Computers and Electronics in Agriculture 98 (2013) 175–182

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Computers and Electronics in Agriculture

journal homepage: www.elsevier .com/locate /compag

Real-time positioning algorithm for variable-geometry air-assistedorchard sprayer

0168-1699/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.compag.2013.08.013

⇑ Corresponding author. Tel.: +386 14 77 14 53.E-mail address: aljaz.osterman@fs.uni-lj.si (A. Osterman).

Aljaz Osterman a,⇑, Tone Godeša b, Marko Hocevar a, Brane Širok a, Matej Stopar b

a Faculty of Mechanical Engineering, University of Ljubljana, Aškerceva 6, 1000 Ljubljana, Sloveniab Agricultural Institute of Slovenia, Hacquetova ulica 17, 1000 Ljubljana, Slovenia

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 January 2013Received in revised form 19 June 2013Accepted 13 August 2013

Keywords:Laser scannerLIDARPositioning algorithmOrchard sprayingVariable-geometry sprayerCanopy contour

An algorithm for positioning of spraying arms based on laser scanner measurements for a variable-geom-etry air-assisted orchard sprayer is proposed. Functioning of the algorithm is presented for a real sprayerintended for experimental spraying in orchards, which has three hydraulically movable spraying armsthat cover one side of a row of trees. The developed algorithm is based on realtime measurements of treecanopies from a laser scanner mounted on the sprayer. According to the measured canopies of trees thespraying arms move linearly and angularly in a plane perpendicular to the row so that spraying nozzleswhich are located at the ends of the arms are optimally positioned. The algorithm calculates the optimalposition for each of the three height segments of a tree (each covered by one arm) based on a simplifiedcontour of the measured canopy of the corresponding row section. Inside the height segments the con-tour is simplified with a linear approximation using the least-squares method. The optimal position foreach arm is then calculated so that the nozzle is directed normally to the linear fit of the contour at a dis-tance for which full coverage of the tree height segment is achieved. The coverage is calculated with con-sideration of the spray angle. Due to sometimes great displacements between positions in consecutivetime steps, calculated positions in each time step may not always be reachable in a real operation ofthe sprayer. Such great displacements are mainly a result of variable growth of trees and angular sensi-tivity of the algorithm. The latter is expressed when a change in the contour shape causes a changeddirection of a normal which further on causes a change in the position of the arm. This change of positioncan be interpreted in relation to the change of the contour shape as amplified proportionally to the dis-tance between the arm and the linear fit. To obtain physically feasible displacements, calculated positionswere smoothed using the unweighted moving average. The effect of moving average width is alsodescribed in the results.

With more target-directed spraying it is expected that the drift and ground deposits of pesticides canbe reduced. In addition, more effective spraying enables changes in the effective dose, resulting in smalleramounts of pesticides used.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

On the basis of general technological development the use ofcertain methods of measurement in agriculture is becomingincreasingly economically viable. Together with the expansionand transfer of technologies from other areas the challengesassociated with the transfer of appropriate horticulture-adaptedalgorithms (which make the technologies functional) are emerg-ing. As far as improvements of spraying in orchards are concerned,the following are