculated by using Matlab
Figure 2 The bounding volume of obstacles such as cylinder andsphere
Then the obtained 06119879 seen as known conditions wasinput to the inverse kinematic model (Formula (4)) to solvethe angle values of the robot joints and the joint values(1205791 = 600000 1205792 = -600000 1205793 = 600000 1205794 = 2999931205795 = 900000 and 1205796 = 450022) were calculated It can beseen that the result is basically consistent with the variablevalues allocated by manual which shows the correctness ofthe kinematics model of the robot
22 Obstacles Modeling In the collision detection thebounding volume is a simple geometric space which containsobjects of complex shape The purpose of adding a boundingvolume to an object is to quickly carry out collision detectionor to filter the exact collision detection The bounding bodytypes include sphere axis aligned bounding box (AABB)directed bounding box (OBB) 8-DOP and convex hull Theobstacles in the actual picking environment are usually notregular geometry so it is difficult to describe them witha precise model [20] To facilitate the collision avoidancepath-planning the axis-aligned bounding box (AABB) wasadopted to establish the obstacles model approximately inthis study Although this modeling method expands theobstacle domain to a certain extent it greatly decreases thecalculation amount of the interference detection between themanipulator and the obstacles and effectively improves theefficiency of the path planning and also makes the plannedpath more secure
The axis-aligned minimum bounding box for a givenpoint set is its minimum bounding box subject to the con-straint that the edges of the box are parallel to the coordinateaxes It is simply the Cartesian product of 119873 intervals eachof which is defined by the minimal and maximal value ofthe corresponding coordinate for the points in 119878 In theobstacles modeling the farthest and nearest points in X Yand Z directions from the vertex collection of the obstacleare obtained firstly and then the AABB box was built byusing these points The AABB box is a simple hexahedronand each of whose side is parallel to a coordinate plane Itslength width and height can be different from each other InFigure 2 two simple 3D objects and their AABB are drawnSome important properties of the AABB can be described asfollows Firstly the points (119909 119910 119911) in the AABB box satisfythe following conditions 119909min le 119909 le 119909max 119910min le 119910 le 119910maxand 119911min le 119911 le 119911max and the points Pmin = [119909min 119910min 119911min]
and Pmax = [119909max 119910max 119911max] were two important pointsof the AABB box The center point c can be calculated bythe equation (c = (Pmin + Pmax)2) A bounding box of theobstacle can clearly be represented by using the two pointsPmin and Pmax
23 Configuration Space Modelling for Harvesting Robot Tosolve a collision avoidance path for the harvesting robot it isvery importance to determine the configuration space of themanipulator For a manipulator with 119899 degrees of freedomsetting 119864(12 n) as a set of active joint values of itin which i is the rotation angle of the 119894-th active joint ofthe manipulator If the point 119875 represents a point on themanipulator then the relative position relationship betweenthe point and the obstacle can be expressed as follows [21]
Γ (119875 (119864)) = 1 the point 119875 is inside the obstacle
0 the rest(6)
where D(119875(119864)) is relative position relationship betweenthe point 119875 and the obstacle when the manipulator is drivenwith the joint value and 119875(119864) is the position coordinate of thepoint 119875 on the manipulator in the basic coordinate systemwhen the joint value is 119864 If the rods of the manipulatorare uniformly dispersed into 119898 points according to the stepsize 119889min (mm)119898 discrete points constitute a point set 119875link The relative positional relation between the whole arm drivenwith the joint value 119864 and the obstacle can be expressed asfollows
Γ (Ε) = 119898sum119894=1
Γ (119875119894 (119864)) (7)
in which D(119864) is the relative positional relationship betweenthe driven manipulator and the obstacle when the joint valueis E
It can be known from formula (6) and formula (7) thatthe manipulator does not interfere with the obstacle only ifD(119864) = 0 The joint configuration spaceΩ is established withthe joint values of themanipulators of n degrees of freedom Ifthe set of the joint value E of themanipulator is represented byH then any point in the joint configuration spaceΩ uniquelycorresponds to one of the elements in the setH and vice versaIn other words the joint configuration spaceΩ and the set Hare bijective
Therefore the relative positional relationship between thedriven manipulator and the obstacle with the joint valueE can be expressed by the following formula in the jointconfiguration space
Ω(119864) = 1 Γ (119864) = 10 Γ (119864) = 0 (8)
where Ω(119864) is the value of the point in the joint con-figuration space Ω with the element in the joint value 119864of the manipulator as the coordinate and represents therelative positional relationship with the obstacle when the
6 Complexity
manipulator is in the position corresponding to 119864 If themanipulator interferes with the obstacle Ω(119864) is equal to 1otherwise Ω(119864) is equal to 0 So the set 119867part (1198641 1198642 119864119889)can represent a set of continuously varying poses of themanipulator the set represents a set of discrete points inthe joint configuration space Ω If a set of discrete points isconnected a path can be obtained where 119889 is the numberof the path control points Only when the following formulais satisfied does the driven manipulator not collide with theobstacle when the joint value set is119867part
where Ψ is the relative positional relationship between themanipulator the obstacle when the joint value set is119867part
Therefore the obstacle path planning is performed on themanipulator that is a set 119867part of joint values is searched inthe joint configuration space Ω so that the set is connectedto the initial configuration joint value 119864s and the targetjoint value 119864g of the manipulator Meanwhile it satisfies thecollision-free condition on the path as shown in (9)
To calculate the configuration space of the joint arm ofthe harvesting robot a simulation model of the robot wasestablished by using two functions of ldquolinkrdquo and ldquodrivebotrdquothat were provided byMatlab Robotics Toolbox Toolbox [22]And then the motion range of the harvesting manipulator inthe actual working environment is calculated and analyzedto carry better out the path-planning of picking operationAccording to the structure of the robot the motion space ofthe robot is mainly determined by the first three joints (1 to 3linkages) and the latter three joints (4 to 6 linkages) have noeffect on the motion space The first three joints determinethe position of the end-effector and the last three jointsdetermine the posture of the end-effector At present thereare mainly three methods for solving the motion space of therobots analytic methods numerical methods and graphicmethods The analytic method is to use algebraic method toobtain the equation about the structure parameters of therobot The advantage of this method is that it can accuratelydescribe the relationship between the structure parameters ofthe robot and the space of the robot but its computation islarge In this study we used analytic method and take Matlabto solve the robotrsquos motion space and the motion space of theharvesting robot can be shown as Figure 3
3 Path-Planning Based on Energy Optimaland Artificial Potential Field
The work process of the grape harvesting robot is as followsFirstly the picking robot acquires the information on numberof fruits in the field of view and the position of each fruitthrough the visual system Secondly the picking sequence isplanned The picking order of all fruits is sorted accordingto certain principles Thirdly controller has robot arm moveto the picking point of first bunch of grape rapidly andthe end effector performs the picking action Fourthly thesecond bunch of fruit is picked according to the above same
procedure until all the fruit is harvested Fifth the robot armreturns to the initial posture and the picking robot controlsthe mobile platform tomove forward and then starts the nextstage of picking Therefore the path planning of the pickingrobot work process is divided into two stages The first stageis to plan the picking sequence and the second stage is to planthe path point for each bunch of fruit picking The schematicdiagram for the path planning of the grape harvesting robotcan be shown as Figure 4
31 Harvesting Sequence Planning Based onMinimumEnergyAs the requirement of multiobjectives harvesting with theaim to get the minimum sum of weighted rotating jointangles in joint space the objective function on six-degree-of-freedom harvesting robot arm task planning based on mini-mum energy principle is proposed By calculating the value ofobjective function the picking sequence with the minimumenergy consumption can be obtained In this paper anobjective function to determine the harvesting sequence ofgrape bunches is proposed The optimal harvesting sequenceis finally determined by calculating the function value thussolves the problem of harvesting task planning
The harvesting sequence can be described in mathe-matically as assuming that the current manipulator is inthe initial position of the harvesting (1199090 1199100 1199110) there are 119899bunches of fruits in the visual area to be picked and the spaceposition coordinates are (119909i 119910i 119911i) and the correspondingspace variables of themanipulator are (1205791i 1205792i 1205793i 1205794i 1205795i 1205796i)in which 119894 = 1 2 119899 Manipulator is required to search foran optimal harvesting sequence from the initial position Allthe fruits are picked sequentially and then returned to theoriginal position It is assumed that the motion parameters(including angular velocity and angular acceleration) of alljoints of a manipulator are the same In order to minimizethe energy in the process of motion when a joint of thearm carry out harvesting task it selects the proper sequenceof harvesting to minimize the total angle of rotation whichindicates that the operating time and energy consumption ofthe joint under this sequence to complete the harvesting taskare minimal The optimization objective of single joint is
119875 = 119899sum119895=1
10038161003816100381610038161003816120579119895 minus 120579119895+110038161003816100381610038161003816 (10)
in which 119875 is the function of optimization objective 120579 is themotion angle of joint and 119899 is the number of the space pointsthat end effector need to move through
However there are multiple joints for the harvestingmanipulator in this study if the minimum sum of the singlejoint angle changes was took as the optimization objectiveand then each joint would have an optimal objective Atthis time the problem of the harvesting sequence of themanipulator is transformed into a multiobjective optimiza-tion problem Considering the angle changes of each jointof the manipulator may not reach the minimum at the sametime in the same harvesting sequence so it is necessary tocoordinate the sub objective functions of each joint to achievethe optimal objective function and the optimum of each jointwhen determine the optimal objective function of the whole
Complexity 7
10001000
500Y axis (mm)
0
X axis (mm)0
minus500minus1000 minus1000
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(a) Motion space in X Y and Z coordinates
minus1000
minus500
0
500
1000
Y ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(b) Motion space in X and Y coordinates
minus1000
minus500
0
500
1000
Z ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(c) Motion space in X and Z coordinates
0 500 1000minus500minus1000Y axis (mm)
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(d) Motion space in Y and Z coordinates
Figure 3 The motion space of the harvesting robot
destination
path point
cutting point①
②
③④
⑤
Figure 4 Schematic diagram for the path planning of the grapeharvesting robot
manipulator Moreover the power of each joint motor isdifferent according to the value of the power of each jointmotor of the manipulator different weights should be givento each joint angle and different weights should also be givento the sub targets of each joint of the manipulator So thesequence planning of the six degree of freedom harvestingmanipulator based on the principle of minimum energy canbe described by the following
1198751015840 = 119898sum119894=1
120596119894119869119894 =119898sum119894=1
119899sum119895=1
120596119894 10038161003816100381610038161003816120579119894119895 minus 120579119894119895+110038161003816100381610038161003816 (11)
where 1198751015840 indicates the objective function of the manipulatorthat can embody the energy consumption of the manipulatormotion 119898 is the number of the joints 120596i is the weight of theobjective function of the 119894th joints and 120579ij indicates the anglevalue of the 119894th joint when the manipulator is locating the 119895thspace point
32 Harvesting Path Generating Based on Artificial PotentialField eory In the process of grape harvesting collision-free path planning under a vineyard environment is themost important issue which need be resolved firstly to avoiddamage the fruits At present there are two main pathplanning methods [23] model-based global path planningand sensor-based local path planning In this study the localpath planning method based on artificial potential field wasadopted
321 Principle of Artificial Potential Field The path planningmethod based on artificial potential field is a virtual forcemethod proposed by Khatib [24] Its basic idea is to designthe motion of the robot in the surrounding environment intoan abstract artificial gravitational fieldThe artificial potentialfield includes the gravitational field and the repulsion field inwhich the object produces the gravitational attraction to theobject and guides the object to move toward it The obstaclesrepel other objects to avoid collisions with it The resultant
8 Complexity
Input the current point coordinates of the end-effector (1199090 1199100 1199110) the terminal coordinates(119909t 119910t 119911t) (the cutting point on the peduncles of grape cluster) the bounding box model ofobstacles 119877(119874s 119874e)Output the path points (119909i 119910i 119911i)
1 Find all collision-free sampling points2 for each sampling points p do
(a) calculate the probability that the current point is the candidate path points(b) find the point whose probability is maximum(c) consider the points as a candidate path point
end3 Repeat the above process until the terminal coordinates is reached
Algorithm 1 Sampling-based path point generating method
force of every point on a path is equal to the sum of allrepulsive forces and gravitational forces on this point
The basic idea of the proposed path planning in thisstudy is that the harvesting point is attractive to the motionof the harvesting manipulator by the virtual force fieldthe anticollision bounding body of grape cluster and otherobstacles are repulsive to it and the path planning is carriedout through the interaction of attraction and repulsion forceThe artificial potential field 119880sum(119883) can be defined by thefollowing [24]
in which119880att(119883) indicates the gravitational field generated bythe target 119880rep(119883) indicates the repulsion field generated bythe obstacles119883 = (119909 119910 119911)119879 is the position of the end-effectorin the workspace Setting the position of the target as119883g andthe gravitational field119880att(119883) can be defined by the following
119880att (119883) = 12119896 (119883 minus 119883119892)2 (13)
where 119896 is a constant about the gravitational field and then thegravitation 119865att(119883) can be solved by calculating the negativegradient value of the gravitational field which is described asFormula (14)
To define the mathematical expression about the repul-sive force field the following two conditions need firstly beconformed [25] (1) the artificial potential field119880sum(119883)mustbe a continuous-differential function and when119883 is equal to119883g the value of119880sum(119883) is 0 (minimum value) (2) Under theeffect of the artificial potential field 119880sum(119883) the system canbe stable Setting 1198830 as the space position of the obstacle therepulsive force field 119880rep(119883) can be defined by the following
119880rep (119883) =12120578(
1119883 minus 1198830 minus
1120588)2 (119883 minus 1198830) lt 120588
0 (119883 minus 1198830) ge 120588 (15)
where 120578 is a constant about the repulsive force field and 120588 isthe maximum range of the impact of the obstacle When the
distance between the obstacle and the end-effector is largerthan120588 the repulsive fieldwould no longer to affect themotionof harvesting robotThe repulsive force 119865rep(119883) can be solvedby calculating the negative gradient value of the repulsiveforce field 119880rep(119883) which is described as the following
120597 (119883 minus 1198830)120597119883 (119883 minus 1198830) lt 1205880 (119883 minus 1198830) ge 120588
(16)
322 Sampling-Based Path Points Generating Method Thearray of the path point sets (119909i 119910i 119911i) are firstly establishedand then the terminal pose of the end-effector is determinedbased on the current pose of the robot and the pose of grapecluster The current point coordinates of the end-effector(1199090 1199100 1199110) the terminal coordinates (119909t 119910t 119911t) (the cuttingpoint on the peduncles of grape cluster) and the boundingbox model of obstacles 119877(119874s 119874e) are given respectivelyAccording to the artificial potential field method new sam-pling points are generated randomly in the neighbourhoodand collision detection is performed on the sampling pointsThe probability that all collision-free sampling points areselected as the candidate path points is calculated and thesampling point with the highest probability is added to thepath array as the following path point Repeat the aboveprocess until the terminal coordinates is reachedThe pseudocode of sampling-based path point generating method is asshown in Algorithm 1
4 Experiments and Results
To validate the performance of the proposed anticollisionpath planning algorithm in a complex orchard a virtualharvesting robot simulation system was developed based onthe virtual reality software platform and then the perfor-mance of path planning method was investigated based onthe developed simulation system
41 Virtual Harvesting Robot Testing System The virtual sim-ulation systemwas implemented on theWindows 7 operatingsystem by using the software tools such as Visual studio 2013
Complexity 9
Figure 5 Schematic diagram for the path planning of the grapeharvesting robot
EON Studio 3Dmax and Solidworks In this study the virtualharvesting robot is constructed according to the actual sizeand workspace of the 6-DOF robot prototype Firstly the 3Dmodel of orchard scene and harvesting robotrsquos body structureis constructed and the kinematics model of the manipulatoris set by D-H parameter methodThen the virtual grape clus-ters and their anticollision space bounding body are drawnunder the virtual environment The collision avoidance pathpoints are computed by the proposed algorithm Finallythe path is simulated by a three-dimensional visualizationmethod The end-effector on the harvesting robot is consistsof three functional parts clamping finger pallet and scissorThe clamping mechanism is mainly responsible for clampingthe peduncle of grape cluster The pallet holds the grapecluster from behind and underneath carrying part of grapegravity to prevent the grape from shaking and slippingWhenthe fingers and pallets lock up the grape cluster the peduncleis cut by the scissors mechanism The software interface isshown as Figure 5
After the collision-free path is planned the joint variablesparameters of the manipulator are calculated by the inversekinematics model and then the forward kinematics methodis used to control the robotrsquos end-effector to the targetposition In the virtual simulation system the collision nodein the EON platform was used to detect collision in thisresearch The node can detect the collision events betweendifferent geometric objects in the virtual environment whichcan monitor the collision between the harvesting robot andthe obstacle in real-time To control the motion behaviorof virtual harvesting robot the modular programming androuting communication mechanism in EON platform wereadoptedThemainmodules involved aremovement rotationposition sensor angle sensor time sensor switch node rout-ing and so on The movement module is mainly used for theclamping behavior control of the end-effector The rotationmodule is used to control the rotation of the six joints of themanipulator and the rotary cutting motion of the actuatorscissors The position and angle sensors are used to perceivethe real-time travel and position of the joint motionThe timesensor is used to control the motion speed and acceleration ofthe joints of the manipulator and the switch nodes are usedto connect the communication between the modules Thecommunications among several functionmodules are carried
out through routing mechanism in the virtual environmentThe routing mechanism is responsible to mainly passesand monitors the running state of each module throughevents and then broadcast the state parameters to otherfunctional modules in real time the coordination of themultifunctional modules is finally realized Events are thedata information transmitted between two domains whichinclude two types Input and Output The Input event is theinformation generated by other sending nodes to change thestate of the receiving node and the Output event is a statethat the state of the node itself changes and outputs theinformation When one of the behavior modules sends thecommand the receiving node gets the instructions throughthe route transfers the nodes through the event driven andrealizes the message driven mechanism
42 Path-Planning Testing and Analysis The path planningtests on multiple harvesting objectives were implementedbase on the developed virtual simulation The cluster numberof the tested grape was set from 2 to 5 and their positionswere randomly given in the configuration space of themanipulator The harvesting sequence was firstly calculatedby the energy optimal and the path points were generatedby artificial potential field The simulation test platformare as follows a laptop (Lenovo T430) with 4G RAM andIntel(R)Core(TM)i5-3230 M CPU260 GHz a Windows7 operating system and a Visual C++ 2008 platform Thestatistics and analysis are made on the path length thenumber of sampling points the collision situation and theaverage time of path planning in each harvesting The resultsof the tests are shown as Table 2 The relationship betweenpath length 119871 and key point 119875i can be described by Formula(17)
119871 = sum1le119894le119870
radic(119909119894 minus 119909119894minus1)2 + (119910119894 minus 119910119894minus1)2 + (119911119894 minus 119911119894minus1)2 (17)
where119870 indicates the number of sampling points of the pathand (119909i 119910i 119911i) is the coordinates of the 119894-th sampling points
From the Table 2 we can see that there are 9 times issuccessful and 1 times failure in the 10 grape harvesting testsThe success rate was 90 the path lengthwas between 44867cm and 147265 cm the number of sampling points wasbetween 90 and 206 and the average time of path planningwas between 98ms and 273 ms It can be seen that the reasonfor the failure of the test was the collision between the endeffector and the anticollision space bounding body of thegrape cluster If the distance between the end effector andgrape cluster is too small the end effector will be easy tocollide with the upper part of the grape cluster when theend effector move closely to the fruit peduncle for harvestingoperationHarvesting path-planning can be optimized by set-ting and adjusting the minimum safety margin between thecutting point and the anticollision space bounding volumeMoreover the average time of path planning increases withthe number of objective and the number of sampling pointsFigure 6 shows a successful grape harvesting path planningThewhite dots are the path points swept by the clamper centerof the end effector during the harvesting
10 Complexity
Table 2 Statistical results of the virtual tests for grape harvesting path-planning
Number ofobjectives Harvesting optimal sequence Length of
path (Lcm)
Number ofsamplingpoints (K)
Collision(YN)
Average timeof planning
(ms)3 B 997888rarrC 997888rarrA 63578 108 N 1522 B 997888rarrA 44867 72 N 1084 C 997888rarrD 997888rarrA 997888rarrB 98523 172 N 2155 B 997888rarrD 997888rarrC 997888rarrA 997888rarr E 136245 206 N 2613 A 997888rarrC 997888rarrB 72333 102 N 1634 B 997888rarrC 997888rarrD 997888rarrA 106158 170 N 2035 E 997888rarrC 997888rarrA 997888rarrB 997888rarr D 147265 216 Y 2742 A 997888rarrB 46365 91 N 983 B 997888rarrC 997888rarrA 75687 127 N 1514 C 997888rarrB 997888rarrD 997888rarrA 104526 162 N 199
(a) (b)
(c)
Figure 6 The path points drew by the proposed path-planning method
5 Discussion
Traditional path planning methods (such as skeleton celldecomposition and subgoal graph etc) are very effective forlower degree of freedom robot (2 to 3 DOF) With theincrease in the degree of freedom of robots these algorithms
will be out of work A collision-free autonomous path plan-ning methodolgy for six-DOF serial harvesting manipulatorunder a dynamic vineyard environment was presented inthis study The kinematical modelling of Six-DOF serialmanipulator the model of obstacles and the configurationspace of harvesting robot was firstly introduced in detail
Complexity 11
And then the harvesting sequence and the anticollision pathpoints were calculated by using the energy optimal and theartificial potential field The virtual tests based on virtualreality were performed to validate the performance of theproposed algorithm Through the virtual simulation test ofthe harvesting path planning the three-dimensional spacepath points of the end-effector of the harvesting manipulatorwere calculated in real time in virtual environment andthe collision detection is analyzed The success rate wasup to 90 It can be known that the simulation systemdesigned in this study has a good practical value to helptest and improve the intelligent behavior algorithm of therobot
To obtain an optimal harvesting path taking the sumof the joint angle of the weighted rotation as the goalthe harvesting sequence planning objective function of thesix-DOF harvesting manipulator is established by usingthe minimum energy principle and the minimum energyconsumption sequence can be obtained by calculating thevalue of the target function In addition the mapping modelof obstacles in the joint configuration space is built on thebasis of sampling method and the artificial potential fieldis used to search the obstacle avoidance path in the jointconfiguration space which improves the generality of thealgorithm However due to the proposed algorithm adoptsrandom sampling strategy the sampling points may collidewith the obstacles so it is necessary to resample If thenumber of maximum sampling point is too small the failureprobability of the path planning increases And if the numberofmaximumsampling point value is too large it will cause thepath to not exist or be difficult to find or the planning time istoo long So the parameters need test repeatedly
6 Conclusion
To conduct an undamaged robotic grape-harvesting in anunstructured vineyard a path planning strategies based onminimum energy and artificial potential field for grapeharvesting robot was developed in this studyThe kinematicalmodel of Six-DOF serial manipulator was firstly constructedby using the D-H method the model of obstacles wasdefined by the axis-aligned bounding box and then theconfiguration space of harvesting robot was described bycombining the obstacles and robot Then the harvestingsequence in path planning was computed by energy optimalmethod and the anticollision path points were generatedbased on the artificial potential field and sampling searchingmethod Finally to verify and test the proposed path planningalgorithm a virtual test system based on virtual reality wasdeveloped 10 times harvesting tests for grape anticollisionpath planning were implemented on the developed sim-ulation system and the success rate was up to 90 Inconclusion the developed approach can effectively plan acollision-free path for the grape harvesting robot in the com-plex vineyard environment However when facing multipleoverlapped and adjoining grape clusters the path planning isstill an issue that needs to be solved and will require furtherresearch
Data Availability
The grape harvesting robot data used to support the findingsof this study are available from the corresponding authorupon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
This work was supported by grants from the National Nat-ural Science Foundation of China (no 51705365) and theNational Key Research and Development Program of China(2017YFD0700100)
References
[1] M A Hossain and I Ferdous ldquoAutonomous robot pathplanning in dynamic environment using a new optimizationtechnique inspired by bacterial foraging techniquerdquo Roboticsand Autonomous Systems vol 64 pp 137ndash141 2015
[2] V San JuanM Santos and JM Andujar ldquoIntelligentUAVMapGeneration and Discrete Path Planning for Search and RescueOperationsrdquoComplexity vol 2018 Article ID 6879419 17 pages2018
[3] L Luo Y Tang Q Lu X Chen P Zhang and X Zou ldquoA visionmethodology for harvesting robot to detect cutting points onpeduncles of double overlapping grape clusters in a vineyardrdquoComputers in Industry vol 99 pp 130ndash139 2018
[4] P Li S-H Lee and H-Y Hsu ldquoReview on fruit harvestingmethod for potential use of automatic fruit harvesting systemsrdquoin Proceedings of the 2011 International Conference on PowerElectronics and EngineeringApplication PEEA 2011 pp 351ndash366China December 2011
[5] W Wei D-T Ouyang S Lu and Y-X Feng ldquoMultiobjectivepath planning under dynamic uncertain environmentrdquo JisuanjiXuebaoChinese Journal of Computers vol 34 no 5 pp 836ndash845 2011
[6] M G Mohanan andA Salgoankar ldquoA survey of roboticmotionplanning in dynamic environmentsrdquo Robotics and AutonomousSystems vol 100 pp 171ndash185 2018
[7] X Hu L Chen B Tang D Cao and H He ldquoDynamicpath planning for autonomous driving on various roads withavoidance of static and moving obstaclesrdquo Mechanical Systemsand Signal Processing vol 100 pp 482ndash500 2018
[8] DDevaurs T Simeon and J Cortes ldquoOptimal Path Planning inComplex Cost Spaces with Sampling-Based Algorithmsrdquo IEEETransactions on Automation Science and Engineering vol 13 no2 pp 415ndash424 2016
[9] R Cui Y Li and W Yan ldquoMutual information-based multi-AUV path planning for scalar field sampling using multi-dimensional RRTrdquo IEEE Transactions on Systems Man andCybernetics Systems vol 46 no 7 pp 993ndash1004 2016
[10] CW Bac J Hemming and E J VanHenten ldquoStem localizationof sweet-pepper plants using the support wire as a visual cuerdquoComputers and Electronics in Agriculture vol 105 pp 111ndash1202014
12 Complexity
[11] L Luo Y Tang X ZouM YeW Feng andG Li ldquoVision-basedextraction of spatial information in grape clusters for harvestingrobotsrdquo Biosystems Engineering vol 151 pp 90ndash104 2016
[12] E J VanHenten J Hemming B A J VanTuijl J G Kornet andJ Bontsema ldquoCollision-free Motion Planning for a CucumberPicking Robotrdquo Biosystems Engineering vol 86 no 2 pp 135ndash144 2003
[13] G Gao G Sun J Na Y Guo and XWu ldquoStructural parameteridentification for 6 DOF industrial robotsrdquoMechanical Systemsand Signal Processing vol 113 pp 145ndash155 2018
[14] K Wei and B Ren ldquoA Method on Dynamic Path Planning forRobotic Manipulator Autonomous Obstacle Avoidance Basedon an Improved RRT Algorithmrdquo Sensors vol 18 no 2 p 5712018
[15] Y Dai and M Zhao ldquoManipulator path-planning avoidingobstacle based on screw theory and ant colony algorithmrdquoJournal of Computational and eoretical Nanoscience vol 13no 1 pp 922ndash927 2016
[16] H Pham and Q Pham ldquoTime-Optimal Path Tracking viaReachability Analysisrdquo in Proceedings of the 2018 IEEE Inter-national Conference on Robotics and Automation (ICRA) pp3007ndash3012 Brisbane QLD May 2018
[17] G Legnani F Casalo P Righettini and B Zappa ldquoA homo-geneous matrix approach to 3D kinematics and dynamics - IIApplications to chains of rigid bodies and serial manipulatorsrdquoMechanism and Machine eory vol 31 no 5 pp 589ndash6051996
[18] J Craig Introduction to Robotics Mechanics and Control 3rdedition 2015
[19] R P Paul B Shimano and G E Mayer ldquoKinematic controlequations for simple manipulatorsrdquo IEEE Transactions on Sys-tems Man and Cybernetics vol 11 no 6 pp 449ndash455 1981
[20] G Zachmann ldquoRapid collision detection by dynamicallyaligned DOP-treesrdquo in Proceedings of the 1998 IEEE VirtualReality Annual International Symposium VRAIS pp 90ndash97March 1998
[21] H Yang L Li and Z Gao ldquoObstacle avoidance path planningof hybrid harvesting manipulator based on joint configurationspacerdquoNongyeGongcheng Xuebao vol 33 no 4 pp 55ndash62 2017
[22] C Peter Robotics Vision amp Control Springer 2nd edition 2017[23] Z Daqi and Y Mingzhong ldquoSurvey on technology of mobile
robot path planningrdquo Control and Decision vol 25 no 7 pp961ndash967 2010
[24] O Khatib ldquoReal-time obstacle avoida nce for manipulators andmobile robotsrdquo International Journal of Robotics Research vol5 no 1 pp 90ndash98 1986
[25] M Fakoor A Kosari and M Jafarzadeh ldquoRevision on fuzzyartificial potential field for humanoid robot path planningin unknown environmentrdquo International Journal of AdvancedMechatronic Systems vol 6 no 4 pp 174ndash183 2015
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4 Complexity
where
119899119909 = c1 [11988823 (119888411988851198886 minus 11990441199046) minus 1199042311990451198886]+ 1199041 (119904411988851198886 + 11988841199046)
119899119910 = 1199041 [11988823 (119888411988851198886 minus 11990441199046) minus 1199042311990451198886]minus 1198881 (119904411988851198886 + 11988841199046)
119899119911 = minus11990423 (119888411988851198886 minus 11990441199046) minus 1198882311990451198886119900119909 = minus1198881 [11988823 (119888411988851199046 + 11990441198886) minus 1199042311990451199046]
minus 1199041 (119904411988851199046 minus 11988841198886)119900119910 = minus1199041 [11988823 (119888411988851199046 + 11990441198886) minus 1199042311990451199046]
+ 1198881 (119904411988851199046 minus 11988841198886)119900119911 = 11990423 (119888411988851199046 + 11990441198886) + 1198882311990451199046119886119909 = 1198881 (minus1198882311988841199045 minus 119904231198885) minus 119904111990441199045119886119910 = 1199041 (minus1198882311988841199045 minus 119904231198885) + 119888111990441199045119886119911 = 1199042311988841199045 minus 119888231198885
119901119909 = 1198881 (119886311988823 minus 119889411990423 + 1198861 + 11988621198882)119901119910 = 1199041 (119886311988823 minus 119889411990423 + 1198861 + 11988621198882)119901119911 = minus119886311990423 minus 119889411988823 minus 1198862119904211988823 = cos (1205792 + 1205793)11990423 = sin (1205792 + 1205793)
(3)
In the robotics grape harvesting the three-dimensionalcoordinates of the cutting point on the peduncle of grapecluster are obtained by the visual system of robot and thetarget position of the end-effector coordinate system Oh canbe calculated by the cutting point position The attitude ofthe end-effector (119899 119900 119886 119901) can be derived by combining withthe growth posture of grape clusters In the case of knowingthe relative position between the target position of the end-effector and the current position the inverse kinematicsmodel is responsible for calculating the satisfied joint variableof the manipulator which can control the manipulator movefrom the current position to the target position To constructthe inverse kinematics model the inverse transformationmethod [19] was used in this study and the calculationformulas of these joint variable (1205791 1205792 1205793 1205794 1205795 1205796) are asshown Formula (4) So the relation between the position ofthe terminal connecting rod and the joint variable of themanipulator can be established
1205791 = arctan119901119910119901119909
1205792 = arctan(11988621199043 minus 1198894) (1198881119901119909 + 1199041119901119910 minus 1198861) minus (1198863 + 11988621198883) 119901119911(1198863 + 11988621198883) (1198881119901119909 + 1199041119901119910 minus 1198861) minus (1198894 minus 11988621199043) 119901119911 minus 1205793
1205793 = arctan11988631198894 minus arctan 119896
radic11988632 + 11988942 minus 11989621205794 = arctan
minus1198861199091199041 + 1198861199101198881minus119886119909119888111988823 minus 119886119910119904111988823 + 11988611991111990423
1205795 = arctanminus119886119909 (1198881119888411988823 + 11990411199044) minus 119886119910 (1199041119888411988823 minus 11988811199044) + 119886119911 (119904231198884)
minus119899119909 (1198881119904411988823 minus 11990411198884) minus 119899119910 (1199041119904411988823 + 11988811198884) + 119899119911 (119904411990423)119899119909 [1198885 (1198881119888411988823 + 11990411199044) minus 1198881119904511990423] + 119899119910 [1198885 (1199041119888411988823 minus 11988811199044) minus 1199041119904511990423] minus 119899119911 (1198884119888511990423 + 119904511988823)
(4)
where 119896 = (1199011199092 + 1199011199102 + 1199011199112 + 11988612 minus 21198861(1198881119901119909 + 1199041119901119910) minus 11988632 minus11988622 minus 11988942)21198862To verify the correctness of the kinematics model the
values of a set of joint variables (1205791 = 1205873 1205792 = -1205873 1205793 =1205873 1205794 = 1205876 1205795 = 1205872 1205796 = 1205874) is artificially allocatedand then these values were input to the forward kinematicmodel (Formula (2)) to solve the terminal pose matrix 06119879
The following 06119879 was calculated by using Matlab
Figure 2 The bounding volume of obstacles such as cylinder andsphere
Then the obtained 06119879 seen as known conditions wasinput to the inverse kinematic model (Formula (4)) to solvethe angle values of the robot joints and the joint values(1205791 = 600000 1205792 = -600000 1205793 = 600000 1205794 = 2999931205795 = 900000 and 1205796 = 450022) were calculated It can beseen that the result is basically consistent with the variablevalues allocated by manual which shows the correctness ofthe kinematics model of the robot
22 Obstacles Modeling In the collision detection thebounding volume is a simple geometric space which containsobjects of complex shape The purpose of adding a boundingvolume to an object is to quickly carry out collision detectionor to filter the exact collision detection The bounding bodytypes include sphere axis aligned bounding box (AABB)directed bounding box (OBB) 8-DOP and convex hull Theobstacles in the actual picking environment are usually notregular geometry so it is difficult to describe them witha precise model [20] To facilitate the collision avoidancepath-planning the axis-aligned bounding box (AABB) wasadopted to establish the obstacles model approximately inthis study Although this modeling method expands theobstacle domain to a certain extent it greatly decreases thecalculation amount of the interference detection between themanipulator and the obstacles and effectively improves theefficiency of the path planning and also makes the plannedpath more secure
The axis-aligned minimum bounding box for a givenpoint set is its minimum bounding box subject to the con-straint that the edges of the box are parallel to the coordinateaxes It is simply the Cartesian product of 119873 intervals eachof which is defined by the minimal and maximal value ofthe corresponding coordinate for the points in 119878 In theobstacles modeling the farthest and nearest points in X Yand Z directions from the vertex collection of the obstacleare obtained firstly and then the AABB box was built byusing these points The AABB box is a simple hexahedronand each of whose side is parallel to a coordinate plane Itslength width and height can be different from each other InFigure 2 two simple 3D objects and their AABB are drawnSome important properties of the AABB can be described asfollows Firstly the points (119909 119910 119911) in the AABB box satisfythe following conditions 119909min le 119909 le 119909max 119910min le 119910 le 119910maxand 119911min le 119911 le 119911max and the points Pmin = [119909min 119910min 119911min]
and Pmax = [119909max 119910max 119911max] were two important pointsof the AABB box The center point c can be calculated bythe equation (c = (Pmin + Pmax)2) A bounding box of theobstacle can clearly be represented by using the two pointsPmin and Pmax
23 Configuration Space Modelling for Harvesting Robot Tosolve a collision avoidance path for the harvesting robot it isvery importance to determine the configuration space of themanipulator For a manipulator with 119899 degrees of freedomsetting 119864(12 n) as a set of active joint values of itin which i is the rotation angle of the 119894-th active joint ofthe manipulator If the point 119875 represents a point on themanipulator then the relative position relationship betweenthe point and the obstacle can be expressed as follows [21]
Γ (119875 (119864)) = 1 the point 119875 is inside the obstacle
0 the rest(6)
where D(119875(119864)) is relative position relationship betweenthe point 119875 and the obstacle when the manipulator is drivenwith the joint value and 119875(119864) is the position coordinate of thepoint 119875 on the manipulator in the basic coordinate systemwhen the joint value is 119864 If the rods of the manipulatorare uniformly dispersed into 119898 points according to the stepsize 119889min (mm)119898 discrete points constitute a point set 119875link The relative positional relation between the whole arm drivenwith the joint value 119864 and the obstacle can be expressed asfollows
Γ (Ε) = 119898sum119894=1
Γ (119875119894 (119864)) (7)
in which D(119864) is the relative positional relationship betweenthe driven manipulator and the obstacle when the joint valueis E
It can be known from formula (6) and formula (7) thatthe manipulator does not interfere with the obstacle only ifD(119864) = 0 The joint configuration spaceΩ is established withthe joint values of themanipulators of n degrees of freedom Ifthe set of the joint value E of themanipulator is represented byH then any point in the joint configuration spaceΩ uniquelycorresponds to one of the elements in the setH and vice versaIn other words the joint configuration spaceΩ and the set Hare bijective
Therefore the relative positional relationship between thedriven manipulator and the obstacle with the joint valueE can be expressed by the following formula in the jointconfiguration space
Ω(119864) = 1 Γ (119864) = 10 Γ (119864) = 0 (8)
where Ω(119864) is the value of the point in the joint con-figuration space Ω with the element in the joint value 119864of the manipulator as the coordinate and represents therelative positional relationship with the obstacle when the
6 Complexity
manipulator is in the position corresponding to 119864 If themanipulator interferes with the obstacle Ω(119864) is equal to 1otherwise Ω(119864) is equal to 0 So the set 119867part (1198641 1198642 119864119889)can represent a set of continuously varying poses of themanipulator the set represents a set of discrete points inthe joint configuration space Ω If a set of discrete points isconnected a path can be obtained where 119889 is the numberof the path control points Only when the following formulais satisfied does the driven manipulator not collide with theobstacle when the joint value set is119867part
where Ψ is the relative positional relationship between themanipulator the obstacle when the joint value set is119867part
Therefore the obstacle path planning is performed on themanipulator that is a set 119867part of joint values is searched inthe joint configuration space Ω so that the set is connectedto the initial configuration joint value 119864s and the targetjoint value 119864g of the manipulator Meanwhile it satisfies thecollision-free condition on the path as shown in (9)
To calculate the configuration space of the joint arm ofthe harvesting robot a simulation model of the robot wasestablished by using two functions of ldquolinkrdquo and ldquodrivebotrdquothat were provided byMatlab Robotics Toolbox Toolbox [22]And then the motion range of the harvesting manipulator inthe actual working environment is calculated and analyzedto carry better out the path-planning of picking operationAccording to the structure of the robot the motion space ofthe robot is mainly determined by the first three joints (1 to 3linkages) and the latter three joints (4 to 6 linkages) have noeffect on the motion space The first three joints determinethe position of the end-effector and the last three jointsdetermine the posture of the end-effector At present thereare mainly three methods for solving the motion space of therobots analytic methods numerical methods and graphicmethods The analytic method is to use algebraic method toobtain the equation about the structure parameters of therobot The advantage of this method is that it can accuratelydescribe the relationship between the structure parameters ofthe robot and the space of the robot but its computation islarge In this study we used analytic method and take Matlabto solve the robotrsquos motion space and the motion space of theharvesting robot can be shown as Figure 3
3 Path-Planning Based on Energy Optimaland Artificial Potential Field
The work process of the grape harvesting robot is as followsFirstly the picking robot acquires the information on numberof fruits in the field of view and the position of each fruitthrough the visual system Secondly the picking sequence isplanned The picking order of all fruits is sorted accordingto certain principles Thirdly controller has robot arm moveto the picking point of first bunch of grape rapidly andthe end effector performs the picking action Fourthly thesecond bunch of fruit is picked according to the above same
procedure until all the fruit is harvested Fifth the robot armreturns to the initial posture and the picking robot controlsthe mobile platform tomove forward and then starts the nextstage of picking Therefore the path planning of the pickingrobot work process is divided into two stages The first stageis to plan the picking sequence and the second stage is to planthe path point for each bunch of fruit picking The schematicdiagram for the path planning of the grape harvesting robotcan be shown as Figure 4
31 Harvesting Sequence Planning Based onMinimumEnergyAs the requirement of multiobjectives harvesting with theaim to get the minimum sum of weighted rotating jointangles in joint space the objective function on six-degree-of-freedom harvesting robot arm task planning based on mini-mum energy principle is proposed By calculating the value ofobjective function the picking sequence with the minimumenergy consumption can be obtained In this paper anobjective function to determine the harvesting sequence ofgrape bunches is proposed The optimal harvesting sequenceis finally determined by calculating the function value thussolves the problem of harvesting task planning
The harvesting sequence can be described in mathe-matically as assuming that the current manipulator is inthe initial position of the harvesting (1199090 1199100 1199110) there are 119899bunches of fruits in the visual area to be picked and the spaceposition coordinates are (119909i 119910i 119911i) and the correspondingspace variables of themanipulator are (1205791i 1205792i 1205793i 1205794i 1205795i 1205796i)in which 119894 = 1 2 119899 Manipulator is required to search foran optimal harvesting sequence from the initial position Allthe fruits are picked sequentially and then returned to theoriginal position It is assumed that the motion parameters(including angular velocity and angular acceleration) of alljoints of a manipulator are the same In order to minimizethe energy in the process of motion when a joint of thearm carry out harvesting task it selects the proper sequenceof harvesting to minimize the total angle of rotation whichindicates that the operating time and energy consumption ofthe joint under this sequence to complete the harvesting taskare minimal The optimization objective of single joint is
119875 = 119899sum119895=1
10038161003816100381610038161003816120579119895 minus 120579119895+110038161003816100381610038161003816 (10)
in which 119875 is the function of optimization objective 120579 is themotion angle of joint and 119899 is the number of the space pointsthat end effector need to move through
However there are multiple joints for the harvestingmanipulator in this study if the minimum sum of the singlejoint angle changes was took as the optimization objectiveand then each joint would have an optimal objective Atthis time the problem of the harvesting sequence of themanipulator is transformed into a multiobjective optimiza-tion problem Considering the angle changes of each jointof the manipulator may not reach the minimum at the sametime in the same harvesting sequence so it is necessary tocoordinate the sub objective functions of each joint to achievethe optimal objective function and the optimum of each jointwhen determine the optimal objective function of the whole
Complexity 7
10001000
500Y axis (mm)
0
X axis (mm)0
minus500minus1000 minus1000
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(a) Motion space in X Y and Z coordinates
minus1000
minus500
0
500
1000
Y ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(b) Motion space in X and Y coordinates
minus1000
minus500
0
500
1000
Z ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(c) Motion space in X and Z coordinates
0 500 1000minus500minus1000Y axis (mm)
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(d) Motion space in Y and Z coordinates
Figure 3 The motion space of the harvesting robot
destination
path point
cutting point①
②
③④
⑤
Figure 4 Schematic diagram for the path planning of the grapeharvesting robot
manipulator Moreover the power of each joint motor isdifferent according to the value of the power of each jointmotor of the manipulator different weights should be givento each joint angle and different weights should also be givento the sub targets of each joint of the manipulator So thesequence planning of the six degree of freedom harvestingmanipulator based on the principle of minimum energy canbe described by the following
1198751015840 = 119898sum119894=1
120596119894119869119894 =119898sum119894=1
119899sum119895=1
120596119894 10038161003816100381610038161003816120579119894119895 minus 120579119894119895+110038161003816100381610038161003816 (11)
where 1198751015840 indicates the objective function of the manipulatorthat can embody the energy consumption of the manipulatormotion 119898 is the number of the joints 120596i is the weight of theobjective function of the 119894th joints and 120579ij indicates the anglevalue of the 119894th joint when the manipulator is locating the 119895thspace point
32 Harvesting Path Generating Based on Artificial PotentialField eory In the process of grape harvesting collision-free path planning under a vineyard environment is themost important issue which need be resolved firstly to avoiddamage the fruits At present there are two main pathplanning methods [23] model-based global path planningand sensor-based local path planning In this study the localpath planning method based on artificial potential field wasadopted
321 Principle of Artificial Potential Field The path planningmethod based on artificial potential field is a virtual forcemethod proposed by Khatib [24] Its basic idea is to designthe motion of the robot in the surrounding environment intoan abstract artificial gravitational fieldThe artificial potentialfield includes the gravitational field and the repulsion field inwhich the object produces the gravitational attraction to theobject and guides the object to move toward it The obstaclesrepel other objects to avoid collisions with it The resultant
8 Complexity
Input the current point coordinates of the end-effector (1199090 1199100 1199110) the terminal coordinates(119909t 119910t 119911t) (the cutting point on the peduncles of grape cluster) the bounding box model ofobstacles 119877(119874s 119874e)Output the path points (119909i 119910i 119911i)
1 Find all collision-free sampling points2 for each sampling points p do
(a) calculate the probability that the current point is the candidate path points(b) find the point whose probability is maximum(c) consider the points as a candidate path point
end3 Repeat the above process until the terminal coordinates is reached
Algorithm 1 Sampling-based path point generating method
force of every point on a path is equal to the sum of allrepulsive forces and gravitational forces on this point
The basic idea of the proposed path planning in thisstudy is that the harvesting point is attractive to the motionof the harvesting manipulator by the virtual force fieldthe anticollision bounding body of grape cluster and otherobstacles are repulsive to it and the path planning is carriedout through the interaction of attraction and repulsion forceThe artificial potential field 119880sum(119883) can be defined by thefollowing [24]
in which119880att(119883) indicates the gravitational field generated bythe target 119880rep(119883) indicates the repulsion field generated bythe obstacles119883 = (119909 119910 119911)119879 is the position of the end-effectorin the workspace Setting the position of the target as119883g andthe gravitational field119880att(119883) can be defined by the following
119880att (119883) = 12119896 (119883 minus 119883119892)2 (13)
where 119896 is a constant about the gravitational field and then thegravitation 119865att(119883) can be solved by calculating the negativegradient value of the gravitational field which is described asFormula (14)
To define the mathematical expression about the repul-sive force field the following two conditions need firstly beconformed [25] (1) the artificial potential field119880sum(119883)mustbe a continuous-differential function and when119883 is equal to119883g the value of119880sum(119883) is 0 (minimum value) (2) Under theeffect of the artificial potential field 119880sum(119883) the system canbe stable Setting 1198830 as the space position of the obstacle therepulsive force field 119880rep(119883) can be defined by the following
119880rep (119883) =12120578(
1119883 minus 1198830 minus
1120588)2 (119883 minus 1198830) lt 120588
0 (119883 minus 1198830) ge 120588 (15)
where 120578 is a constant about the repulsive force field and 120588 isthe maximum range of the impact of the obstacle When the
distance between the obstacle and the end-effector is largerthan120588 the repulsive fieldwould no longer to affect themotionof harvesting robotThe repulsive force 119865rep(119883) can be solvedby calculating the negative gradient value of the repulsiveforce field 119880rep(119883) which is described as the following
120597 (119883 minus 1198830)120597119883 (119883 minus 1198830) lt 1205880 (119883 minus 1198830) ge 120588
(16)
322 Sampling-Based Path Points Generating Method Thearray of the path point sets (119909i 119910i 119911i) are firstly establishedand then the terminal pose of the end-effector is determinedbased on the current pose of the robot and the pose of grapecluster The current point coordinates of the end-effector(1199090 1199100 1199110) the terminal coordinates (119909t 119910t 119911t) (the cuttingpoint on the peduncles of grape cluster) and the boundingbox model of obstacles 119877(119874s 119874e) are given respectivelyAccording to the artificial potential field method new sam-pling points are generated randomly in the neighbourhoodand collision detection is performed on the sampling pointsThe probability that all collision-free sampling points areselected as the candidate path points is calculated and thesampling point with the highest probability is added to thepath array as the following path point Repeat the aboveprocess until the terminal coordinates is reachedThe pseudocode of sampling-based path point generating method is asshown in Algorithm 1
4 Experiments and Results
To validate the performance of the proposed anticollisionpath planning algorithm in a complex orchard a virtualharvesting robot simulation system was developed based onthe virtual reality software platform and then the perfor-mance of path planning method was investigated based onthe developed simulation system
41 Virtual Harvesting Robot Testing System The virtual sim-ulation systemwas implemented on theWindows 7 operatingsystem by using the software tools such as Visual studio 2013
Complexity 9
Figure 5 Schematic diagram for the path planning of the grapeharvesting robot
EON Studio 3Dmax and Solidworks In this study the virtualharvesting robot is constructed according to the actual sizeand workspace of the 6-DOF robot prototype Firstly the 3Dmodel of orchard scene and harvesting robotrsquos body structureis constructed and the kinematics model of the manipulatoris set by D-H parameter methodThen the virtual grape clus-ters and their anticollision space bounding body are drawnunder the virtual environment The collision avoidance pathpoints are computed by the proposed algorithm Finallythe path is simulated by a three-dimensional visualizationmethod The end-effector on the harvesting robot is consistsof three functional parts clamping finger pallet and scissorThe clamping mechanism is mainly responsible for clampingthe peduncle of grape cluster The pallet holds the grapecluster from behind and underneath carrying part of grapegravity to prevent the grape from shaking and slippingWhenthe fingers and pallets lock up the grape cluster the peduncleis cut by the scissors mechanism The software interface isshown as Figure 5
After the collision-free path is planned the joint variablesparameters of the manipulator are calculated by the inversekinematics model and then the forward kinematics methodis used to control the robotrsquos end-effector to the targetposition In the virtual simulation system the collision nodein the EON platform was used to detect collision in thisresearch The node can detect the collision events betweendifferent geometric objects in the virtual environment whichcan monitor the collision between the harvesting robot andthe obstacle in real-time To control the motion behaviorof virtual harvesting robot the modular programming androuting communication mechanism in EON platform wereadoptedThemainmodules involved aremovement rotationposition sensor angle sensor time sensor switch node rout-ing and so on The movement module is mainly used for theclamping behavior control of the end-effector The rotationmodule is used to control the rotation of the six joints of themanipulator and the rotary cutting motion of the actuatorscissors The position and angle sensors are used to perceivethe real-time travel and position of the joint motionThe timesensor is used to control the motion speed and acceleration ofthe joints of the manipulator and the switch nodes are usedto connect the communication between the modules Thecommunications among several functionmodules are carried
out through routing mechanism in the virtual environmentThe routing mechanism is responsible to mainly passesand monitors the running state of each module throughevents and then broadcast the state parameters to otherfunctional modules in real time the coordination of themultifunctional modules is finally realized Events are thedata information transmitted between two domains whichinclude two types Input and Output The Input event is theinformation generated by other sending nodes to change thestate of the receiving node and the Output event is a statethat the state of the node itself changes and outputs theinformation When one of the behavior modules sends thecommand the receiving node gets the instructions throughthe route transfers the nodes through the event driven andrealizes the message driven mechanism
42 Path-Planning Testing and Analysis The path planningtests on multiple harvesting objectives were implementedbase on the developed virtual simulation The cluster numberof the tested grape was set from 2 to 5 and their positionswere randomly given in the configuration space of themanipulator The harvesting sequence was firstly calculatedby the energy optimal and the path points were generatedby artificial potential field The simulation test platformare as follows a laptop (Lenovo T430) with 4G RAM andIntel(R)Core(TM)i5-3230 M CPU260 GHz a Windows7 operating system and a Visual C++ 2008 platform Thestatistics and analysis are made on the path length thenumber of sampling points the collision situation and theaverage time of path planning in each harvesting The resultsof the tests are shown as Table 2 The relationship betweenpath length 119871 and key point 119875i can be described by Formula(17)
119871 = sum1le119894le119870
radic(119909119894 minus 119909119894minus1)2 + (119910119894 minus 119910119894minus1)2 + (119911119894 minus 119911119894minus1)2 (17)
where119870 indicates the number of sampling points of the pathand (119909i 119910i 119911i) is the coordinates of the 119894-th sampling points
From the Table 2 we can see that there are 9 times issuccessful and 1 times failure in the 10 grape harvesting testsThe success rate was 90 the path lengthwas between 44867cm and 147265 cm the number of sampling points wasbetween 90 and 206 and the average time of path planningwas between 98ms and 273 ms It can be seen that the reasonfor the failure of the test was the collision between the endeffector and the anticollision space bounding body of thegrape cluster If the distance between the end effector andgrape cluster is too small the end effector will be easy tocollide with the upper part of the grape cluster when theend effector move closely to the fruit peduncle for harvestingoperationHarvesting path-planning can be optimized by set-ting and adjusting the minimum safety margin between thecutting point and the anticollision space bounding volumeMoreover the average time of path planning increases withthe number of objective and the number of sampling pointsFigure 6 shows a successful grape harvesting path planningThewhite dots are the path points swept by the clamper centerof the end effector during the harvesting
10 Complexity
Table 2 Statistical results of the virtual tests for grape harvesting path-planning
Number ofobjectives Harvesting optimal sequence Length of
path (Lcm)
Number ofsamplingpoints (K)
Collision(YN)
Average timeof planning
(ms)3 B 997888rarrC 997888rarrA 63578 108 N 1522 B 997888rarrA 44867 72 N 1084 C 997888rarrD 997888rarrA 997888rarrB 98523 172 N 2155 B 997888rarrD 997888rarrC 997888rarrA 997888rarr E 136245 206 N 2613 A 997888rarrC 997888rarrB 72333 102 N 1634 B 997888rarrC 997888rarrD 997888rarrA 106158 170 N 2035 E 997888rarrC 997888rarrA 997888rarrB 997888rarr D 147265 216 Y 2742 A 997888rarrB 46365 91 N 983 B 997888rarrC 997888rarrA 75687 127 N 1514 C 997888rarrB 997888rarrD 997888rarrA 104526 162 N 199
(a) (b)
(c)
Figure 6 The path points drew by the proposed path-planning method
5 Discussion
Traditional path planning methods (such as skeleton celldecomposition and subgoal graph etc) are very effective forlower degree of freedom robot (2 to 3 DOF) With theincrease in the degree of freedom of robots these algorithms
will be out of work A collision-free autonomous path plan-ning methodolgy for six-DOF serial harvesting manipulatorunder a dynamic vineyard environment was presented inthis study The kinematical modelling of Six-DOF serialmanipulator the model of obstacles and the configurationspace of harvesting robot was firstly introduced in detail
Complexity 11
And then the harvesting sequence and the anticollision pathpoints were calculated by using the energy optimal and theartificial potential field The virtual tests based on virtualreality were performed to validate the performance of theproposed algorithm Through the virtual simulation test ofthe harvesting path planning the three-dimensional spacepath points of the end-effector of the harvesting manipulatorwere calculated in real time in virtual environment andthe collision detection is analyzed The success rate wasup to 90 It can be known that the simulation systemdesigned in this study has a good practical value to helptest and improve the intelligent behavior algorithm of therobot
To obtain an optimal harvesting path taking the sumof the joint angle of the weighted rotation as the goalthe harvesting sequence planning objective function of thesix-DOF harvesting manipulator is established by usingthe minimum energy principle and the minimum energyconsumption sequence can be obtained by calculating thevalue of the target function In addition the mapping modelof obstacles in the joint configuration space is built on thebasis of sampling method and the artificial potential fieldis used to search the obstacle avoidance path in the jointconfiguration space which improves the generality of thealgorithm However due to the proposed algorithm adoptsrandom sampling strategy the sampling points may collidewith the obstacles so it is necessary to resample If thenumber of maximum sampling point is too small the failureprobability of the path planning increases And if the numberofmaximumsampling point value is too large it will cause thepath to not exist or be difficult to find or the planning time istoo long So the parameters need test repeatedly
6 Conclusion
To conduct an undamaged robotic grape-harvesting in anunstructured vineyard a path planning strategies based onminimum energy and artificial potential field for grapeharvesting robot was developed in this studyThe kinematicalmodel of Six-DOF serial manipulator was firstly constructedby using the D-H method the model of obstacles wasdefined by the axis-aligned bounding box and then theconfiguration space of harvesting robot was described bycombining the obstacles and robot Then the harvestingsequence in path planning was computed by energy optimalmethod and the anticollision path points were generatedbased on the artificial potential field and sampling searchingmethod Finally to verify and test the proposed path planningalgorithm a virtual test system based on virtual reality wasdeveloped 10 times harvesting tests for grape anticollisionpath planning were implemented on the developed sim-ulation system and the success rate was up to 90 Inconclusion the developed approach can effectively plan acollision-free path for the grape harvesting robot in the com-plex vineyard environment However when facing multipleoverlapped and adjoining grape clusters the path planning isstill an issue that needs to be solved and will require furtherresearch
Data Availability
The grape harvesting robot data used to support the findingsof this study are available from the corresponding authorupon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
This work was supported by grants from the National Nat-ural Science Foundation of China (no 51705365) and theNational Key Research and Development Program of China(2017YFD0700100)
References
[1] M A Hossain and I Ferdous ldquoAutonomous robot pathplanning in dynamic environment using a new optimizationtechnique inspired by bacterial foraging techniquerdquo Roboticsand Autonomous Systems vol 64 pp 137ndash141 2015
[2] V San JuanM Santos and JM Andujar ldquoIntelligentUAVMapGeneration and Discrete Path Planning for Search and RescueOperationsrdquoComplexity vol 2018 Article ID 6879419 17 pages2018
[3] L Luo Y Tang Q Lu X Chen P Zhang and X Zou ldquoA visionmethodology for harvesting robot to detect cutting points onpeduncles of double overlapping grape clusters in a vineyardrdquoComputers in Industry vol 99 pp 130ndash139 2018
[4] P Li S-H Lee and H-Y Hsu ldquoReview on fruit harvestingmethod for potential use of automatic fruit harvesting systemsrdquoin Proceedings of the 2011 International Conference on PowerElectronics and EngineeringApplication PEEA 2011 pp 351ndash366China December 2011
[5] W Wei D-T Ouyang S Lu and Y-X Feng ldquoMultiobjectivepath planning under dynamic uncertain environmentrdquo JisuanjiXuebaoChinese Journal of Computers vol 34 no 5 pp 836ndash845 2011
[6] M G Mohanan andA Salgoankar ldquoA survey of roboticmotionplanning in dynamic environmentsrdquo Robotics and AutonomousSystems vol 100 pp 171ndash185 2018
[7] X Hu L Chen B Tang D Cao and H He ldquoDynamicpath planning for autonomous driving on various roads withavoidance of static and moving obstaclesrdquo Mechanical Systemsand Signal Processing vol 100 pp 482ndash500 2018
[8] DDevaurs T Simeon and J Cortes ldquoOptimal Path Planning inComplex Cost Spaces with Sampling-Based Algorithmsrdquo IEEETransactions on Automation Science and Engineering vol 13 no2 pp 415ndash424 2016
[9] R Cui Y Li and W Yan ldquoMutual information-based multi-AUV path planning for scalar field sampling using multi-dimensional RRTrdquo IEEE Transactions on Systems Man andCybernetics Systems vol 46 no 7 pp 993ndash1004 2016
[10] CW Bac J Hemming and E J VanHenten ldquoStem localizationof sweet-pepper plants using the support wire as a visual cuerdquoComputers and Electronics in Agriculture vol 105 pp 111ndash1202014
12 Complexity
[11] L Luo Y Tang X ZouM YeW Feng andG Li ldquoVision-basedextraction of spatial information in grape clusters for harvestingrobotsrdquo Biosystems Engineering vol 151 pp 90ndash104 2016
[12] E J VanHenten J Hemming B A J VanTuijl J G Kornet andJ Bontsema ldquoCollision-free Motion Planning for a CucumberPicking Robotrdquo Biosystems Engineering vol 86 no 2 pp 135ndash144 2003
[13] G Gao G Sun J Na Y Guo and XWu ldquoStructural parameteridentification for 6 DOF industrial robotsrdquoMechanical Systemsand Signal Processing vol 113 pp 145ndash155 2018
[14] K Wei and B Ren ldquoA Method on Dynamic Path Planning forRobotic Manipulator Autonomous Obstacle Avoidance Basedon an Improved RRT Algorithmrdquo Sensors vol 18 no 2 p 5712018
[15] Y Dai and M Zhao ldquoManipulator path-planning avoidingobstacle based on screw theory and ant colony algorithmrdquoJournal of Computational and eoretical Nanoscience vol 13no 1 pp 922ndash927 2016
[16] H Pham and Q Pham ldquoTime-Optimal Path Tracking viaReachability Analysisrdquo in Proceedings of the 2018 IEEE Inter-national Conference on Robotics and Automation (ICRA) pp3007ndash3012 Brisbane QLD May 2018
[17] G Legnani F Casalo P Righettini and B Zappa ldquoA homo-geneous matrix approach to 3D kinematics and dynamics - IIApplications to chains of rigid bodies and serial manipulatorsrdquoMechanism and Machine eory vol 31 no 5 pp 589ndash6051996
[18] J Craig Introduction to Robotics Mechanics and Control 3rdedition 2015
[19] R P Paul B Shimano and G E Mayer ldquoKinematic controlequations for simple manipulatorsrdquo IEEE Transactions on Sys-tems Man and Cybernetics vol 11 no 6 pp 449ndash455 1981
[20] G Zachmann ldquoRapid collision detection by dynamicallyaligned DOP-treesrdquo in Proceedings of the 1998 IEEE VirtualReality Annual International Symposium VRAIS pp 90ndash97March 1998
[21] H Yang L Li and Z Gao ldquoObstacle avoidance path planningof hybrid harvesting manipulator based on joint configurationspacerdquoNongyeGongcheng Xuebao vol 33 no 4 pp 55ndash62 2017
[22] C Peter Robotics Vision amp Control Springer 2nd edition 2017[23] Z Daqi and Y Mingzhong ldquoSurvey on technology of mobile
robot path planningrdquo Control and Decision vol 25 no 7 pp961ndash967 2010
[24] O Khatib ldquoReal-time obstacle avoida nce for manipulators andmobile robotsrdquo International Journal of Robotics Research vol5 no 1 pp 90ndash98 1986
[25] M Fakoor A Kosari and M Jafarzadeh ldquoRevision on fuzzyartificial potential field for humanoid robot path planningin unknown environmentrdquo International Journal of AdvancedMechatronic Systems vol 6 no 4 pp 174ndash183 2015
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Submit your manuscripts atwwwhindawicom
Complexity 5
Bounding boxPＧＲ
PＧＣＨ
Figure 2 The bounding volume of obstacles such as cylinder andsphere
Then the obtained 06119879 seen as known conditions wasinput to the inverse kinematic model (Formula (4)) to solvethe angle values of the robot joints and the joint values(1205791 = 600000 1205792 = -600000 1205793 = 600000 1205794 = 2999931205795 = 900000 and 1205796 = 450022) were calculated It can beseen that the result is basically consistent with the variablevalues allocated by manual which shows the correctness ofthe kinematics model of the robot
22 Obstacles Modeling In the collision detection thebounding volume is a simple geometric space which containsobjects of complex shape The purpose of adding a boundingvolume to an object is to quickly carry out collision detectionor to filter the exact collision detection The bounding bodytypes include sphere axis aligned bounding box (AABB)directed bounding box (OBB) 8-DOP and convex hull Theobstacles in the actual picking environment are usually notregular geometry so it is difficult to describe them witha precise model [20] To facilitate the collision avoidancepath-planning the axis-aligned bounding box (AABB) wasadopted to establish the obstacles model approximately inthis study Although this modeling method expands theobstacle domain to a certain extent it greatly decreases thecalculation amount of the interference detection between themanipulator and the obstacles and effectively improves theefficiency of the path planning and also makes the plannedpath more secure
The axis-aligned minimum bounding box for a givenpoint set is its minimum bounding box subject to the con-straint that the edges of the box are parallel to the coordinateaxes It is simply the Cartesian product of 119873 intervals eachof which is defined by the minimal and maximal value ofthe corresponding coordinate for the points in 119878 In theobstacles modeling the farthest and nearest points in X Yand Z directions from the vertex collection of the obstacleare obtained firstly and then the AABB box was built byusing these points The AABB box is a simple hexahedronand each of whose side is parallel to a coordinate plane Itslength width and height can be different from each other InFigure 2 two simple 3D objects and their AABB are drawnSome important properties of the AABB can be described asfollows Firstly the points (119909 119910 119911) in the AABB box satisfythe following conditions 119909min le 119909 le 119909max 119910min le 119910 le 119910maxand 119911min le 119911 le 119911max and the points Pmin = [119909min 119910min 119911min]
and Pmax = [119909max 119910max 119911max] were two important pointsof the AABB box The center point c can be calculated bythe equation (c = (Pmin + Pmax)2) A bounding box of theobstacle can clearly be represented by using the two pointsPmin and Pmax
23 Configuration Space Modelling for Harvesting Robot Tosolve a collision avoidance path for the harvesting robot it isvery importance to determine the configuration space of themanipulator For a manipulator with 119899 degrees of freedomsetting 119864(12 n) as a set of active joint values of itin which i is the rotation angle of the 119894-th active joint ofthe manipulator If the point 119875 represents a point on themanipulator then the relative position relationship betweenthe point and the obstacle can be expressed as follows [21]
Γ (119875 (119864)) = 1 the point 119875 is inside the obstacle
0 the rest(6)
where D(119875(119864)) is relative position relationship betweenthe point 119875 and the obstacle when the manipulator is drivenwith the joint value and 119875(119864) is the position coordinate of thepoint 119875 on the manipulator in the basic coordinate systemwhen the joint value is 119864 If the rods of the manipulatorare uniformly dispersed into 119898 points according to the stepsize 119889min (mm)119898 discrete points constitute a point set 119875link The relative positional relation between the whole arm drivenwith the joint value 119864 and the obstacle can be expressed asfollows
Γ (Ε) = 119898sum119894=1
Γ (119875119894 (119864)) (7)
in which D(119864) is the relative positional relationship betweenthe driven manipulator and the obstacle when the joint valueis E
It can be known from formula (6) and formula (7) thatthe manipulator does not interfere with the obstacle only ifD(119864) = 0 The joint configuration spaceΩ is established withthe joint values of themanipulators of n degrees of freedom Ifthe set of the joint value E of themanipulator is represented byH then any point in the joint configuration spaceΩ uniquelycorresponds to one of the elements in the setH and vice versaIn other words the joint configuration spaceΩ and the set Hare bijective
Therefore the relative positional relationship between thedriven manipulator and the obstacle with the joint valueE can be expressed by the following formula in the jointconfiguration space
Ω(119864) = 1 Γ (119864) = 10 Γ (119864) = 0 (8)
where Ω(119864) is the value of the point in the joint con-figuration space Ω with the element in the joint value 119864of the manipulator as the coordinate and represents therelative positional relationship with the obstacle when the
6 Complexity
manipulator is in the position corresponding to 119864 If themanipulator interferes with the obstacle Ω(119864) is equal to 1otherwise Ω(119864) is equal to 0 So the set 119867part (1198641 1198642 119864119889)can represent a set of continuously varying poses of themanipulator the set represents a set of discrete points inthe joint configuration space Ω If a set of discrete points isconnected a path can be obtained where 119889 is the numberof the path control points Only when the following formulais satisfied does the driven manipulator not collide with theobstacle when the joint value set is119867part
where Ψ is the relative positional relationship between themanipulator the obstacle when the joint value set is119867part
Therefore the obstacle path planning is performed on themanipulator that is a set 119867part of joint values is searched inthe joint configuration space Ω so that the set is connectedto the initial configuration joint value 119864s and the targetjoint value 119864g of the manipulator Meanwhile it satisfies thecollision-free condition on the path as shown in (9)
To calculate the configuration space of the joint arm ofthe harvesting robot a simulation model of the robot wasestablished by using two functions of ldquolinkrdquo and ldquodrivebotrdquothat were provided byMatlab Robotics Toolbox Toolbox [22]And then the motion range of the harvesting manipulator inthe actual working environment is calculated and analyzedto carry better out the path-planning of picking operationAccording to the structure of the robot the motion space ofthe robot is mainly determined by the first three joints (1 to 3linkages) and the latter three joints (4 to 6 linkages) have noeffect on the motion space The first three joints determinethe position of the end-effector and the last three jointsdetermine the posture of the end-effector At present thereare mainly three methods for solving the motion space of therobots analytic methods numerical methods and graphicmethods The analytic method is to use algebraic method toobtain the equation about the structure parameters of therobot The advantage of this method is that it can accuratelydescribe the relationship between the structure parameters ofthe robot and the space of the robot but its computation islarge In this study we used analytic method and take Matlabto solve the robotrsquos motion space and the motion space of theharvesting robot can be shown as Figure 3
3 Path-Planning Based on Energy Optimaland Artificial Potential Field
The work process of the grape harvesting robot is as followsFirstly the picking robot acquires the information on numberof fruits in the field of view and the position of each fruitthrough the visual system Secondly the picking sequence isplanned The picking order of all fruits is sorted accordingto certain principles Thirdly controller has robot arm moveto the picking point of first bunch of grape rapidly andthe end effector performs the picking action Fourthly thesecond bunch of fruit is picked according to the above same
procedure until all the fruit is harvested Fifth the robot armreturns to the initial posture and the picking robot controlsthe mobile platform tomove forward and then starts the nextstage of picking Therefore the path planning of the pickingrobot work process is divided into two stages The first stageis to plan the picking sequence and the second stage is to planthe path point for each bunch of fruit picking The schematicdiagram for the path planning of the grape harvesting robotcan be shown as Figure 4
31 Harvesting Sequence Planning Based onMinimumEnergyAs the requirement of multiobjectives harvesting with theaim to get the minimum sum of weighted rotating jointangles in joint space the objective function on six-degree-of-freedom harvesting robot arm task planning based on mini-mum energy principle is proposed By calculating the value ofobjective function the picking sequence with the minimumenergy consumption can be obtained In this paper anobjective function to determine the harvesting sequence ofgrape bunches is proposed The optimal harvesting sequenceis finally determined by calculating the function value thussolves the problem of harvesting task planning
The harvesting sequence can be described in mathe-matically as assuming that the current manipulator is inthe initial position of the harvesting (1199090 1199100 1199110) there are 119899bunches of fruits in the visual area to be picked and the spaceposition coordinates are (119909i 119910i 119911i) and the correspondingspace variables of themanipulator are (1205791i 1205792i 1205793i 1205794i 1205795i 1205796i)in which 119894 = 1 2 119899 Manipulator is required to search foran optimal harvesting sequence from the initial position Allthe fruits are picked sequentially and then returned to theoriginal position It is assumed that the motion parameters(including angular velocity and angular acceleration) of alljoints of a manipulator are the same In order to minimizethe energy in the process of motion when a joint of thearm carry out harvesting task it selects the proper sequenceof harvesting to minimize the total angle of rotation whichindicates that the operating time and energy consumption ofthe joint under this sequence to complete the harvesting taskare minimal The optimization objective of single joint is
119875 = 119899sum119895=1
10038161003816100381610038161003816120579119895 minus 120579119895+110038161003816100381610038161003816 (10)
in which 119875 is the function of optimization objective 120579 is themotion angle of joint and 119899 is the number of the space pointsthat end effector need to move through
However there are multiple joints for the harvestingmanipulator in this study if the minimum sum of the singlejoint angle changes was took as the optimization objectiveand then each joint would have an optimal objective Atthis time the problem of the harvesting sequence of themanipulator is transformed into a multiobjective optimiza-tion problem Considering the angle changes of each jointof the manipulator may not reach the minimum at the sametime in the same harvesting sequence so it is necessary tocoordinate the sub objective functions of each joint to achievethe optimal objective function and the optimum of each jointwhen determine the optimal objective function of the whole
Complexity 7
10001000
500Y axis (mm)
0
X axis (mm)0
minus500minus1000 minus1000
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(a) Motion space in X Y and Z coordinates
minus1000
minus500
0
500
1000
Y ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(b) Motion space in X and Y coordinates
minus1000
minus500
0
500
1000
Z ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(c) Motion space in X and Z coordinates
0 500 1000minus500minus1000Y axis (mm)
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(d) Motion space in Y and Z coordinates
Figure 3 The motion space of the harvesting robot
destination
path point
cutting point①
②
③④
⑤
Figure 4 Schematic diagram for the path planning of the grapeharvesting robot
manipulator Moreover the power of each joint motor isdifferent according to the value of the power of each jointmotor of the manipulator different weights should be givento each joint angle and different weights should also be givento the sub targets of each joint of the manipulator So thesequence planning of the six degree of freedom harvestingmanipulator based on the principle of minimum energy canbe described by the following
1198751015840 = 119898sum119894=1
120596119894119869119894 =119898sum119894=1
119899sum119895=1
120596119894 10038161003816100381610038161003816120579119894119895 minus 120579119894119895+110038161003816100381610038161003816 (11)
where 1198751015840 indicates the objective function of the manipulatorthat can embody the energy consumption of the manipulatormotion 119898 is the number of the joints 120596i is the weight of theobjective function of the 119894th joints and 120579ij indicates the anglevalue of the 119894th joint when the manipulator is locating the 119895thspace point
32 Harvesting Path Generating Based on Artificial PotentialField eory In the process of grape harvesting collision-free path planning under a vineyard environment is themost important issue which need be resolved firstly to avoiddamage the fruits At present there are two main pathplanning methods [23] model-based global path planningand sensor-based local path planning In this study the localpath planning method based on artificial potential field wasadopted
321 Principle of Artificial Potential Field The path planningmethod based on artificial potential field is a virtual forcemethod proposed by Khatib [24] Its basic idea is to designthe motion of the robot in the surrounding environment intoan abstract artificial gravitational fieldThe artificial potentialfield includes the gravitational field and the repulsion field inwhich the object produces the gravitational attraction to theobject and guides the object to move toward it The obstaclesrepel other objects to avoid collisions with it The resultant
8 Complexity
Input the current point coordinates of the end-effector (1199090 1199100 1199110) the terminal coordinates(119909t 119910t 119911t) (the cutting point on the peduncles of grape cluster) the bounding box model ofobstacles 119877(119874s 119874e)Output the path points (119909i 119910i 119911i)
1 Find all collision-free sampling points2 for each sampling points p do
(a) calculate the probability that the current point is the candidate path points(b) find the point whose probability is maximum(c) consider the points as a candidate path point
end3 Repeat the above process until the terminal coordinates is reached
Algorithm 1 Sampling-based path point generating method
force of every point on a path is equal to the sum of allrepulsive forces and gravitational forces on this point
The basic idea of the proposed path planning in thisstudy is that the harvesting point is attractive to the motionof the harvesting manipulator by the virtual force fieldthe anticollision bounding body of grape cluster and otherobstacles are repulsive to it and the path planning is carriedout through the interaction of attraction and repulsion forceThe artificial potential field 119880sum(119883) can be defined by thefollowing [24]
in which119880att(119883) indicates the gravitational field generated bythe target 119880rep(119883) indicates the repulsion field generated bythe obstacles119883 = (119909 119910 119911)119879 is the position of the end-effectorin the workspace Setting the position of the target as119883g andthe gravitational field119880att(119883) can be defined by the following
119880att (119883) = 12119896 (119883 minus 119883119892)2 (13)
where 119896 is a constant about the gravitational field and then thegravitation 119865att(119883) can be solved by calculating the negativegradient value of the gravitational field which is described asFormula (14)
To define the mathematical expression about the repul-sive force field the following two conditions need firstly beconformed [25] (1) the artificial potential field119880sum(119883)mustbe a continuous-differential function and when119883 is equal to119883g the value of119880sum(119883) is 0 (minimum value) (2) Under theeffect of the artificial potential field 119880sum(119883) the system canbe stable Setting 1198830 as the space position of the obstacle therepulsive force field 119880rep(119883) can be defined by the following
119880rep (119883) =12120578(
1119883 minus 1198830 minus
1120588)2 (119883 minus 1198830) lt 120588
0 (119883 minus 1198830) ge 120588 (15)
where 120578 is a constant about the repulsive force field and 120588 isthe maximum range of the impact of the obstacle When the
distance between the obstacle and the end-effector is largerthan120588 the repulsive fieldwould no longer to affect themotionof harvesting robotThe repulsive force 119865rep(119883) can be solvedby calculating the negative gradient value of the repulsiveforce field 119880rep(119883) which is described as the following
120597 (119883 minus 1198830)120597119883 (119883 minus 1198830) lt 1205880 (119883 minus 1198830) ge 120588
(16)
322 Sampling-Based Path Points Generating Method Thearray of the path point sets (119909i 119910i 119911i) are firstly establishedand then the terminal pose of the end-effector is determinedbased on the current pose of the robot and the pose of grapecluster The current point coordinates of the end-effector(1199090 1199100 1199110) the terminal coordinates (119909t 119910t 119911t) (the cuttingpoint on the peduncles of grape cluster) and the boundingbox model of obstacles 119877(119874s 119874e) are given respectivelyAccording to the artificial potential field method new sam-pling points are generated randomly in the neighbourhoodand collision detection is performed on the sampling pointsThe probability that all collision-free sampling points areselected as the candidate path points is calculated and thesampling point with the highest probability is added to thepath array as the following path point Repeat the aboveprocess until the terminal coordinates is reachedThe pseudocode of sampling-based path point generating method is asshown in Algorithm 1
4 Experiments and Results
To validate the performance of the proposed anticollisionpath planning algorithm in a complex orchard a virtualharvesting robot simulation system was developed based onthe virtual reality software platform and then the perfor-mance of path planning method was investigated based onthe developed simulation system
41 Virtual Harvesting Robot Testing System The virtual sim-ulation systemwas implemented on theWindows 7 operatingsystem by using the software tools such as Visual studio 2013
Complexity 9
Figure 5 Schematic diagram for the path planning of the grapeharvesting robot
EON Studio 3Dmax and Solidworks In this study the virtualharvesting robot is constructed according to the actual sizeand workspace of the 6-DOF robot prototype Firstly the 3Dmodel of orchard scene and harvesting robotrsquos body structureis constructed and the kinematics model of the manipulatoris set by D-H parameter methodThen the virtual grape clus-ters and their anticollision space bounding body are drawnunder the virtual environment The collision avoidance pathpoints are computed by the proposed algorithm Finallythe path is simulated by a three-dimensional visualizationmethod The end-effector on the harvesting robot is consistsof three functional parts clamping finger pallet and scissorThe clamping mechanism is mainly responsible for clampingthe peduncle of grape cluster The pallet holds the grapecluster from behind and underneath carrying part of grapegravity to prevent the grape from shaking and slippingWhenthe fingers and pallets lock up the grape cluster the peduncleis cut by the scissors mechanism The software interface isshown as Figure 5
After the collision-free path is planned the joint variablesparameters of the manipulator are calculated by the inversekinematics model and then the forward kinematics methodis used to control the robotrsquos end-effector to the targetposition In the virtual simulation system the collision nodein the EON platform was used to detect collision in thisresearch The node can detect the collision events betweendifferent geometric objects in the virtual environment whichcan monitor the collision between the harvesting robot andthe obstacle in real-time To control the motion behaviorof virtual harvesting robot the modular programming androuting communication mechanism in EON platform wereadoptedThemainmodules involved aremovement rotationposition sensor angle sensor time sensor switch node rout-ing and so on The movement module is mainly used for theclamping behavior control of the end-effector The rotationmodule is used to control the rotation of the six joints of themanipulator and the rotary cutting motion of the actuatorscissors The position and angle sensors are used to perceivethe real-time travel and position of the joint motionThe timesensor is used to control the motion speed and acceleration ofthe joints of the manipulator and the switch nodes are usedto connect the communication between the modules Thecommunications among several functionmodules are carried
out through routing mechanism in the virtual environmentThe routing mechanism is responsible to mainly passesand monitors the running state of each module throughevents and then broadcast the state parameters to otherfunctional modules in real time the coordination of themultifunctional modules is finally realized Events are thedata information transmitted between two domains whichinclude two types Input and Output The Input event is theinformation generated by other sending nodes to change thestate of the receiving node and the Output event is a statethat the state of the node itself changes and outputs theinformation When one of the behavior modules sends thecommand the receiving node gets the instructions throughthe route transfers the nodes through the event driven andrealizes the message driven mechanism
42 Path-Planning Testing and Analysis The path planningtests on multiple harvesting objectives were implementedbase on the developed virtual simulation The cluster numberof the tested grape was set from 2 to 5 and their positionswere randomly given in the configuration space of themanipulator The harvesting sequence was firstly calculatedby the energy optimal and the path points were generatedby artificial potential field The simulation test platformare as follows a laptop (Lenovo T430) with 4G RAM andIntel(R)Core(TM)i5-3230 M CPU260 GHz a Windows7 operating system and a Visual C++ 2008 platform Thestatistics and analysis are made on the path length thenumber of sampling points the collision situation and theaverage time of path planning in each harvesting The resultsof the tests are shown as Table 2 The relationship betweenpath length 119871 and key point 119875i can be described by Formula(17)
119871 = sum1le119894le119870
radic(119909119894 minus 119909119894minus1)2 + (119910119894 minus 119910119894minus1)2 + (119911119894 minus 119911119894minus1)2 (17)
where119870 indicates the number of sampling points of the pathand (119909i 119910i 119911i) is the coordinates of the 119894-th sampling points
From the Table 2 we can see that there are 9 times issuccessful and 1 times failure in the 10 grape harvesting testsThe success rate was 90 the path lengthwas between 44867cm and 147265 cm the number of sampling points wasbetween 90 and 206 and the average time of path planningwas between 98ms and 273 ms It can be seen that the reasonfor the failure of the test was the collision between the endeffector and the anticollision space bounding body of thegrape cluster If the distance between the end effector andgrape cluster is too small the end effector will be easy tocollide with the upper part of the grape cluster when theend effector move closely to the fruit peduncle for harvestingoperationHarvesting path-planning can be optimized by set-ting and adjusting the minimum safety margin between thecutting point and the anticollision space bounding volumeMoreover the average time of path planning increases withthe number of objective and the number of sampling pointsFigure 6 shows a successful grape harvesting path planningThewhite dots are the path points swept by the clamper centerof the end effector during the harvesting
10 Complexity
Table 2 Statistical results of the virtual tests for grape harvesting path-planning
Number ofobjectives Harvesting optimal sequence Length of
path (Lcm)
Number ofsamplingpoints (K)
Collision(YN)
Average timeof planning
(ms)3 B 997888rarrC 997888rarrA 63578 108 N 1522 B 997888rarrA 44867 72 N 1084 C 997888rarrD 997888rarrA 997888rarrB 98523 172 N 2155 B 997888rarrD 997888rarrC 997888rarrA 997888rarr E 136245 206 N 2613 A 997888rarrC 997888rarrB 72333 102 N 1634 B 997888rarrC 997888rarrD 997888rarrA 106158 170 N 2035 E 997888rarrC 997888rarrA 997888rarrB 997888rarr D 147265 216 Y 2742 A 997888rarrB 46365 91 N 983 B 997888rarrC 997888rarrA 75687 127 N 1514 C 997888rarrB 997888rarrD 997888rarrA 104526 162 N 199
(a) (b)
(c)
Figure 6 The path points drew by the proposed path-planning method
5 Discussion
Traditional path planning methods (such as skeleton celldecomposition and subgoal graph etc) are very effective forlower degree of freedom robot (2 to 3 DOF) With theincrease in the degree of freedom of robots these algorithms
will be out of work A collision-free autonomous path plan-ning methodolgy for six-DOF serial harvesting manipulatorunder a dynamic vineyard environment was presented inthis study The kinematical modelling of Six-DOF serialmanipulator the model of obstacles and the configurationspace of harvesting robot was firstly introduced in detail
Complexity 11
And then the harvesting sequence and the anticollision pathpoints were calculated by using the energy optimal and theartificial potential field The virtual tests based on virtualreality were performed to validate the performance of theproposed algorithm Through the virtual simulation test ofthe harvesting path planning the three-dimensional spacepath points of the end-effector of the harvesting manipulatorwere calculated in real time in virtual environment andthe collision detection is analyzed The success rate wasup to 90 It can be known that the simulation systemdesigned in this study has a good practical value to helptest and improve the intelligent behavior algorithm of therobot
To obtain an optimal harvesting path taking the sumof the joint angle of the weighted rotation as the goalthe harvesting sequence planning objective function of thesix-DOF harvesting manipulator is established by usingthe minimum energy principle and the minimum energyconsumption sequence can be obtained by calculating thevalue of the target function In addition the mapping modelof obstacles in the joint configuration space is built on thebasis of sampling method and the artificial potential fieldis used to search the obstacle avoidance path in the jointconfiguration space which improves the generality of thealgorithm However due to the proposed algorithm adoptsrandom sampling strategy the sampling points may collidewith the obstacles so it is necessary to resample If thenumber of maximum sampling point is too small the failureprobability of the path planning increases And if the numberofmaximumsampling point value is too large it will cause thepath to not exist or be difficult to find or the planning time istoo long So the parameters need test repeatedly
6 Conclusion
To conduct an undamaged robotic grape-harvesting in anunstructured vineyard a path planning strategies based onminimum energy and artificial potential field for grapeharvesting robot was developed in this studyThe kinematicalmodel of Six-DOF serial manipulator was firstly constructedby using the D-H method the model of obstacles wasdefined by the axis-aligned bounding box and then theconfiguration space of harvesting robot was described bycombining the obstacles and robot Then the harvestingsequence in path planning was computed by energy optimalmethod and the anticollision path points were generatedbased on the artificial potential field and sampling searchingmethod Finally to verify and test the proposed path planningalgorithm a virtual test system based on virtual reality wasdeveloped 10 times harvesting tests for grape anticollisionpath planning were implemented on the developed sim-ulation system and the success rate was up to 90 Inconclusion the developed approach can effectively plan acollision-free path for the grape harvesting robot in the com-plex vineyard environment However when facing multipleoverlapped and adjoining grape clusters the path planning isstill an issue that needs to be solved and will require furtherresearch
Data Availability
The grape harvesting robot data used to support the findingsof this study are available from the corresponding authorupon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
This work was supported by grants from the National Nat-ural Science Foundation of China (no 51705365) and theNational Key Research and Development Program of China(2017YFD0700100)
References
[1] M A Hossain and I Ferdous ldquoAutonomous robot pathplanning in dynamic environment using a new optimizationtechnique inspired by bacterial foraging techniquerdquo Roboticsand Autonomous Systems vol 64 pp 137ndash141 2015
[2] V San JuanM Santos and JM Andujar ldquoIntelligentUAVMapGeneration and Discrete Path Planning for Search and RescueOperationsrdquoComplexity vol 2018 Article ID 6879419 17 pages2018
[3] L Luo Y Tang Q Lu X Chen P Zhang and X Zou ldquoA visionmethodology for harvesting robot to detect cutting points onpeduncles of double overlapping grape clusters in a vineyardrdquoComputers in Industry vol 99 pp 130ndash139 2018
[4] P Li S-H Lee and H-Y Hsu ldquoReview on fruit harvestingmethod for potential use of automatic fruit harvesting systemsrdquoin Proceedings of the 2011 International Conference on PowerElectronics and EngineeringApplication PEEA 2011 pp 351ndash366China December 2011
[5] W Wei D-T Ouyang S Lu and Y-X Feng ldquoMultiobjectivepath planning under dynamic uncertain environmentrdquo JisuanjiXuebaoChinese Journal of Computers vol 34 no 5 pp 836ndash845 2011
[6] M G Mohanan andA Salgoankar ldquoA survey of roboticmotionplanning in dynamic environmentsrdquo Robotics and AutonomousSystems vol 100 pp 171ndash185 2018
[7] X Hu L Chen B Tang D Cao and H He ldquoDynamicpath planning for autonomous driving on various roads withavoidance of static and moving obstaclesrdquo Mechanical Systemsand Signal Processing vol 100 pp 482ndash500 2018
[8] DDevaurs T Simeon and J Cortes ldquoOptimal Path Planning inComplex Cost Spaces with Sampling-Based Algorithmsrdquo IEEETransactions on Automation Science and Engineering vol 13 no2 pp 415ndash424 2016
[9] R Cui Y Li and W Yan ldquoMutual information-based multi-AUV path planning for scalar field sampling using multi-dimensional RRTrdquo IEEE Transactions on Systems Man andCybernetics Systems vol 46 no 7 pp 993ndash1004 2016
[10] CW Bac J Hemming and E J VanHenten ldquoStem localizationof sweet-pepper plants using the support wire as a visual cuerdquoComputers and Electronics in Agriculture vol 105 pp 111ndash1202014
12 Complexity
[11] L Luo Y Tang X ZouM YeW Feng andG Li ldquoVision-basedextraction of spatial information in grape clusters for harvestingrobotsrdquo Biosystems Engineering vol 151 pp 90ndash104 2016
[12] E J VanHenten J Hemming B A J VanTuijl J G Kornet andJ Bontsema ldquoCollision-free Motion Planning for a CucumberPicking Robotrdquo Biosystems Engineering vol 86 no 2 pp 135ndash144 2003
[13] G Gao G Sun J Na Y Guo and XWu ldquoStructural parameteridentification for 6 DOF industrial robotsrdquoMechanical Systemsand Signal Processing vol 113 pp 145ndash155 2018
[14] K Wei and B Ren ldquoA Method on Dynamic Path Planning forRobotic Manipulator Autonomous Obstacle Avoidance Basedon an Improved RRT Algorithmrdquo Sensors vol 18 no 2 p 5712018
[15] Y Dai and M Zhao ldquoManipulator path-planning avoidingobstacle based on screw theory and ant colony algorithmrdquoJournal of Computational and eoretical Nanoscience vol 13no 1 pp 922ndash927 2016
[16] H Pham and Q Pham ldquoTime-Optimal Path Tracking viaReachability Analysisrdquo in Proceedings of the 2018 IEEE Inter-national Conference on Robotics and Automation (ICRA) pp3007ndash3012 Brisbane QLD May 2018
[17] G Legnani F Casalo P Righettini and B Zappa ldquoA homo-geneous matrix approach to 3D kinematics and dynamics - IIApplications to chains of rigid bodies and serial manipulatorsrdquoMechanism and Machine eory vol 31 no 5 pp 589ndash6051996
[18] J Craig Introduction to Robotics Mechanics and Control 3rdedition 2015
[19] R P Paul B Shimano and G E Mayer ldquoKinematic controlequations for simple manipulatorsrdquo IEEE Transactions on Sys-tems Man and Cybernetics vol 11 no 6 pp 449ndash455 1981
[20] G Zachmann ldquoRapid collision detection by dynamicallyaligned DOP-treesrdquo in Proceedings of the 1998 IEEE VirtualReality Annual International Symposium VRAIS pp 90ndash97March 1998
[21] H Yang L Li and Z Gao ldquoObstacle avoidance path planningof hybrid harvesting manipulator based on joint configurationspacerdquoNongyeGongcheng Xuebao vol 33 no 4 pp 55ndash62 2017
[22] C Peter Robotics Vision amp Control Springer 2nd edition 2017[23] Z Daqi and Y Mingzhong ldquoSurvey on technology of mobile
robot path planningrdquo Control and Decision vol 25 no 7 pp961ndash967 2010
[24] O Khatib ldquoReal-time obstacle avoida nce for manipulators andmobile robotsrdquo International Journal of Robotics Research vol5 no 1 pp 90ndash98 1986
[25] M Fakoor A Kosari and M Jafarzadeh ldquoRevision on fuzzyartificial potential field for humanoid robot path planningin unknown environmentrdquo International Journal of AdvancedMechatronic Systems vol 6 no 4 pp 174ndash183 2015
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6 Complexity
manipulator is in the position corresponding to 119864 If themanipulator interferes with the obstacle Ω(119864) is equal to 1otherwise Ω(119864) is equal to 0 So the set 119867part (1198641 1198642 119864119889)can represent a set of continuously varying poses of themanipulator the set represents a set of discrete points inthe joint configuration space Ω If a set of discrete points isconnected a path can be obtained where 119889 is the numberof the path control points Only when the following formulais satisfied does the driven manipulator not collide with theobstacle when the joint value set is119867part
where Ψ is the relative positional relationship between themanipulator the obstacle when the joint value set is119867part
Therefore the obstacle path planning is performed on themanipulator that is a set 119867part of joint values is searched inthe joint configuration space Ω so that the set is connectedto the initial configuration joint value 119864s and the targetjoint value 119864g of the manipulator Meanwhile it satisfies thecollision-free condition on the path as shown in (9)
To calculate the configuration space of the joint arm ofthe harvesting robot a simulation model of the robot wasestablished by using two functions of ldquolinkrdquo and ldquodrivebotrdquothat were provided byMatlab Robotics Toolbox Toolbox [22]And then the motion range of the harvesting manipulator inthe actual working environment is calculated and analyzedto carry better out the path-planning of picking operationAccording to the structure of the robot the motion space ofthe robot is mainly determined by the first three joints (1 to 3linkages) and the latter three joints (4 to 6 linkages) have noeffect on the motion space The first three joints determinethe position of the end-effector and the last three jointsdetermine the posture of the end-effector At present thereare mainly three methods for solving the motion space of therobots analytic methods numerical methods and graphicmethods The analytic method is to use algebraic method toobtain the equation about the structure parameters of therobot The advantage of this method is that it can accuratelydescribe the relationship between the structure parameters ofthe robot and the space of the robot but its computation islarge In this study we used analytic method and take Matlabto solve the robotrsquos motion space and the motion space of theharvesting robot can be shown as Figure 3
3 Path-Planning Based on Energy Optimaland Artificial Potential Field
The work process of the grape harvesting robot is as followsFirstly the picking robot acquires the information on numberof fruits in the field of view and the position of each fruitthrough the visual system Secondly the picking sequence isplanned The picking order of all fruits is sorted accordingto certain principles Thirdly controller has robot arm moveto the picking point of first bunch of grape rapidly andthe end effector performs the picking action Fourthly thesecond bunch of fruit is picked according to the above same
procedure until all the fruit is harvested Fifth the robot armreturns to the initial posture and the picking robot controlsthe mobile platform tomove forward and then starts the nextstage of picking Therefore the path planning of the pickingrobot work process is divided into two stages The first stageis to plan the picking sequence and the second stage is to planthe path point for each bunch of fruit picking The schematicdiagram for the path planning of the grape harvesting robotcan be shown as Figure 4
31 Harvesting Sequence Planning Based onMinimumEnergyAs the requirement of multiobjectives harvesting with theaim to get the minimum sum of weighted rotating jointangles in joint space the objective function on six-degree-of-freedom harvesting robot arm task planning based on mini-mum energy principle is proposed By calculating the value ofobjective function the picking sequence with the minimumenergy consumption can be obtained In this paper anobjective function to determine the harvesting sequence ofgrape bunches is proposed The optimal harvesting sequenceis finally determined by calculating the function value thussolves the problem of harvesting task planning
The harvesting sequence can be described in mathe-matically as assuming that the current manipulator is inthe initial position of the harvesting (1199090 1199100 1199110) there are 119899bunches of fruits in the visual area to be picked and the spaceposition coordinates are (119909i 119910i 119911i) and the correspondingspace variables of themanipulator are (1205791i 1205792i 1205793i 1205794i 1205795i 1205796i)in which 119894 = 1 2 119899 Manipulator is required to search foran optimal harvesting sequence from the initial position Allthe fruits are picked sequentially and then returned to theoriginal position It is assumed that the motion parameters(including angular velocity and angular acceleration) of alljoints of a manipulator are the same In order to minimizethe energy in the process of motion when a joint of thearm carry out harvesting task it selects the proper sequenceof harvesting to minimize the total angle of rotation whichindicates that the operating time and energy consumption ofthe joint under this sequence to complete the harvesting taskare minimal The optimization objective of single joint is
119875 = 119899sum119895=1
10038161003816100381610038161003816120579119895 minus 120579119895+110038161003816100381610038161003816 (10)
in which 119875 is the function of optimization objective 120579 is themotion angle of joint and 119899 is the number of the space pointsthat end effector need to move through
However there are multiple joints for the harvestingmanipulator in this study if the minimum sum of the singlejoint angle changes was took as the optimization objectiveand then each joint would have an optimal objective Atthis time the problem of the harvesting sequence of themanipulator is transformed into a multiobjective optimiza-tion problem Considering the angle changes of each jointof the manipulator may not reach the minimum at the sametime in the same harvesting sequence so it is necessary tocoordinate the sub objective functions of each joint to achievethe optimal objective function and the optimum of each jointwhen determine the optimal objective function of the whole
Complexity 7
10001000
500Y axis (mm)
0
X axis (mm)0
minus500minus1000 minus1000
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(a) Motion space in X Y and Z coordinates
minus1000
minus500
0
500
1000
Y ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(b) Motion space in X and Y coordinates
minus1000
minus500
0
500
1000
Z ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(c) Motion space in X and Z coordinates
0 500 1000minus500minus1000Y axis (mm)
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(d) Motion space in Y and Z coordinates
Figure 3 The motion space of the harvesting robot
destination
path point
cutting point①
②
③④
⑤
Figure 4 Schematic diagram for the path planning of the grapeharvesting robot
manipulator Moreover the power of each joint motor isdifferent according to the value of the power of each jointmotor of the manipulator different weights should be givento each joint angle and different weights should also be givento the sub targets of each joint of the manipulator So thesequence planning of the six degree of freedom harvestingmanipulator based on the principle of minimum energy canbe described by the following
1198751015840 = 119898sum119894=1
120596119894119869119894 =119898sum119894=1
119899sum119895=1
120596119894 10038161003816100381610038161003816120579119894119895 minus 120579119894119895+110038161003816100381610038161003816 (11)
where 1198751015840 indicates the objective function of the manipulatorthat can embody the energy consumption of the manipulatormotion 119898 is the number of the joints 120596i is the weight of theobjective function of the 119894th joints and 120579ij indicates the anglevalue of the 119894th joint when the manipulator is locating the 119895thspace point
32 Harvesting Path Generating Based on Artificial PotentialField eory In the process of grape harvesting collision-free path planning under a vineyard environment is themost important issue which need be resolved firstly to avoiddamage the fruits At present there are two main pathplanning methods [23] model-based global path planningand sensor-based local path planning In this study the localpath planning method based on artificial potential field wasadopted
321 Principle of Artificial Potential Field The path planningmethod based on artificial potential field is a virtual forcemethod proposed by Khatib [24] Its basic idea is to designthe motion of the robot in the surrounding environment intoan abstract artificial gravitational fieldThe artificial potentialfield includes the gravitational field and the repulsion field inwhich the object produces the gravitational attraction to theobject and guides the object to move toward it The obstaclesrepel other objects to avoid collisions with it The resultant
8 Complexity
Input the current point coordinates of the end-effector (1199090 1199100 1199110) the terminal coordinates(119909t 119910t 119911t) (the cutting point on the peduncles of grape cluster) the bounding box model ofobstacles 119877(119874s 119874e)Output the path points (119909i 119910i 119911i)
1 Find all collision-free sampling points2 for each sampling points p do
(a) calculate the probability that the current point is the candidate path points(b) find the point whose probability is maximum(c) consider the points as a candidate path point
end3 Repeat the above process until the terminal coordinates is reached
Algorithm 1 Sampling-based path point generating method
force of every point on a path is equal to the sum of allrepulsive forces and gravitational forces on this point
The basic idea of the proposed path planning in thisstudy is that the harvesting point is attractive to the motionof the harvesting manipulator by the virtual force fieldthe anticollision bounding body of grape cluster and otherobstacles are repulsive to it and the path planning is carriedout through the interaction of attraction and repulsion forceThe artificial potential field 119880sum(119883) can be defined by thefollowing [24]
in which119880att(119883) indicates the gravitational field generated bythe target 119880rep(119883) indicates the repulsion field generated bythe obstacles119883 = (119909 119910 119911)119879 is the position of the end-effectorin the workspace Setting the position of the target as119883g andthe gravitational field119880att(119883) can be defined by the following
119880att (119883) = 12119896 (119883 minus 119883119892)2 (13)
where 119896 is a constant about the gravitational field and then thegravitation 119865att(119883) can be solved by calculating the negativegradient value of the gravitational field which is described asFormula (14)
To define the mathematical expression about the repul-sive force field the following two conditions need firstly beconformed [25] (1) the artificial potential field119880sum(119883)mustbe a continuous-differential function and when119883 is equal to119883g the value of119880sum(119883) is 0 (minimum value) (2) Under theeffect of the artificial potential field 119880sum(119883) the system canbe stable Setting 1198830 as the space position of the obstacle therepulsive force field 119880rep(119883) can be defined by the following
119880rep (119883) =12120578(
1119883 minus 1198830 minus
1120588)2 (119883 minus 1198830) lt 120588
0 (119883 minus 1198830) ge 120588 (15)
where 120578 is a constant about the repulsive force field and 120588 isthe maximum range of the impact of the obstacle When the
distance between the obstacle and the end-effector is largerthan120588 the repulsive fieldwould no longer to affect themotionof harvesting robotThe repulsive force 119865rep(119883) can be solvedby calculating the negative gradient value of the repulsiveforce field 119880rep(119883) which is described as the following
120597 (119883 minus 1198830)120597119883 (119883 minus 1198830) lt 1205880 (119883 minus 1198830) ge 120588
(16)
322 Sampling-Based Path Points Generating Method Thearray of the path point sets (119909i 119910i 119911i) are firstly establishedand then the terminal pose of the end-effector is determinedbased on the current pose of the robot and the pose of grapecluster The current point coordinates of the end-effector(1199090 1199100 1199110) the terminal coordinates (119909t 119910t 119911t) (the cuttingpoint on the peduncles of grape cluster) and the boundingbox model of obstacles 119877(119874s 119874e) are given respectivelyAccording to the artificial potential field method new sam-pling points are generated randomly in the neighbourhoodand collision detection is performed on the sampling pointsThe probability that all collision-free sampling points areselected as the candidate path points is calculated and thesampling point with the highest probability is added to thepath array as the following path point Repeat the aboveprocess until the terminal coordinates is reachedThe pseudocode of sampling-based path point generating method is asshown in Algorithm 1
4 Experiments and Results
To validate the performance of the proposed anticollisionpath planning algorithm in a complex orchard a virtualharvesting robot simulation system was developed based onthe virtual reality software platform and then the perfor-mance of path planning method was investigated based onthe developed simulation system
41 Virtual Harvesting Robot Testing System The virtual sim-ulation systemwas implemented on theWindows 7 operatingsystem by using the software tools such as Visual studio 2013
Complexity 9
Figure 5 Schematic diagram for the path planning of the grapeharvesting robot
EON Studio 3Dmax and Solidworks In this study the virtualharvesting robot is constructed according to the actual sizeand workspace of the 6-DOF robot prototype Firstly the 3Dmodel of orchard scene and harvesting robotrsquos body structureis constructed and the kinematics model of the manipulatoris set by D-H parameter methodThen the virtual grape clus-ters and their anticollision space bounding body are drawnunder the virtual environment The collision avoidance pathpoints are computed by the proposed algorithm Finallythe path is simulated by a three-dimensional visualizationmethod The end-effector on the harvesting robot is consistsof three functional parts clamping finger pallet and scissorThe clamping mechanism is mainly responsible for clampingthe peduncle of grape cluster The pallet holds the grapecluster from behind and underneath carrying part of grapegravity to prevent the grape from shaking and slippingWhenthe fingers and pallets lock up the grape cluster the peduncleis cut by the scissors mechanism The software interface isshown as Figure 5
After the collision-free path is planned the joint variablesparameters of the manipulator are calculated by the inversekinematics model and then the forward kinematics methodis used to control the robotrsquos end-effector to the targetposition In the virtual simulation system the collision nodein the EON platform was used to detect collision in thisresearch The node can detect the collision events betweendifferent geometric objects in the virtual environment whichcan monitor the collision between the harvesting robot andthe obstacle in real-time To control the motion behaviorof virtual harvesting robot the modular programming androuting communication mechanism in EON platform wereadoptedThemainmodules involved aremovement rotationposition sensor angle sensor time sensor switch node rout-ing and so on The movement module is mainly used for theclamping behavior control of the end-effector The rotationmodule is used to control the rotation of the six joints of themanipulator and the rotary cutting motion of the actuatorscissors The position and angle sensors are used to perceivethe real-time travel and position of the joint motionThe timesensor is used to control the motion speed and acceleration ofthe joints of the manipulator and the switch nodes are usedto connect the communication between the modules Thecommunications among several functionmodules are carried
out through routing mechanism in the virtual environmentThe routing mechanism is responsible to mainly passesand monitors the running state of each module throughevents and then broadcast the state parameters to otherfunctional modules in real time the coordination of themultifunctional modules is finally realized Events are thedata information transmitted between two domains whichinclude two types Input and Output The Input event is theinformation generated by other sending nodes to change thestate of the receiving node and the Output event is a statethat the state of the node itself changes and outputs theinformation When one of the behavior modules sends thecommand the receiving node gets the instructions throughthe route transfers the nodes through the event driven andrealizes the message driven mechanism
42 Path-Planning Testing and Analysis The path planningtests on multiple harvesting objectives were implementedbase on the developed virtual simulation The cluster numberof the tested grape was set from 2 to 5 and their positionswere randomly given in the configuration space of themanipulator The harvesting sequence was firstly calculatedby the energy optimal and the path points were generatedby artificial potential field The simulation test platformare as follows a laptop (Lenovo T430) with 4G RAM andIntel(R)Core(TM)i5-3230 M CPU260 GHz a Windows7 operating system and a Visual C++ 2008 platform Thestatistics and analysis are made on the path length thenumber of sampling points the collision situation and theaverage time of path planning in each harvesting The resultsof the tests are shown as Table 2 The relationship betweenpath length 119871 and key point 119875i can be described by Formula(17)
119871 = sum1le119894le119870
radic(119909119894 minus 119909119894minus1)2 + (119910119894 minus 119910119894minus1)2 + (119911119894 minus 119911119894minus1)2 (17)
where119870 indicates the number of sampling points of the pathand (119909i 119910i 119911i) is the coordinates of the 119894-th sampling points
From the Table 2 we can see that there are 9 times issuccessful and 1 times failure in the 10 grape harvesting testsThe success rate was 90 the path lengthwas between 44867cm and 147265 cm the number of sampling points wasbetween 90 and 206 and the average time of path planningwas between 98ms and 273 ms It can be seen that the reasonfor the failure of the test was the collision between the endeffector and the anticollision space bounding body of thegrape cluster If the distance between the end effector andgrape cluster is too small the end effector will be easy tocollide with the upper part of the grape cluster when theend effector move closely to the fruit peduncle for harvestingoperationHarvesting path-planning can be optimized by set-ting and adjusting the minimum safety margin between thecutting point and the anticollision space bounding volumeMoreover the average time of path planning increases withthe number of objective and the number of sampling pointsFigure 6 shows a successful grape harvesting path planningThewhite dots are the path points swept by the clamper centerof the end effector during the harvesting
10 Complexity
Table 2 Statistical results of the virtual tests for grape harvesting path-planning
Number ofobjectives Harvesting optimal sequence Length of
path (Lcm)
Number ofsamplingpoints (K)
Collision(YN)
Average timeof planning
(ms)3 B 997888rarrC 997888rarrA 63578 108 N 1522 B 997888rarrA 44867 72 N 1084 C 997888rarrD 997888rarrA 997888rarrB 98523 172 N 2155 B 997888rarrD 997888rarrC 997888rarrA 997888rarr E 136245 206 N 2613 A 997888rarrC 997888rarrB 72333 102 N 1634 B 997888rarrC 997888rarrD 997888rarrA 106158 170 N 2035 E 997888rarrC 997888rarrA 997888rarrB 997888rarr D 147265 216 Y 2742 A 997888rarrB 46365 91 N 983 B 997888rarrC 997888rarrA 75687 127 N 1514 C 997888rarrB 997888rarrD 997888rarrA 104526 162 N 199
(a) (b)
(c)
Figure 6 The path points drew by the proposed path-planning method
5 Discussion
Traditional path planning methods (such as skeleton celldecomposition and subgoal graph etc) are very effective forlower degree of freedom robot (2 to 3 DOF) With theincrease in the degree of freedom of robots these algorithms
will be out of work A collision-free autonomous path plan-ning methodolgy for six-DOF serial harvesting manipulatorunder a dynamic vineyard environment was presented inthis study The kinematical modelling of Six-DOF serialmanipulator the model of obstacles and the configurationspace of harvesting robot was firstly introduced in detail
Complexity 11
And then the harvesting sequence and the anticollision pathpoints were calculated by using the energy optimal and theartificial potential field The virtual tests based on virtualreality were performed to validate the performance of theproposed algorithm Through the virtual simulation test ofthe harvesting path planning the three-dimensional spacepath points of the end-effector of the harvesting manipulatorwere calculated in real time in virtual environment andthe collision detection is analyzed The success rate wasup to 90 It can be known that the simulation systemdesigned in this study has a good practical value to helptest and improve the intelligent behavior algorithm of therobot
To obtain an optimal harvesting path taking the sumof the joint angle of the weighted rotation as the goalthe harvesting sequence planning objective function of thesix-DOF harvesting manipulator is established by usingthe minimum energy principle and the minimum energyconsumption sequence can be obtained by calculating thevalue of the target function In addition the mapping modelof obstacles in the joint configuration space is built on thebasis of sampling method and the artificial potential fieldis used to search the obstacle avoidance path in the jointconfiguration space which improves the generality of thealgorithm However due to the proposed algorithm adoptsrandom sampling strategy the sampling points may collidewith the obstacles so it is necessary to resample If thenumber of maximum sampling point is too small the failureprobability of the path planning increases And if the numberofmaximumsampling point value is too large it will cause thepath to not exist or be difficult to find or the planning time istoo long So the parameters need test repeatedly
6 Conclusion
To conduct an undamaged robotic grape-harvesting in anunstructured vineyard a path planning strategies based onminimum energy and artificial potential field for grapeharvesting robot was developed in this studyThe kinematicalmodel of Six-DOF serial manipulator was firstly constructedby using the D-H method the model of obstacles wasdefined by the axis-aligned bounding box and then theconfiguration space of harvesting robot was described bycombining the obstacles and robot Then the harvestingsequence in path planning was computed by energy optimalmethod and the anticollision path points were generatedbased on the artificial potential field and sampling searchingmethod Finally to verify and test the proposed path planningalgorithm a virtual test system based on virtual reality wasdeveloped 10 times harvesting tests for grape anticollisionpath planning were implemented on the developed sim-ulation system and the success rate was up to 90 Inconclusion the developed approach can effectively plan acollision-free path for the grape harvesting robot in the com-plex vineyard environment However when facing multipleoverlapped and adjoining grape clusters the path planning isstill an issue that needs to be solved and will require furtherresearch
Data Availability
The grape harvesting robot data used to support the findingsof this study are available from the corresponding authorupon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
This work was supported by grants from the National Nat-ural Science Foundation of China (no 51705365) and theNational Key Research and Development Program of China(2017YFD0700100)
References
[1] M A Hossain and I Ferdous ldquoAutonomous robot pathplanning in dynamic environment using a new optimizationtechnique inspired by bacterial foraging techniquerdquo Roboticsand Autonomous Systems vol 64 pp 137ndash141 2015
[2] V San JuanM Santos and JM Andujar ldquoIntelligentUAVMapGeneration and Discrete Path Planning for Search and RescueOperationsrdquoComplexity vol 2018 Article ID 6879419 17 pages2018
[3] L Luo Y Tang Q Lu X Chen P Zhang and X Zou ldquoA visionmethodology for harvesting robot to detect cutting points onpeduncles of double overlapping grape clusters in a vineyardrdquoComputers in Industry vol 99 pp 130ndash139 2018
[4] P Li S-H Lee and H-Y Hsu ldquoReview on fruit harvestingmethod for potential use of automatic fruit harvesting systemsrdquoin Proceedings of the 2011 International Conference on PowerElectronics and EngineeringApplication PEEA 2011 pp 351ndash366China December 2011
[5] W Wei D-T Ouyang S Lu and Y-X Feng ldquoMultiobjectivepath planning under dynamic uncertain environmentrdquo JisuanjiXuebaoChinese Journal of Computers vol 34 no 5 pp 836ndash845 2011
[6] M G Mohanan andA Salgoankar ldquoA survey of roboticmotionplanning in dynamic environmentsrdquo Robotics and AutonomousSystems vol 100 pp 171ndash185 2018
[7] X Hu L Chen B Tang D Cao and H He ldquoDynamicpath planning for autonomous driving on various roads withavoidance of static and moving obstaclesrdquo Mechanical Systemsand Signal Processing vol 100 pp 482ndash500 2018
[8] DDevaurs T Simeon and J Cortes ldquoOptimal Path Planning inComplex Cost Spaces with Sampling-Based Algorithmsrdquo IEEETransactions on Automation Science and Engineering vol 13 no2 pp 415ndash424 2016
[9] R Cui Y Li and W Yan ldquoMutual information-based multi-AUV path planning for scalar field sampling using multi-dimensional RRTrdquo IEEE Transactions on Systems Man andCybernetics Systems vol 46 no 7 pp 993ndash1004 2016
[10] CW Bac J Hemming and E J VanHenten ldquoStem localizationof sweet-pepper plants using the support wire as a visual cuerdquoComputers and Electronics in Agriculture vol 105 pp 111ndash1202014
12 Complexity
[11] L Luo Y Tang X ZouM YeW Feng andG Li ldquoVision-basedextraction of spatial information in grape clusters for harvestingrobotsrdquo Biosystems Engineering vol 151 pp 90ndash104 2016
[12] E J VanHenten J Hemming B A J VanTuijl J G Kornet andJ Bontsema ldquoCollision-free Motion Planning for a CucumberPicking Robotrdquo Biosystems Engineering vol 86 no 2 pp 135ndash144 2003
[13] G Gao G Sun J Na Y Guo and XWu ldquoStructural parameteridentification for 6 DOF industrial robotsrdquoMechanical Systemsand Signal Processing vol 113 pp 145ndash155 2018
[14] K Wei and B Ren ldquoA Method on Dynamic Path Planning forRobotic Manipulator Autonomous Obstacle Avoidance Basedon an Improved RRT Algorithmrdquo Sensors vol 18 no 2 p 5712018
[15] Y Dai and M Zhao ldquoManipulator path-planning avoidingobstacle based on screw theory and ant colony algorithmrdquoJournal of Computational and eoretical Nanoscience vol 13no 1 pp 922ndash927 2016
[16] H Pham and Q Pham ldquoTime-Optimal Path Tracking viaReachability Analysisrdquo in Proceedings of the 2018 IEEE Inter-national Conference on Robotics and Automation (ICRA) pp3007ndash3012 Brisbane QLD May 2018
[17] G Legnani F Casalo P Righettini and B Zappa ldquoA homo-geneous matrix approach to 3D kinematics and dynamics - IIApplications to chains of rigid bodies and serial manipulatorsrdquoMechanism and Machine eory vol 31 no 5 pp 589ndash6051996
[18] J Craig Introduction to Robotics Mechanics and Control 3rdedition 2015
[19] R P Paul B Shimano and G E Mayer ldquoKinematic controlequations for simple manipulatorsrdquo IEEE Transactions on Sys-tems Man and Cybernetics vol 11 no 6 pp 449ndash455 1981
[20] G Zachmann ldquoRapid collision detection by dynamicallyaligned DOP-treesrdquo in Proceedings of the 1998 IEEE VirtualReality Annual International Symposium VRAIS pp 90ndash97March 1998
[21] H Yang L Li and Z Gao ldquoObstacle avoidance path planningof hybrid harvesting manipulator based on joint configurationspacerdquoNongyeGongcheng Xuebao vol 33 no 4 pp 55ndash62 2017
[22] C Peter Robotics Vision amp Control Springer 2nd edition 2017[23] Z Daqi and Y Mingzhong ldquoSurvey on technology of mobile
robot path planningrdquo Control and Decision vol 25 no 7 pp961ndash967 2010
[24] O Khatib ldquoReal-time obstacle avoida nce for manipulators andmobile robotsrdquo International Journal of Robotics Research vol5 no 1 pp 90ndash98 1986
[25] M Fakoor A Kosari and M Jafarzadeh ldquoRevision on fuzzyartificial potential field for humanoid robot path planningin unknown environmentrdquo International Journal of AdvancedMechatronic Systems vol 6 no 4 pp 174ndash183 2015
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Submit your manuscripts atwwwhindawicom
Complexity 7
10001000
500Y axis (mm)
0
X axis (mm)0
minus500minus1000 minus1000
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(a) Motion space in X Y and Z coordinates
minus1000
minus500
0
500
1000
Y ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(b) Motion space in X and Y coordinates
minus1000
minus500
0
500
1000
Z ax
is (m
m)
0 500 1000minus500minus1000X axis (mm)
(c) Motion space in X and Z coordinates
0 500 1000minus500minus1000Y axis (mm)
minus1000
minus500
0
500
1000
Z ax
is (m
m)
(d) Motion space in Y and Z coordinates
Figure 3 The motion space of the harvesting robot
destination
path point
cutting point①
②
③④
⑤
Figure 4 Schematic diagram for the path planning of the grapeharvesting robot
manipulator Moreover the power of each joint motor isdifferent according to the value of the power of each jointmotor of the manipulator different weights should be givento each joint angle and different weights should also be givento the sub targets of each joint of the manipulator So thesequence planning of the six degree of freedom harvestingmanipulator based on the principle of minimum energy canbe described by the following
1198751015840 = 119898sum119894=1
120596119894119869119894 =119898sum119894=1
119899sum119895=1
120596119894 10038161003816100381610038161003816120579119894119895 minus 120579119894119895+110038161003816100381610038161003816 (11)
where 1198751015840 indicates the objective function of the manipulatorthat can embody the energy consumption of the manipulatormotion 119898 is the number of the joints 120596i is the weight of theobjective function of the 119894th joints and 120579ij indicates the anglevalue of the 119894th joint when the manipulator is locating the 119895thspace point
32 Harvesting Path Generating Based on Artificial PotentialField eory In the process of grape harvesting collision-free path planning under a vineyard environment is themost important issue which need be resolved firstly to avoiddamage the fruits At present there are two main pathplanning methods [23] model-based global path planningand sensor-based local path planning In this study the localpath planning method based on artificial potential field wasadopted
321 Principle of Artificial Potential Field The path planningmethod based on artificial potential field is a virtual forcemethod proposed by Khatib [24] Its basic idea is to designthe motion of the robot in the surrounding environment intoan abstract artificial gravitational fieldThe artificial potentialfield includes the gravitational field and the repulsion field inwhich the object produces the gravitational attraction to theobject and guides the object to move toward it The obstaclesrepel other objects to avoid collisions with it The resultant
8 Complexity
Input the current point coordinates of the end-effector (1199090 1199100 1199110) the terminal coordinates(119909t 119910t 119911t) (the cutting point on the peduncles of grape cluster) the bounding box model ofobstacles 119877(119874s 119874e)Output the path points (119909i 119910i 119911i)
1 Find all collision-free sampling points2 for each sampling points p do
(a) calculate the probability that the current point is the candidate path points(b) find the point whose probability is maximum(c) consider the points as a candidate path point
end3 Repeat the above process until the terminal coordinates is reached
Algorithm 1 Sampling-based path point generating method
force of every point on a path is equal to the sum of allrepulsive forces and gravitational forces on this point
The basic idea of the proposed path planning in thisstudy is that the harvesting point is attractive to the motionof the harvesting manipulator by the virtual force fieldthe anticollision bounding body of grape cluster and otherobstacles are repulsive to it and the path planning is carriedout through the interaction of attraction and repulsion forceThe artificial potential field 119880sum(119883) can be defined by thefollowing [24]
in which119880att(119883) indicates the gravitational field generated bythe target 119880rep(119883) indicates the repulsion field generated bythe obstacles119883 = (119909 119910 119911)119879 is the position of the end-effectorin the workspace Setting the position of the target as119883g andthe gravitational field119880att(119883) can be defined by the following
119880att (119883) = 12119896 (119883 minus 119883119892)2 (13)
where 119896 is a constant about the gravitational field and then thegravitation 119865att(119883) can be solved by calculating the negativegradient value of the gravitational field which is described asFormula (14)
To define the mathematical expression about the repul-sive force field the following two conditions need firstly beconformed [25] (1) the artificial potential field119880sum(119883)mustbe a continuous-differential function and when119883 is equal to119883g the value of119880sum(119883) is 0 (minimum value) (2) Under theeffect of the artificial potential field 119880sum(119883) the system canbe stable Setting 1198830 as the space position of the obstacle therepulsive force field 119880rep(119883) can be defined by the following
119880rep (119883) =12120578(
1119883 minus 1198830 minus
1120588)2 (119883 minus 1198830) lt 120588
0 (119883 minus 1198830) ge 120588 (15)
where 120578 is a constant about the repulsive force field and 120588 isthe maximum range of the impact of the obstacle When the
distance between the obstacle and the end-effector is largerthan120588 the repulsive fieldwould no longer to affect themotionof harvesting robotThe repulsive force 119865rep(119883) can be solvedby calculating the negative gradient value of the repulsiveforce field 119880rep(119883) which is described as the following
120597 (119883 minus 1198830)120597119883 (119883 minus 1198830) lt 1205880 (119883 minus 1198830) ge 120588
(16)
322 Sampling-Based Path Points Generating Method Thearray of the path point sets (119909i 119910i 119911i) are firstly establishedand then the terminal pose of the end-effector is determinedbased on the current pose of the robot and the pose of grapecluster The current point coordinates of the end-effector(1199090 1199100 1199110) the terminal coordinates (119909t 119910t 119911t) (the cuttingpoint on the peduncles of grape cluster) and the boundingbox model of obstacles 119877(119874s 119874e) are given respectivelyAccording to the artificial potential field method new sam-pling points are generated randomly in the neighbourhoodand collision detection is performed on the sampling pointsThe probability that all collision-free sampling points areselected as the candidate path points is calculated and thesampling point with the highest probability is added to thepath array as the following path point Repeat the aboveprocess until the terminal coordinates is reachedThe pseudocode of sampling-based path point generating method is asshown in Algorithm 1
4 Experiments and Results
To validate the performance of the proposed anticollisionpath planning algorithm in a complex orchard a virtualharvesting robot simulation system was developed based onthe virtual reality software platform and then the perfor-mance of path planning method was investigated based onthe developed simulation system
41 Virtual Harvesting Robot Testing System The virtual sim-ulation systemwas implemented on theWindows 7 operatingsystem by using the software tools such as Visual studio 2013
Complexity 9
Figure 5 Schematic diagram for the path planning of the grapeharvesting robot
EON Studio 3Dmax and Solidworks In this study the virtualharvesting robot is constructed according to the actual sizeand workspace of the 6-DOF robot prototype Firstly the 3Dmodel of orchard scene and harvesting robotrsquos body structureis constructed and the kinematics model of the manipulatoris set by D-H parameter methodThen the virtual grape clus-ters and their anticollision space bounding body are drawnunder the virtual environment The collision avoidance pathpoints are computed by the proposed algorithm Finallythe path is simulated by a three-dimensional visualizationmethod The end-effector on the harvesting robot is consistsof three functional parts clamping finger pallet and scissorThe clamping mechanism is mainly responsible for clampingthe peduncle of grape cluster The pallet holds the grapecluster from behind and underneath carrying part of grapegravity to prevent the grape from shaking and slippingWhenthe fingers and pallets lock up the grape cluster the peduncleis cut by the scissors mechanism The software interface isshown as Figure 5
After the collision-free path is planned the joint variablesparameters of the manipulator are calculated by the inversekinematics model and then the forward kinematics methodis used to control the robotrsquos end-effector to the targetposition In the virtual simulation system the collision nodein the EON platform was used to detect collision in thisresearch The node can detect the collision events betweendifferent geometric objects in the virtual environment whichcan monitor the collision between the harvesting robot andthe obstacle in real-time To control the motion behaviorof virtual harvesting robot the modular programming androuting communication mechanism in EON platform wereadoptedThemainmodules involved aremovement rotationposition sensor angle sensor time sensor switch node rout-ing and so on The movement module is mainly used for theclamping behavior control of the end-effector The rotationmodule is used to control the rotation of the six joints of themanipulator and the rotary cutting motion of the actuatorscissors The position and angle sensors are used to perceivethe real-time travel and position of the joint motionThe timesensor is used to control the motion speed and acceleration ofthe joints of the manipulator and the switch nodes are usedto connect the communication between the modules Thecommunications among several functionmodules are carried
out through routing mechanism in the virtual environmentThe routing mechanism is responsible to mainly passesand monitors the running state of each module throughevents and then broadcast the state parameters to otherfunctional modules in real time the coordination of themultifunctional modules is finally realized Events are thedata information transmitted between two domains whichinclude two types Input and Output The Input event is theinformation generated by other sending nodes to change thestate of the receiving node and the Output event is a statethat the state of the node itself changes and outputs theinformation When one of the behavior modules sends thecommand the receiving node gets the instructions throughthe route transfers the nodes through the event driven andrealizes the message driven mechanism
42 Path-Planning Testing and Analysis The path planningtests on multiple harvesting objectives were implementedbase on the developed virtual simulation The cluster numberof the tested grape was set from 2 to 5 and their positionswere randomly given in the configuration space of themanipulator The harvesting sequence was firstly calculatedby the energy optimal and the path points were generatedby artificial potential field The simulation test platformare as follows a laptop (Lenovo T430) with 4G RAM andIntel(R)Core(TM)i5-3230 M CPU260 GHz a Windows7 operating system and a Visual C++ 2008 platform Thestatistics and analysis are made on the path length thenumber of sampling points the collision situation and theaverage time of path planning in each harvesting The resultsof the tests are shown as Table 2 The relationship betweenpath length 119871 and key point 119875i can be described by Formula(17)
119871 = sum1le119894le119870
radic(119909119894 minus 119909119894minus1)2 + (119910119894 minus 119910119894minus1)2 + (119911119894 minus 119911119894minus1)2 (17)
where119870 indicates the number of sampling points of the pathand (119909i 119910i 119911i) is the coordinates of the 119894-th sampling points
From the Table 2 we can see that there are 9 times issuccessful and 1 times failure in the 10 grape harvesting testsThe success rate was 90 the path lengthwas between 44867cm and 147265 cm the number of sampling points wasbetween 90 and 206 and the average time of path planningwas between 98ms and 273 ms It can be seen that the reasonfor the failure of the test was the collision between the endeffector and the anticollision space bounding body of thegrape cluster If the distance between the end effector andgrape cluster is too small the end effector will be easy tocollide with the upper part of the grape cluster when theend effector move closely to the fruit peduncle for harvestingoperationHarvesting path-planning can be optimized by set-ting and adjusting the minimum safety margin between thecutting point and the anticollision space bounding volumeMoreover the average time of path planning increases withthe number of objective and the number of sampling pointsFigure 6 shows a successful grape harvesting path planningThewhite dots are the path points swept by the clamper centerof the end effector during the harvesting
10 Complexity
Table 2 Statistical results of the virtual tests for grape harvesting path-planning
Number ofobjectives Harvesting optimal sequence Length of
path (Lcm)
Number ofsamplingpoints (K)
Collision(YN)
Average timeof planning
(ms)3 B 997888rarrC 997888rarrA 63578 108 N 1522 B 997888rarrA 44867 72 N 1084 C 997888rarrD 997888rarrA 997888rarrB 98523 172 N 2155 B 997888rarrD 997888rarrC 997888rarrA 997888rarr E 136245 206 N 2613 A 997888rarrC 997888rarrB 72333 102 N 1634 B 997888rarrC 997888rarrD 997888rarrA 106158 170 N 2035 E 997888rarrC 997888rarrA 997888rarrB 997888rarr D 147265 216 Y 2742 A 997888rarrB 46365 91 N 983 B 997888rarrC 997888rarrA 75687 127 N 1514 C 997888rarrB 997888rarrD 997888rarrA 104526 162 N 199
(a) (b)
(c)
Figure 6 The path points drew by the proposed path-planning method
5 Discussion
Traditional path planning methods (such as skeleton celldecomposition and subgoal graph etc) are very effective forlower degree of freedom robot (2 to 3 DOF) With theincrease in the degree of freedom of robots these algorithms
will be out of work A collision-free autonomous path plan-ning methodolgy for six-DOF serial harvesting manipulatorunder a dynamic vineyard environment was presented inthis study The kinematical modelling of Six-DOF serialmanipulator the model of obstacles and the configurationspace of harvesting robot was firstly introduced in detail
Complexity 11
And then the harvesting sequence and the anticollision pathpoints were calculated by using the energy optimal and theartificial potential field The virtual tests based on virtualreality were performed to validate the performance of theproposed algorithm Through the virtual simulation test ofthe harvesting path planning the three-dimensional spacepath points of the end-effector of the harvesting manipulatorwere calculated in real time in virtual environment andthe collision detection is analyzed The success rate wasup to 90 It can be known that the simulation systemdesigned in this study has a good practical value to helptest and improve the intelligent behavior algorithm of therobot
To obtain an optimal harvesting path taking the sumof the joint angle of the weighted rotation as the goalthe harvesting sequence planning objective function of thesix-DOF harvesting manipulator is established by usingthe minimum energy principle and the minimum energyconsumption sequence can be obtained by calculating thevalue of the target function In addition the mapping modelof obstacles in the joint configuration space is built on thebasis of sampling method and the artificial potential fieldis used to search the obstacle avoidance path in the jointconfiguration space which improves the generality of thealgorithm However due to the proposed algorithm adoptsrandom sampling strategy the sampling points may collidewith the obstacles so it is necessary to resample If thenumber of maximum sampling point is too small the failureprobability of the path planning increases And if the numberofmaximumsampling point value is too large it will cause thepath to not exist or be difficult to find or the planning time istoo long So the parameters need test repeatedly
6 Conclusion
To conduct an undamaged robotic grape-harvesting in anunstructured vineyard a path planning strategies based onminimum energy and artificial potential field for grapeharvesting robot was developed in this studyThe kinematicalmodel of Six-DOF serial manipulator was firstly constructedby using the D-H method the model of obstacles wasdefined by the axis-aligned bounding box and then theconfiguration space of harvesting robot was described bycombining the obstacles and robot Then the harvestingsequence in path planning was computed by energy optimalmethod and the anticollision path points were generatedbased on the artificial potential field and sampling searchingmethod Finally to verify and test the proposed path planningalgorithm a virtual test system based on virtual reality wasdeveloped 10 times harvesting tests for grape anticollisionpath planning were implemented on the developed sim-ulation system and the success rate was up to 90 Inconclusion the developed approach can effectively plan acollision-free path for the grape harvesting robot in the com-plex vineyard environment However when facing multipleoverlapped and adjoining grape clusters the path planning isstill an issue that needs to be solved and will require furtherresearch
Data Availability
The grape harvesting robot data used to support the findingsof this study are available from the corresponding authorupon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
This work was supported by grants from the National Nat-ural Science Foundation of China (no 51705365) and theNational Key Research and Development Program of China(2017YFD0700100)
References
[1] M A Hossain and I Ferdous ldquoAutonomous robot pathplanning in dynamic environment using a new optimizationtechnique inspired by bacterial foraging techniquerdquo Roboticsand Autonomous Systems vol 64 pp 137ndash141 2015
[2] V San JuanM Santos and JM Andujar ldquoIntelligentUAVMapGeneration and Discrete Path Planning for Search and RescueOperationsrdquoComplexity vol 2018 Article ID 6879419 17 pages2018
[3] L Luo Y Tang Q Lu X Chen P Zhang and X Zou ldquoA visionmethodology for harvesting robot to detect cutting points onpeduncles of double overlapping grape clusters in a vineyardrdquoComputers in Industry vol 99 pp 130ndash139 2018
[4] P Li S-H Lee and H-Y Hsu ldquoReview on fruit harvestingmethod for potential use of automatic fruit harvesting systemsrdquoin Proceedings of the 2011 International Conference on PowerElectronics and EngineeringApplication PEEA 2011 pp 351ndash366China December 2011
[5] W Wei D-T Ouyang S Lu and Y-X Feng ldquoMultiobjectivepath planning under dynamic uncertain environmentrdquo JisuanjiXuebaoChinese Journal of Computers vol 34 no 5 pp 836ndash845 2011
[6] M G Mohanan andA Salgoankar ldquoA survey of roboticmotionplanning in dynamic environmentsrdquo Robotics and AutonomousSystems vol 100 pp 171ndash185 2018
[7] X Hu L Chen B Tang D Cao and H He ldquoDynamicpath planning for autonomous driving on various roads withavoidance of static and moving obstaclesrdquo Mechanical Systemsand Signal Processing vol 100 pp 482ndash500 2018
[8] DDevaurs T Simeon and J Cortes ldquoOptimal Path Planning inComplex Cost Spaces with Sampling-Based Algorithmsrdquo IEEETransactions on Automation Science and Engineering vol 13 no2 pp 415ndash424 2016
[9] R Cui Y Li and W Yan ldquoMutual information-based multi-AUV path planning for scalar field sampling using multi-dimensional RRTrdquo IEEE Transactions on Systems Man andCybernetics Systems vol 46 no 7 pp 993ndash1004 2016
[10] CW Bac J Hemming and E J VanHenten ldquoStem localizationof sweet-pepper plants using the support wire as a visual cuerdquoComputers and Electronics in Agriculture vol 105 pp 111ndash1202014
12 Complexity
[11] L Luo Y Tang X ZouM YeW Feng andG Li ldquoVision-basedextraction of spatial information in grape clusters for harvestingrobotsrdquo Biosystems Engineering vol 151 pp 90ndash104 2016
[12] E J VanHenten J Hemming B A J VanTuijl J G Kornet andJ Bontsema ldquoCollision-free Motion Planning for a CucumberPicking Robotrdquo Biosystems Engineering vol 86 no 2 pp 135ndash144 2003
[13] G Gao G Sun J Na Y Guo and XWu ldquoStructural parameteridentification for 6 DOF industrial robotsrdquoMechanical Systemsand Signal Processing vol 113 pp 145ndash155 2018
[14] K Wei and B Ren ldquoA Method on Dynamic Path Planning forRobotic Manipulator Autonomous Obstacle Avoidance Basedon an Improved RRT Algorithmrdquo Sensors vol 18 no 2 p 5712018
[15] Y Dai and M Zhao ldquoManipulator path-planning avoidingobstacle based on screw theory and ant colony algorithmrdquoJournal of Computational and eoretical Nanoscience vol 13no 1 pp 922ndash927 2016
[16] H Pham and Q Pham ldquoTime-Optimal Path Tracking viaReachability Analysisrdquo in Proceedings of the 2018 IEEE Inter-national Conference on Robotics and Automation (ICRA) pp3007ndash3012 Brisbane QLD May 2018
[17] G Legnani F Casalo P Righettini and B Zappa ldquoA homo-geneous matrix approach to 3D kinematics and dynamics - IIApplications to chains of rigid bodies and serial manipulatorsrdquoMechanism and Machine eory vol 31 no 5 pp 589ndash6051996
[18] J Craig Introduction to Robotics Mechanics and Control 3rdedition 2015
[19] R P Paul B Shimano and G E Mayer ldquoKinematic controlequations for simple manipulatorsrdquo IEEE Transactions on Sys-tems Man and Cybernetics vol 11 no 6 pp 449ndash455 1981
[20] G Zachmann ldquoRapid collision detection by dynamicallyaligned DOP-treesrdquo in Proceedings of the 1998 IEEE VirtualReality Annual International Symposium VRAIS pp 90ndash97March 1998
[21] H Yang L Li and Z Gao ldquoObstacle avoidance path planningof hybrid harvesting manipulator based on joint configurationspacerdquoNongyeGongcheng Xuebao vol 33 no 4 pp 55ndash62 2017
[22] C Peter Robotics Vision amp Control Springer 2nd edition 2017[23] Z Daqi and Y Mingzhong ldquoSurvey on technology of mobile
robot path planningrdquo Control and Decision vol 25 no 7 pp961ndash967 2010
[24] O Khatib ldquoReal-time obstacle avoida nce for manipulators andmobile robotsrdquo International Journal of Robotics Research vol5 no 1 pp 90ndash98 1986
[25] M Fakoor A Kosari and M Jafarzadeh ldquoRevision on fuzzyartificial potential field for humanoid robot path planningin unknown environmentrdquo International Journal of AdvancedMechatronic Systems vol 6 no 4 pp 174ndash183 2015
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
8 Complexity
Input the current point coordinates of the end-effector (1199090 1199100 1199110) the terminal coordinates(119909t 119910t 119911t) (the cutting point on the peduncles of grape cluster) the bounding box model ofobstacles 119877(119874s 119874e)Output the path points (119909i 119910i 119911i)
1 Find all collision-free sampling points2 for each sampling points p do
(a) calculate the probability that the current point is the candidate path points(b) find the point whose probability is maximum(c) consider the points as a candidate path point
end3 Repeat the above process until the terminal coordinates is reached
Algorithm 1 Sampling-based path point generating method
force of every point on a path is equal to the sum of allrepulsive forces and gravitational forces on this point
The basic idea of the proposed path planning in thisstudy is that the harvesting point is attractive to the motionof the harvesting manipulator by the virtual force fieldthe anticollision bounding body of grape cluster and otherobstacles are repulsive to it and the path planning is carriedout through the interaction of attraction and repulsion forceThe artificial potential field 119880sum(119883) can be defined by thefollowing [24]
in which119880att(119883) indicates the gravitational field generated bythe target 119880rep(119883) indicates the repulsion field generated bythe obstacles119883 = (119909 119910 119911)119879 is the position of the end-effectorin the workspace Setting the position of the target as119883g andthe gravitational field119880att(119883) can be defined by the following
119880att (119883) = 12119896 (119883 minus 119883119892)2 (13)
where 119896 is a constant about the gravitational field and then thegravitation 119865att(119883) can be solved by calculating the negativegradient value of the gravitational field which is described asFormula (14)
To define the mathematical expression about the repul-sive force field the following two conditions need firstly beconformed [25] (1) the artificial potential field119880sum(119883)mustbe a continuous-differential function and when119883 is equal to119883g the value of119880sum(119883) is 0 (minimum value) (2) Under theeffect of the artificial potential field 119880sum(119883) the system canbe stable Setting 1198830 as the space position of the obstacle therepulsive force field 119880rep(119883) can be defined by the following
119880rep (119883) =12120578(
1119883 minus 1198830 minus
1120588)2 (119883 minus 1198830) lt 120588
0 (119883 minus 1198830) ge 120588 (15)
where 120578 is a constant about the repulsive force field and 120588 isthe maximum range of the impact of the obstacle When the
distance between the obstacle and the end-effector is largerthan120588 the repulsive fieldwould no longer to affect themotionof harvesting robotThe repulsive force 119865rep(119883) can be solvedby calculating the negative gradient value of the repulsiveforce field 119880rep(119883) which is described as the following
120597 (119883 minus 1198830)120597119883 (119883 minus 1198830) lt 1205880 (119883 minus 1198830) ge 120588
(16)
322 Sampling-Based Path Points Generating Method Thearray of the path point sets (119909i 119910i 119911i) are firstly establishedand then the terminal pose of the end-effector is determinedbased on the current pose of the robot and the pose of grapecluster The current point coordinates of the end-effector(1199090 1199100 1199110) the terminal coordinates (119909t 119910t 119911t) (the cuttingpoint on the peduncles of grape cluster) and the boundingbox model of obstacles 119877(119874s 119874e) are given respectivelyAccording to the artificial potential field method new sam-pling points are generated randomly in the neighbourhoodand collision detection is performed on the sampling pointsThe probability that all collision-free sampling points areselected as the candidate path points is calculated and thesampling point with the highest probability is added to thepath array as the following path point Repeat the aboveprocess until the terminal coordinates is reachedThe pseudocode of sampling-based path point generating method is asshown in Algorithm 1
4 Experiments and Results
To validate the performance of the proposed anticollisionpath planning algorithm in a complex orchard a virtualharvesting robot simulation system was developed based onthe virtual reality software platform and then the perfor-mance of path planning method was investigated based onthe developed simulation system
41 Virtual Harvesting Robot Testing System The virtual sim-ulation systemwas implemented on theWindows 7 operatingsystem by using the software tools such as Visual studio 2013
Complexity 9
Figure 5 Schematic diagram for the path planning of the grapeharvesting robot
EON Studio 3Dmax and Solidworks In this study the virtualharvesting robot is constructed according to the actual sizeand workspace of the 6-DOF robot prototype Firstly the 3Dmodel of orchard scene and harvesting robotrsquos body structureis constructed and the kinematics model of the manipulatoris set by D-H parameter methodThen the virtual grape clus-ters and their anticollision space bounding body are drawnunder the virtual environment The collision avoidance pathpoints are computed by the proposed algorithm Finallythe path is simulated by a three-dimensional visualizationmethod The end-effector on the harvesting robot is consistsof three functional parts clamping finger pallet and scissorThe clamping mechanism is mainly responsible for clampingthe peduncle of grape cluster The pallet holds the grapecluster from behind and underneath carrying part of grapegravity to prevent the grape from shaking and slippingWhenthe fingers and pallets lock up the grape cluster the peduncleis cut by the scissors mechanism The software interface isshown as Figure 5
After the collision-free path is planned the joint variablesparameters of the manipulator are calculated by the inversekinematics model and then the forward kinematics methodis used to control the robotrsquos end-effector to the targetposition In the virtual simulation system the collision nodein the EON platform was used to detect collision in thisresearch The node can detect the collision events betweendifferent geometric objects in the virtual environment whichcan monitor the collision between the harvesting robot andthe obstacle in real-time To control the motion behaviorof virtual harvesting robot the modular programming androuting communication mechanism in EON platform wereadoptedThemainmodules involved aremovement rotationposition sensor angle sensor time sensor switch node rout-ing and so on The movement module is mainly used for theclamping behavior control of the end-effector The rotationmodule is used to control the rotation of the six joints of themanipulator and the rotary cutting motion of the actuatorscissors The position and angle sensors are used to perceivethe real-time travel and position of the joint motionThe timesensor is used to control the motion speed and acceleration ofthe joints of the manipulator and the switch nodes are usedto connect the communication between the modules Thecommunications among several functionmodules are carried
out through routing mechanism in the virtual environmentThe routing mechanism is responsible to mainly passesand monitors the running state of each module throughevents and then broadcast the state parameters to otherfunctional modules in real time the coordination of themultifunctional modules is finally realized Events are thedata information transmitted between two domains whichinclude two types Input and Output The Input event is theinformation generated by other sending nodes to change thestate of the receiving node and the Output event is a statethat the state of the node itself changes and outputs theinformation When one of the behavior modules sends thecommand the receiving node gets the instructions throughthe route transfers the nodes through the event driven andrealizes the message driven mechanism
42 Path-Planning Testing and Analysis The path planningtests on multiple harvesting objectives were implementedbase on the developed virtual simulation The cluster numberof the tested grape was set from 2 to 5 and their positionswere randomly given in the configuration space of themanipulator The harvesting sequence was firstly calculatedby the energy optimal and the path points were generatedby artificial potential field The simulation test platformare as follows a laptop (Lenovo T430) with 4G RAM andIntel(R)Core(TM)i5-3230 M CPU260 GHz a Windows7 operating system and a Visual C++ 2008 platform Thestatistics and analysis are made on the path length thenumber of sampling points the collision situation and theaverage time of path planning in each harvesting The resultsof the tests are shown as Table 2 The relationship betweenpath length 119871 and key point 119875i can be described by Formula(17)
119871 = sum1le119894le119870
radic(119909119894 minus 119909119894minus1)2 + (119910119894 minus 119910119894minus1)2 + (119911119894 minus 119911119894minus1)2 (17)
where119870 indicates the number of sampling points of the pathand (119909i 119910i 119911i) is the coordinates of the 119894-th sampling points
From the Table 2 we can see that there are 9 times issuccessful and 1 times failure in the 10 grape harvesting testsThe success rate was 90 the path lengthwas between 44867cm and 147265 cm the number of sampling points wasbetween 90 and 206 and the average time of path planningwas between 98ms and 273 ms It can be seen that the reasonfor the failure of the test was the collision between the endeffector and the anticollision space bounding body of thegrape cluster If the distance between the end effector andgrape cluster is too small the end effector will be easy tocollide with the upper part of the grape cluster when theend effector move closely to the fruit peduncle for harvestingoperationHarvesting path-planning can be optimized by set-ting and adjusting the minimum safety margin between thecutting point and the anticollision space bounding volumeMoreover the average time of path planning increases withthe number of objective and the number of sampling pointsFigure 6 shows a successful grape harvesting path planningThewhite dots are the path points swept by the clamper centerof the end effector during the harvesting
10 Complexity
Table 2 Statistical results of the virtual tests for grape harvesting path-planning
Number ofobjectives Harvesting optimal sequence Length of
path (Lcm)
Number ofsamplingpoints (K)
Collision(YN)
Average timeof planning
(ms)3 B 997888rarrC 997888rarrA 63578 108 N 1522 B 997888rarrA 44867 72 N 1084 C 997888rarrD 997888rarrA 997888rarrB 98523 172 N 2155 B 997888rarrD 997888rarrC 997888rarrA 997888rarr E 136245 206 N 2613 A 997888rarrC 997888rarrB 72333 102 N 1634 B 997888rarrC 997888rarrD 997888rarrA 106158 170 N 2035 E 997888rarrC 997888rarrA 997888rarrB 997888rarr D 147265 216 Y 2742 A 997888rarrB 46365 91 N 983 B 997888rarrC 997888rarrA 75687 127 N 1514 C 997888rarrB 997888rarrD 997888rarrA 104526 162 N 199
(a) (b)
(c)
Figure 6 The path points drew by the proposed path-planning method
5 Discussion
Traditional path planning methods (such as skeleton celldecomposition and subgoal graph etc) are very effective forlower degree of freedom robot (2 to 3 DOF) With theincrease in the degree of freedom of robots these algorithms
will be out of work A collision-free autonomous path plan-ning methodolgy for six-DOF serial harvesting manipulatorunder a dynamic vineyard environment was presented inthis study The kinematical modelling of Six-DOF serialmanipulator the model of obstacles and the configurationspace of harvesting robot was firstly introduced in detail
Complexity 11
And then the harvesting sequence and the anticollision pathpoints were calculated by using the energy optimal and theartificial potential field The virtual tests based on virtualreality were performed to validate the performance of theproposed algorithm Through the virtual simulation test ofthe harvesting path planning the three-dimensional spacepath points of the end-effector of the harvesting manipulatorwere calculated in real time in virtual environment andthe collision detection is analyzed The success rate wasup to 90 It can be known that the simulation systemdesigned in this study has a good practical value to helptest and improve the intelligent behavior algorithm of therobot
To obtain an optimal harvesting path taking the sumof the joint angle of the weighted rotation as the goalthe harvesting sequence planning objective function of thesix-DOF harvesting manipulator is established by usingthe minimum energy principle and the minimum energyconsumption sequence can be obtained by calculating thevalue of the target function In addition the mapping modelof obstacles in the joint configuration space is built on thebasis of sampling method and the artificial potential fieldis used to search the obstacle avoidance path in the jointconfiguration space which improves the generality of thealgorithm However due to the proposed algorithm adoptsrandom sampling strategy the sampling points may collidewith the obstacles so it is necessary to resample If thenumber of maximum sampling point is too small the failureprobability of the path planning increases And if the numberofmaximumsampling point value is too large it will cause thepath to not exist or be difficult to find or the planning time istoo long So the parameters need test repeatedly
6 Conclusion
To conduct an undamaged robotic grape-harvesting in anunstructured vineyard a path planning strategies based onminimum energy and artificial potential field for grapeharvesting robot was developed in this studyThe kinematicalmodel of Six-DOF serial manipulator was firstly constructedby using the D-H method the model of obstacles wasdefined by the axis-aligned bounding box and then theconfiguration space of harvesting robot was described bycombining the obstacles and robot Then the harvestingsequence in path planning was computed by energy optimalmethod and the anticollision path points were generatedbased on the artificial potential field and sampling searchingmethod Finally to verify and test the proposed path planningalgorithm a virtual test system based on virtual reality wasdeveloped 10 times harvesting tests for grape anticollisionpath planning were implemented on the developed sim-ulation system and the success rate was up to 90 Inconclusion the developed approach can effectively plan acollision-free path for the grape harvesting robot in the com-plex vineyard environment However when facing multipleoverlapped and adjoining grape clusters the path planning isstill an issue that needs to be solved and will require furtherresearch
Data Availability
The grape harvesting robot data used to support the findingsof this study are available from the corresponding authorupon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
This work was supported by grants from the National Nat-ural Science Foundation of China (no 51705365) and theNational Key Research and Development Program of China(2017YFD0700100)
References
[1] M A Hossain and I Ferdous ldquoAutonomous robot pathplanning in dynamic environment using a new optimizationtechnique inspired by bacterial foraging techniquerdquo Roboticsand Autonomous Systems vol 64 pp 137ndash141 2015
[2] V San JuanM Santos and JM Andujar ldquoIntelligentUAVMapGeneration and Discrete Path Planning for Search and RescueOperationsrdquoComplexity vol 2018 Article ID 6879419 17 pages2018
[3] L Luo Y Tang Q Lu X Chen P Zhang and X Zou ldquoA visionmethodology for harvesting robot to detect cutting points onpeduncles of double overlapping grape clusters in a vineyardrdquoComputers in Industry vol 99 pp 130ndash139 2018
[4] P Li S-H Lee and H-Y Hsu ldquoReview on fruit harvestingmethod for potential use of automatic fruit harvesting systemsrdquoin Proceedings of the 2011 International Conference on PowerElectronics and EngineeringApplication PEEA 2011 pp 351ndash366China December 2011
[5] W Wei D-T Ouyang S Lu and Y-X Feng ldquoMultiobjectivepath planning under dynamic uncertain environmentrdquo JisuanjiXuebaoChinese Journal of Computers vol 34 no 5 pp 836ndash845 2011
[6] M G Mohanan andA Salgoankar ldquoA survey of roboticmotionplanning in dynamic environmentsrdquo Robotics and AutonomousSystems vol 100 pp 171ndash185 2018
[7] X Hu L Chen B Tang D Cao and H He ldquoDynamicpath planning for autonomous driving on various roads withavoidance of static and moving obstaclesrdquo Mechanical Systemsand Signal Processing vol 100 pp 482ndash500 2018
[8] DDevaurs T Simeon and J Cortes ldquoOptimal Path Planning inComplex Cost Spaces with Sampling-Based Algorithmsrdquo IEEETransactions on Automation Science and Engineering vol 13 no2 pp 415ndash424 2016
[9] R Cui Y Li and W Yan ldquoMutual information-based multi-AUV path planning for scalar field sampling using multi-dimensional RRTrdquo IEEE Transactions on Systems Man andCybernetics Systems vol 46 no 7 pp 993ndash1004 2016
[10] CW Bac J Hemming and E J VanHenten ldquoStem localizationof sweet-pepper plants using the support wire as a visual cuerdquoComputers and Electronics in Agriculture vol 105 pp 111ndash1202014
12 Complexity
[11] L Luo Y Tang X ZouM YeW Feng andG Li ldquoVision-basedextraction of spatial information in grape clusters for harvestingrobotsrdquo Biosystems Engineering vol 151 pp 90ndash104 2016
[12] E J VanHenten J Hemming B A J VanTuijl J G Kornet andJ Bontsema ldquoCollision-free Motion Planning for a CucumberPicking Robotrdquo Biosystems Engineering vol 86 no 2 pp 135ndash144 2003
[13] G Gao G Sun J Na Y Guo and XWu ldquoStructural parameteridentification for 6 DOF industrial robotsrdquoMechanical Systemsand Signal Processing vol 113 pp 145ndash155 2018
[14] K Wei and B Ren ldquoA Method on Dynamic Path Planning forRobotic Manipulator Autonomous Obstacle Avoidance Basedon an Improved RRT Algorithmrdquo Sensors vol 18 no 2 p 5712018
[15] Y Dai and M Zhao ldquoManipulator path-planning avoidingobstacle based on screw theory and ant colony algorithmrdquoJournal of Computational and eoretical Nanoscience vol 13no 1 pp 922ndash927 2016
[16] H Pham and Q Pham ldquoTime-Optimal Path Tracking viaReachability Analysisrdquo in Proceedings of the 2018 IEEE Inter-national Conference on Robotics and Automation (ICRA) pp3007ndash3012 Brisbane QLD May 2018
[17] G Legnani F Casalo P Righettini and B Zappa ldquoA homo-geneous matrix approach to 3D kinematics and dynamics - IIApplications to chains of rigid bodies and serial manipulatorsrdquoMechanism and Machine eory vol 31 no 5 pp 589ndash6051996
[18] J Craig Introduction to Robotics Mechanics and Control 3rdedition 2015
[19] R P Paul B Shimano and G E Mayer ldquoKinematic controlequations for simple manipulatorsrdquo IEEE Transactions on Sys-tems Man and Cybernetics vol 11 no 6 pp 449ndash455 1981
[20] G Zachmann ldquoRapid collision detection by dynamicallyaligned DOP-treesrdquo in Proceedings of the 1998 IEEE VirtualReality Annual International Symposium VRAIS pp 90ndash97March 1998
[21] H Yang L Li and Z Gao ldquoObstacle avoidance path planningof hybrid harvesting manipulator based on joint configurationspacerdquoNongyeGongcheng Xuebao vol 33 no 4 pp 55ndash62 2017
[22] C Peter Robotics Vision amp Control Springer 2nd edition 2017[23] Z Daqi and Y Mingzhong ldquoSurvey on technology of mobile
robot path planningrdquo Control and Decision vol 25 no 7 pp961ndash967 2010
[24] O Khatib ldquoReal-time obstacle avoida nce for manipulators andmobile robotsrdquo International Journal of Robotics Research vol5 no 1 pp 90ndash98 1986
[25] M Fakoor A Kosari and M Jafarzadeh ldquoRevision on fuzzyartificial potential field for humanoid robot path planningin unknown environmentrdquo International Journal of AdvancedMechatronic Systems vol 6 no 4 pp 174ndash183 2015
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Complexity 9
Figure 5 Schematic diagram for the path planning of the grapeharvesting robot
EON Studio 3Dmax and Solidworks In this study the virtualharvesting robot is constructed according to the actual sizeand workspace of the 6-DOF robot prototype Firstly the 3Dmodel of orchard scene and harvesting robotrsquos body structureis constructed and the kinematics model of the manipulatoris set by D-H parameter methodThen the virtual grape clus-ters and their anticollision space bounding body are drawnunder the virtual environment The collision avoidance pathpoints are computed by the proposed algorithm Finallythe path is simulated by a three-dimensional visualizationmethod The end-effector on the harvesting robot is consistsof three functional parts clamping finger pallet and scissorThe clamping mechanism is mainly responsible for clampingthe peduncle of grape cluster The pallet holds the grapecluster from behind and underneath carrying part of grapegravity to prevent the grape from shaking and slippingWhenthe fingers and pallets lock up the grape cluster the peduncleis cut by the scissors mechanism The software interface isshown as Figure 5
After the collision-free path is planned the joint variablesparameters of the manipulator are calculated by the inversekinematics model and then the forward kinematics methodis used to control the robotrsquos end-effector to the targetposition In the virtual simulation system the collision nodein the EON platform was used to detect collision in thisresearch The node can detect the collision events betweendifferent geometric objects in the virtual environment whichcan monitor the collision between the harvesting robot andthe obstacle in real-time To control the motion behaviorof virtual harvesting robot the modular programming androuting communication mechanism in EON platform wereadoptedThemainmodules involved aremovement rotationposition sensor angle sensor time sensor switch node rout-ing and so on The movement module is mainly used for theclamping behavior control of the end-effector The rotationmodule is used to control the rotation of the six joints of themanipulator and the rotary cutting motion of the actuatorscissors The position and angle sensors are used to perceivethe real-time travel and position of the joint motionThe timesensor is used to control the motion speed and acceleration ofthe joints of the manipulator and the switch nodes are usedto connect the communication between the modules Thecommunications among several functionmodules are carried
out through routing mechanism in the virtual environmentThe routing mechanism is responsible to mainly passesand monitors the running state of each module throughevents and then broadcast the state parameters to otherfunctional modules in real time the coordination of themultifunctional modules is finally realized Events are thedata information transmitted between two domains whichinclude two types Input and Output The Input event is theinformation generated by other sending nodes to change thestate of the receiving node and the Output event is a statethat the state of the node itself changes and outputs theinformation When one of the behavior modules sends thecommand the receiving node gets the instructions throughthe route transfers the nodes through the event driven andrealizes the message driven mechanism
42 Path-Planning Testing and Analysis The path planningtests on multiple harvesting objectives were implementedbase on the developed virtual simulation The cluster numberof the tested grape was set from 2 to 5 and their positionswere randomly given in the configuration space of themanipulator The harvesting sequence was firstly calculatedby the energy optimal and the path points were generatedby artificial potential field The simulation test platformare as follows a laptop (Lenovo T430) with 4G RAM andIntel(R)Core(TM)i5-3230 M CPU260 GHz a Windows7 operating system and a Visual C++ 2008 platform Thestatistics and analysis are made on the path length thenumber of sampling points the collision situation and theaverage time of path planning in each harvesting The resultsof the tests are shown as Table 2 The relationship betweenpath length 119871 and key point 119875i can be described by Formula(17)
119871 = sum1le119894le119870
radic(119909119894 minus 119909119894minus1)2 + (119910119894 minus 119910119894minus1)2 + (119911119894 minus 119911119894minus1)2 (17)
where119870 indicates the number of sampling points of the pathand (119909i 119910i 119911i) is the coordinates of the 119894-th sampling points
From the Table 2 we can see that there are 9 times issuccessful and 1 times failure in the 10 grape harvesting testsThe success rate was 90 the path lengthwas between 44867cm and 147265 cm the number of sampling points wasbetween 90 and 206 and the average time of path planningwas between 98ms and 273 ms It can be seen that the reasonfor the failure of the test was the collision between the endeffector and the anticollision space bounding body of thegrape cluster If the distance between the end effector andgrape cluster is too small the end effector will be easy tocollide with the upper part of the grape cluster when theend effector move closely to the fruit peduncle for harvestingoperationHarvesting path-planning can be optimized by set-ting and adjusting the minimum safety margin between thecutting point and the anticollision space bounding volumeMoreover the average time of path planning increases withthe number of objective and the number of sampling pointsFigure 6 shows a successful grape harvesting path planningThewhite dots are the path points swept by the clamper centerof the end effector during the harvesting
10 Complexity
Table 2 Statistical results of the virtual tests for grape harvesting path-planning
Number ofobjectives Harvesting optimal sequence Length of
path (Lcm)
Number ofsamplingpoints (K)
Collision(YN)
Average timeof planning
(ms)3 B 997888rarrC 997888rarrA 63578 108 N 1522 B 997888rarrA 44867 72 N 1084 C 997888rarrD 997888rarrA 997888rarrB 98523 172 N 2155 B 997888rarrD 997888rarrC 997888rarrA 997888rarr E 136245 206 N 2613 A 997888rarrC 997888rarrB 72333 102 N 1634 B 997888rarrC 997888rarrD 997888rarrA 106158 170 N 2035 E 997888rarrC 997888rarrA 997888rarrB 997888rarr D 147265 216 Y 2742 A 997888rarrB 46365 91 N 983 B 997888rarrC 997888rarrA 75687 127 N 1514 C 997888rarrB 997888rarrD 997888rarrA 104526 162 N 199
(a) (b)
(c)
Figure 6 The path points drew by the proposed path-planning method
5 Discussion
Traditional path planning methods (such as skeleton celldecomposition and subgoal graph etc) are very effective forlower degree of freedom robot (2 to 3 DOF) With theincrease in the degree of freedom of robots these algorithms
will be out of work A collision-free autonomous path plan-ning methodolgy for six-DOF serial harvesting manipulatorunder a dynamic vineyard environment was presented inthis study The kinematical modelling of Six-DOF serialmanipulator the model of obstacles and the configurationspace of harvesting robot was firstly introduced in detail
Complexity 11
And then the harvesting sequence and the anticollision pathpoints were calculated by using the energy optimal and theartificial potential field The virtual tests based on virtualreality were performed to validate the performance of theproposed algorithm Through the virtual simulation test ofthe harvesting path planning the three-dimensional spacepath points of the end-effector of the harvesting manipulatorwere calculated in real time in virtual environment andthe collision detection is analyzed The success rate wasup to 90 It can be known that the simulation systemdesigned in this study has a good practical value to helptest and improve the intelligent behavior algorithm of therobot
To obtain an optimal harvesting path taking the sumof the joint angle of the weighted rotation as the goalthe harvesting sequence planning objective function of thesix-DOF harvesting manipulator is established by usingthe minimum energy principle and the minimum energyconsumption sequence can be obtained by calculating thevalue of the target function In addition the mapping modelof obstacles in the joint configuration space is built on thebasis of sampling method and the artificial potential fieldis used to search the obstacle avoidance path in the jointconfiguration space which improves the generality of thealgorithm However due to the proposed algorithm adoptsrandom sampling strategy the sampling points may collidewith the obstacles so it is necessary to resample If thenumber of maximum sampling point is too small the failureprobability of the path planning increases And if the numberofmaximumsampling point value is too large it will cause thepath to not exist or be difficult to find or the planning time istoo long So the parameters need test repeatedly
6 Conclusion
To conduct an undamaged robotic grape-harvesting in anunstructured vineyard a path planning strategies based onminimum energy and artificial potential field for grapeharvesting robot was developed in this studyThe kinematicalmodel of Six-DOF serial manipulator was firstly constructedby using the D-H method the model of obstacles wasdefined by the axis-aligned bounding box and then theconfiguration space of harvesting robot was described bycombining the obstacles and robot Then the harvestingsequence in path planning was computed by energy optimalmethod and the anticollision path points were generatedbased on the artificial potential field and sampling searchingmethod Finally to verify and test the proposed path planningalgorithm a virtual test system based on virtual reality wasdeveloped 10 times harvesting tests for grape anticollisionpath planning were implemented on the developed sim-ulation system and the success rate was up to 90 Inconclusion the developed approach can effectively plan acollision-free path for the grape harvesting robot in the com-plex vineyard environment However when facing multipleoverlapped and adjoining grape clusters the path planning isstill an issue that needs to be solved and will require furtherresearch
Data Availability
The grape harvesting robot data used to support the findingsof this study are available from the corresponding authorupon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
This work was supported by grants from the National Nat-ural Science Foundation of China (no 51705365) and theNational Key Research and Development Program of China(2017YFD0700100)
References
[1] M A Hossain and I Ferdous ldquoAutonomous robot pathplanning in dynamic environment using a new optimizationtechnique inspired by bacterial foraging techniquerdquo Roboticsand Autonomous Systems vol 64 pp 137ndash141 2015
[2] V San JuanM Santos and JM Andujar ldquoIntelligentUAVMapGeneration and Discrete Path Planning for Search and RescueOperationsrdquoComplexity vol 2018 Article ID 6879419 17 pages2018
[3] L Luo Y Tang Q Lu X Chen P Zhang and X Zou ldquoA visionmethodology for harvesting robot to detect cutting points onpeduncles of double overlapping grape clusters in a vineyardrdquoComputers in Industry vol 99 pp 130ndash139 2018
[4] P Li S-H Lee and H-Y Hsu ldquoReview on fruit harvestingmethod for potential use of automatic fruit harvesting systemsrdquoin Proceedings of the 2011 International Conference on PowerElectronics and EngineeringApplication PEEA 2011 pp 351ndash366China December 2011
[5] W Wei D-T Ouyang S Lu and Y-X Feng ldquoMultiobjectivepath planning under dynamic uncertain environmentrdquo JisuanjiXuebaoChinese Journal of Computers vol 34 no 5 pp 836ndash845 2011
[6] M G Mohanan andA Salgoankar ldquoA survey of roboticmotionplanning in dynamic environmentsrdquo Robotics and AutonomousSystems vol 100 pp 171ndash185 2018
[7] X Hu L Chen B Tang D Cao and H He ldquoDynamicpath planning for autonomous driving on various roads withavoidance of static and moving obstaclesrdquo Mechanical Systemsand Signal Processing vol 100 pp 482ndash500 2018
[8] DDevaurs T Simeon and J Cortes ldquoOptimal Path Planning inComplex Cost Spaces with Sampling-Based Algorithmsrdquo IEEETransactions on Automation Science and Engineering vol 13 no2 pp 415ndash424 2016
[9] R Cui Y Li and W Yan ldquoMutual information-based multi-AUV path planning for scalar field sampling using multi-dimensional RRTrdquo IEEE Transactions on Systems Man andCybernetics Systems vol 46 no 7 pp 993ndash1004 2016
[10] CW Bac J Hemming and E J VanHenten ldquoStem localizationof sweet-pepper plants using the support wire as a visual cuerdquoComputers and Electronics in Agriculture vol 105 pp 111ndash1202014
12 Complexity
[11] L Luo Y Tang X ZouM YeW Feng andG Li ldquoVision-basedextraction of spatial information in grape clusters for harvestingrobotsrdquo Biosystems Engineering vol 151 pp 90ndash104 2016
[12] E J VanHenten J Hemming B A J VanTuijl J G Kornet andJ Bontsema ldquoCollision-free Motion Planning for a CucumberPicking Robotrdquo Biosystems Engineering vol 86 no 2 pp 135ndash144 2003
[13] G Gao G Sun J Na Y Guo and XWu ldquoStructural parameteridentification for 6 DOF industrial robotsrdquoMechanical Systemsand Signal Processing vol 113 pp 145ndash155 2018
[14] K Wei and B Ren ldquoA Method on Dynamic Path Planning forRobotic Manipulator Autonomous Obstacle Avoidance Basedon an Improved RRT Algorithmrdquo Sensors vol 18 no 2 p 5712018
[15] Y Dai and M Zhao ldquoManipulator path-planning avoidingobstacle based on screw theory and ant colony algorithmrdquoJournal of Computational and eoretical Nanoscience vol 13no 1 pp 922ndash927 2016
[16] H Pham and Q Pham ldquoTime-Optimal Path Tracking viaReachability Analysisrdquo in Proceedings of the 2018 IEEE Inter-national Conference on Robotics and Automation (ICRA) pp3007ndash3012 Brisbane QLD May 2018
[17] G Legnani F Casalo P Righettini and B Zappa ldquoA homo-geneous matrix approach to 3D kinematics and dynamics - IIApplications to chains of rigid bodies and serial manipulatorsrdquoMechanism and Machine eory vol 31 no 5 pp 589ndash6051996
[18] J Craig Introduction to Robotics Mechanics and Control 3rdedition 2015
[19] R P Paul B Shimano and G E Mayer ldquoKinematic controlequations for simple manipulatorsrdquo IEEE Transactions on Sys-tems Man and Cybernetics vol 11 no 6 pp 449ndash455 1981
[20] G Zachmann ldquoRapid collision detection by dynamicallyaligned DOP-treesrdquo in Proceedings of the 1998 IEEE VirtualReality Annual International Symposium VRAIS pp 90ndash97March 1998
[21] H Yang L Li and Z Gao ldquoObstacle avoidance path planningof hybrid harvesting manipulator based on joint configurationspacerdquoNongyeGongcheng Xuebao vol 33 no 4 pp 55ndash62 2017
[22] C Peter Robotics Vision amp Control Springer 2nd edition 2017[23] Z Daqi and Y Mingzhong ldquoSurvey on technology of mobile
robot path planningrdquo Control and Decision vol 25 no 7 pp961ndash967 2010
[24] O Khatib ldquoReal-time obstacle avoida nce for manipulators andmobile robotsrdquo International Journal of Robotics Research vol5 no 1 pp 90ndash98 1986
[25] M Fakoor A Kosari and M Jafarzadeh ldquoRevision on fuzzyartificial potential field for humanoid robot path planningin unknown environmentrdquo International Journal of AdvancedMechatronic Systems vol 6 no 4 pp 174ndash183 2015
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
10 Complexity
Table 2 Statistical results of the virtual tests for grape harvesting path-planning
Number ofobjectives Harvesting optimal sequence Length of
path (Lcm)
Number ofsamplingpoints (K)
Collision(YN)
Average timeof planning
(ms)3 B 997888rarrC 997888rarrA 63578 108 N 1522 B 997888rarrA 44867 72 N 1084 C 997888rarrD 997888rarrA 997888rarrB 98523 172 N 2155 B 997888rarrD 997888rarrC 997888rarrA 997888rarr E 136245 206 N 2613 A 997888rarrC 997888rarrB 72333 102 N 1634 B 997888rarrC 997888rarrD 997888rarrA 106158 170 N 2035 E 997888rarrC 997888rarrA 997888rarrB 997888rarr D 147265 216 Y 2742 A 997888rarrB 46365 91 N 983 B 997888rarrC 997888rarrA 75687 127 N 1514 C 997888rarrB 997888rarrD 997888rarrA 104526 162 N 199
(a) (b)
(c)
Figure 6 The path points drew by the proposed path-planning method
5 Discussion
Traditional path planning methods (such as skeleton celldecomposition and subgoal graph etc) are very effective forlower degree of freedom robot (2 to 3 DOF) With theincrease in the degree of freedom of robots these algorithms
will be out of work A collision-free autonomous path plan-ning methodolgy for six-DOF serial harvesting manipulatorunder a dynamic vineyard environment was presented inthis study The kinematical modelling of Six-DOF serialmanipulator the model of obstacles and the configurationspace of harvesting robot was firstly introduced in detail
Complexity 11
And then the harvesting sequence and the anticollision pathpoints were calculated by using the energy optimal and theartificial potential field The virtual tests based on virtualreality were performed to validate the performance of theproposed algorithm Through the virtual simulation test ofthe harvesting path planning the three-dimensional spacepath points of the end-effector of the harvesting manipulatorwere calculated in real time in virtual environment andthe collision detection is analyzed The success rate wasup to 90 It can be known that the simulation systemdesigned in this study has a good practical value to helptest and improve the intelligent behavior algorithm of therobot
To obtain an optimal harvesting path taking the sumof the joint angle of the weighted rotation as the goalthe harvesting sequence planning objective function of thesix-DOF harvesting manipulator is established by usingthe minimum energy principle and the minimum energyconsumption sequence can be obtained by calculating thevalue of the target function In addition the mapping modelof obstacles in the joint configuration space is built on thebasis of sampling method and the artificial potential fieldis used to search the obstacle avoidance path in the jointconfiguration space which improves the generality of thealgorithm However due to the proposed algorithm adoptsrandom sampling strategy the sampling points may collidewith the obstacles so it is necessary to resample If thenumber of maximum sampling point is too small the failureprobability of the path planning increases And if the numberofmaximumsampling point value is too large it will cause thepath to not exist or be difficult to find or the planning time istoo long So the parameters need test repeatedly
6 Conclusion
To conduct an undamaged robotic grape-harvesting in anunstructured vineyard a path planning strategies based onminimum energy and artificial potential field for grapeharvesting robot was developed in this studyThe kinematicalmodel of Six-DOF serial manipulator was firstly constructedby using the D-H method the model of obstacles wasdefined by the axis-aligned bounding box and then theconfiguration space of harvesting robot was described bycombining the obstacles and robot Then the harvestingsequence in path planning was computed by energy optimalmethod and the anticollision path points were generatedbased on the artificial potential field and sampling searchingmethod Finally to verify and test the proposed path planningalgorithm a virtual test system based on virtual reality wasdeveloped 10 times harvesting tests for grape anticollisionpath planning were implemented on the developed sim-ulation system and the success rate was up to 90 Inconclusion the developed approach can effectively plan acollision-free path for the grape harvesting robot in the com-plex vineyard environment However when facing multipleoverlapped and adjoining grape clusters the path planning isstill an issue that needs to be solved and will require furtherresearch
Data Availability
The grape harvesting robot data used to support the findingsof this study are available from the corresponding authorupon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
This work was supported by grants from the National Nat-ural Science Foundation of China (no 51705365) and theNational Key Research and Development Program of China(2017YFD0700100)
References
[1] M A Hossain and I Ferdous ldquoAutonomous robot pathplanning in dynamic environment using a new optimizationtechnique inspired by bacterial foraging techniquerdquo Roboticsand Autonomous Systems vol 64 pp 137ndash141 2015
[2] V San JuanM Santos and JM Andujar ldquoIntelligentUAVMapGeneration and Discrete Path Planning for Search and RescueOperationsrdquoComplexity vol 2018 Article ID 6879419 17 pages2018
[3] L Luo Y Tang Q Lu X Chen P Zhang and X Zou ldquoA visionmethodology for harvesting robot to detect cutting points onpeduncles of double overlapping grape clusters in a vineyardrdquoComputers in Industry vol 99 pp 130ndash139 2018
[4] P Li S-H Lee and H-Y Hsu ldquoReview on fruit harvestingmethod for potential use of automatic fruit harvesting systemsrdquoin Proceedings of the 2011 International Conference on PowerElectronics and EngineeringApplication PEEA 2011 pp 351ndash366China December 2011
[5] W Wei D-T Ouyang S Lu and Y-X Feng ldquoMultiobjectivepath planning under dynamic uncertain environmentrdquo JisuanjiXuebaoChinese Journal of Computers vol 34 no 5 pp 836ndash845 2011
[6] M G Mohanan andA Salgoankar ldquoA survey of roboticmotionplanning in dynamic environmentsrdquo Robotics and AutonomousSystems vol 100 pp 171ndash185 2018
[7] X Hu L Chen B Tang D Cao and H He ldquoDynamicpath planning for autonomous driving on various roads withavoidance of static and moving obstaclesrdquo Mechanical Systemsand Signal Processing vol 100 pp 482ndash500 2018
[8] DDevaurs T Simeon and J Cortes ldquoOptimal Path Planning inComplex Cost Spaces with Sampling-Based Algorithmsrdquo IEEETransactions on Automation Science and Engineering vol 13 no2 pp 415ndash424 2016
[9] R Cui Y Li and W Yan ldquoMutual information-based multi-AUV path planning for scalar field sampling using multi-dimensional RRTrdquo IEEE Transactions on Systems Man andCybernetics Systems vol 46 no 7 pp 993ndash1004 2016
[10] CW Bac J Hemming and E J VanHenten ldquoStem localizationof sweet-pepper plants using the support wire as a visual cuerdquoComputers and Electronics in Agriculture vol 105 pp 111ndash1202014
12 Complexity
[11] L Luo Y Tang X ZouM YeW Feng andG Li ldquoVision-basedextraction of spatial information in grape clusters for harvestingrobotsrdquo Biosystems Engineering vol 151 pp 90ndash104 2016
[12] E J VanHenten J Hemming B A J VanTuijl J G Kornet andJ Bontsema ldquoCollision-free Motion Planning for a CucumberPicking Robotrdquo Biosystems Engineering vol 86 no 2 pp 135ndash144 2003
[13] G Gao G Sun J Na Y Guo and XWu ldquoStructural parameteridentification for 6 DOF industrial robotsrdquoMechanical Systemsand Signal Processing vol 113 pp 145ndash155 2018
[14] K Wei and B Ren ldquoA Method on Dynamic Path Planning forRobotic Manipulator Autonomous Obstacle Avoidance Basedon an Improved RRT Algorithmrdquo Sensors vol 18 no 2 p 5712018
[15] Y Dai and M Zhao ldquoManipulator path-planning avoidingobstacle based on screw theory and ant colony algorithmrdquoJournal of Computational and eoretical Nanoscience vol 13no 1 pp 922ndash927 2016
[16] H Pham and Q Pham ldquoTime-Optimal Path Tracking viaReachability Analysisrdquo in Proceedings of the 2018 IEEE Inter-national Conference on Robotics and Automation (ICRA) pp3007ndash3012 Brisbane QLD May 2018
[17] G Legnani F Casalo P Righettini and B Zappa ldquoA homo-geneous matrix approach to 3D kinematics and dynamics - IIApplications to chains of rigid bodies and serial manipulatorsrdquoMechanism and Machine eory vol 31 no 5 pp 589ndash6051996
[18] J Craig Introduction to Robotics Mechanics and Control 3rdedition 2015
[19] R P Paul B Shimano and G E Mayer ldquoKinematic controlequations for simple manipulatorsrdquo IEEE Transactions on Sys-tems Man and Cybernetics vol 11 no 6 pp 449ndash455 1981
[20] G Zachmann ldquoRapid collision detection by dynamicallyaligned DOP-treesrdquo in Proceedings of the 1998 IEEE VirtualReality Annual International Symposium VRAIS pp 90ndash97March 1998
[21] H Yang L Li and Z Gao ldquoObstacle avoidance path planningof hybrid harvesting manipulator based on joint configurationspacerdquoNongyeGongcheng Xuebao vol 33 no 4 pp 55ndash62 2017
[22] C Peter Robotics Vision amp Control Springer 2nd edition 2017[23] Z Daqi and Y Mingzhong ldquoSurvey on technology of mobile
robot path planningrdquo Control and Decision vol 25 no 7 pp961ndash967 2010
[24] O Khatib ldquoReal-time obstacle avoida nce for manipulators andmobile robotsrdquo International Journal of Robotics Research vol5 no 1 pp 90ndash98 1986
[25] M Fakoor A Kosari and M Jafarzadeh ldquoRevision on fuzzyartificial potential field for humanoid robot path planningin unknown environmentrdquo International Journal of AdvancedMechatronic Systems vol 6 no 4 pp 174ndash183 2015
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Complexity 11
And then the harvesting sequence and the anticollision pathpoints were calculated by using the energy optimal and theartificial potential field The virtual tests based on virtualreality were performed to validate the performance of theproposed algorithm Through the virtual simulation test ofthe harvesting path planning the three-dimensional spacepath points of the end-effector of the harvesting manipulatorwere calculated in real time in virtual environment andthe collision detection is analyzed The success rate wasup to 90 It can be known that the simulation systemdesigned in this study has a good practical value to helptest and improve the intelligent behavior algorithm of therobot
To obtain an optimal harvesting path taking the sumof the joint angle of the weighted rotation as the goalthe harvesting sequence planning objective function of thesix-DOF harvesting manipulator is established by usingthe minimum energy principle and the minimum energyconsumption sequence can be obtained by calculating thevalue of the target function In addition the mapping modelof obstacles in the joint configuration space is built on thebasis of sampling method and the artificial potential fieldis used to search the obstacle avoidance path in the jointconfiguration space which improves the generality of thealgorithm However due to the proposed algorithm adoptsrandom sampling strategy the sampling points may collidewith the obstacles so it is necessary to resample If thenumber of maximum sampling point is too small the failureprobability of the path planning increases And if the numberofmaximumsampling point value is too large it will cause thepath to not exist or be difficult to find or the planning time istoo long So the parameters need test repeatedly
6 Conclusion
To conduct an undamaged robotic grape-harvesting in anunstructured vineyard a path planning strategies based onminimum energy and artificial potential field for grapeharvesting robot was developed in this studyThe kinematicalmodel of Six-DOF serial manipulator was firstly constructedby using the D-H method the model of obstacles wasdefined by the axis-aligned bounding box and then theconfiguration space of harvesting robot was described bycombining the obstacles and robot Then the harvestingsequence in path planning was computed by energy optimalmethod and the anticollision path points were generatedbased on the artificial potential field and sampling searchingmethod Finally to verify and test the proposed path planningalgorithm a virtual test system based on virtual reality wasdeveloped 10 times harvesting tests for grape anticollisionpath planning were implemented on the developed sim-ulation system and the success rate was up to 90 Inconclusion the developed approach can effectively plan acollision-free path for the grape harvesting robot in the com-plex vineyard environment However when facing multipleoverlapped and adjoining grape clusters the path planning isstill an issue that needs to be solved and will require furtherresearch
Data Availability
The grape harvesting robot data used to support the findingsof this study are available from the corresponding authorupon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
This work was supported by grants from the National Nat-ural Science Foundation of China (no 51705365) and theNational Key Research and Development Program of China(2017YFD0700100)
References
[1] M A Hossain and I Ferdous ldquoAutonomous robot pathplanning in dynamic environment using a new optimizationtechnique inspired by bacterial foraging techniquerdquo Roboticsand Autonomous Systems vol 64 pp 137ndash141 2015
[2] V San JuanM Santos and JM Andujar ldquoIntelligentUAVMapGeneration and Discrete Path Planning for Search and RescueOperationsrdquoComplexity vol 2018 Article ID 6879419 17 pages2018
[3] L Luo Y Tang Q Lu X Chen P Zhang and X Zou ldquoA visionmethodology for harvesting robot to detect cutting points onpeduncles of double overlapping grape clusters in a vineyardrdquoComputers in Industry vol 99 pp 130ndash139 2018
[4] P Li S-H Lee and H-Y Hsu ldquoReview on fruit harvestingmethod for potential use of automatic fruit harvesting systemsrdquoin Proceedings of the 2011 International Conference on PowerElectronics and EngineeringApplication PEEA 2011 pp 351ndash366China December 2011
[5] W Wei D-T Ouyang S Lu and Y-X Feng ldquoMultiobjectivepath planning under dynamic uncertain environmentrdquo JisuanjiXuebaoChinese Journal of Computers vol 34 no 5 pp 836ndash845 2011
[6] M G Mohanan andA Salgoankar ldquoA survey of roboticmotionplanning in dynamic environmentsrdquo Robotics and AutonomousSystems vol 100 pp 171ndash185 2018
[7] X Hu L Chen B Tang D Cao and H He ldquoDynamicpath planning for autonomous driving on various roads withavoidance of static and moving obstaclesrdquo Mechanical Systemsand Signal Processing vol 100 pp 482ndash500 2018
[8] DDevaurs T Simeon and J Cortes ldquoOptimal Path Planning inComplex Cost Spaces with Sampling-Based Algorithmsrdquo IEEETransactions on Automation Science and Engineering vol 13 no2 pp 415ndash424 2016
[9] R Cui Y Li and W Yan ldquoMutual information-based multi-AUV path planning for scalar field sampling using multi-dimensional RRTrdquo IEEE Transactions on Systems Man andCybernetics Systems vol 46 no 7 pp 993ndash1004 2016
[10] CW Bac J Hemming and E J VanHenten ldquoStem localizationof sweet-pepper plants using the support wire as a visual cuerdquoComputers and Electronics in Agriculture vol 105 pp 111ndash1202014
12 Complexity
[11] L Luo Y Tang X ZouM YeW Feng andG Li ldquoVision-basedextraction of spatial information in grape clusters for harvestingrobotsrdquo Biosystems Engineering vol 151 pp 90ndash104 2016
[12] E J VanHenten J Hemming B A J VanTuijl J G Kornet andJ Bontsema ldquoCollision-free Motion Planning for a CucumberPicking Robotrdquo Biosystems Engineering vol 86 no 2 pp 135ndash144 2003
[13] G Gao G Sun J Na Y Guo and XWu ldquoStructural parameteridentification for 6 DOF industrial robotsrdquoMechanical Systemsand Signal Processing vol 113 pp 145ndash155 2018
[14] K Wei and B Ren ldquoA Method on Dynamic Path Planning forRobotic Manipulator Autonomous Obstacle Avoidance Basedon an Improved RRT Algorithmrdquo Sensors vol 18 no 2 p 5712018
[15] Y Dai and M Zhao ldquoManipulator path-planning avoidingobstacle based on screw theory and ant colony algorithmrdquoJournal of Computational and eoretical Nanoscience vol 13no 1 pp 922ndash927 2016
[16] H Pham and Q Pham ldquoTime-Optimal Path Tracking viaReachability Analysisrdquo in Proceedings of the 2018 IEEE Inter-national Conference on Robotics and Automation (ICRA) pp3007ndash3012 Brisbane QLD May 2018
[17] G Legnani F Casalo P Righettini and B Zappa ldquoA homo-geneous matrix approach to 3D kinematics and dynamics - IIApplications to chains of rigid bodies and serial manipulatorsrdquoMechanism and Machine eory vol 31 no 5 pp 589ndash6051996
[18] J Craig Introduction to Robotics Mechanics and Control 3rdedition 2015
[19] R P Paul B Shimano and G E Mayer ldquoKinematic controlequations for simple manipulatorsrdquo IEEE Transactions on Sys-tems Man and Cybernetics vol 11 no 6 pp 449ndash455 1981
[20] G Zachmann ldquoRapid collision detection by dynamicallyaligned DOP-treesrdquo in Proceedings of the 1998 IEEE VirtualReality Annual International Symposium VRAIS pp 90ndash97March 1998
[21] H Yang L Li and Z Gao ldquoObstacle avoidance path planningof hybrid harvesting manipulator based on joint configurationspacerdquoNongyeGongcheng Xuebao vol 33 no 4 pp 55ndash62 2017
[22] C Peter Robotics Vision amp Control Springer 2nd edition 2017[23] Z Daqi and Y Mingzhong ldquoSurvey on technology of mobile
robot path planningrdquo Control and Decision vol 25 no 7 pp961ndash967 2010
[24] O Khatib ldquoReal-time obstacle avoida nce for manipulators andmobile robotsrdquo International Journal of Robotics Research vol5 no 1 pp 90ndash98 1986
[25] M Fakoor A Kosari and M Jafarzadeh ldquoRevision on fuzzyartificial potential field for humanoid robot path planningin unknown environmentrdquo International Journal of AdvancedMechatronic Systems vol 6 no 4 pp 174ndash183 2015
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
12 Complexity
[11] L Luo Y Tang X ZouM YeW Feng andG Li ldquoVision-basedextraction of spatial information in grape clusters for harvestingrobotsrdquo Biosystems Engineering vol 151 pp 90ndash104 2016
[12] E J VanHenten J Hemming B A J VanTuijl J G Kornet andJ Bontsema ldquoCollision-free Motion Planning for a CucumberPicking Robotrdquo Biosystems Engineering vol 86 no 2 pp 135ndash144 2003
[13] G Gao G Sun J Na Y Guo and XWu ldquoStructural parameteridentification for 6 DOF industrial robotsrdquoMechanical Systemsand Signal Processing vol 113 pp 145ndash155 2018
[14] K Wei and B Ren ldquoA Method on Dynamic Path Planning forRobotic Manipulator Autonomous Obstacle Avoidance Basedon an Improved RRT Algorithmrdquo Sensors vol 18 no 2 p 5712018
[15] Y Dai and M Zhao ldquoManipulator path-planning avoidingobstacle based on screw theory and ant colony algorithmrdquoJournal of Computational and eoretical Nanoscience vol 13no 1 pp 922ndash927 2016
[16] H Pham and Q Pham ldquoTime-Optimal Path Tracking viaReachability Analysisrdquo in Proceedings of the 2018 IEEE Inter-national Conference on Robotics and Automation (ICRA) pp3007ndash3012 Brisbane QLD May 2018
[17] G Legnani F Casalo P Righettini and B Zappa ldquoA homo-geneous matrix approach to 3D kinematics and dynamics - IIApplications to chains of rigid bodies and serial manipulatorsrdquoMechanism and Machine eory vol 31 no 5 pp 589ndash6051996
[18] J Craig Introduction to Robotics Mechanics and Control 3rdedition 2015
[19] R P Paul B Shimano and G E Mayer ldquoKinematic controlequations for simple manipulatorsrdquo IEEE Transactions on Sys-tems Man and Cybernetics vol 11 no 6 pp 449ndash455 1981
[20] G Zachmann ldquoRapid collision detection by dynamicallyaligned DOP-treesrdquo in Proceedings of the 1998 IEEE VirtualReality Annual International Symposium VRAIS pp 90ndash97March 1998
[21] H Yang L Li and Z Gao ldquoObstacle avoidance path planningof hybrid harvesting manipulator based on joint configurationspacerdquoNongyeGongcheng Xuebao vol 33 no 4 pp 55ndash62 2017
[22] C Peter Robotics Vision amp Control Springer 2nd edition 2017[23] Z Daqi and Y Mingzhong ldquoSurvey on technology of mobile
robot path planningrdquo Control and Decision vol 25 no 7 pp961ndash967 2010
[24] O Khatib ldquoReal-time obstacle avoida nce for manipulators andmobile robotsrdquo International Journal of Robotics Research vol5 no 1 pp 90ndash98 1986
[25] M Fakoor A Kosari and M Jafarzadeh ldquoRevision on fuzzyartificial potential field for humanoid robot path planningin unknown environmentrdquo International Journal of AdvancedMechatronic Systems vol 6 no 4 pp 174ndash183 2015
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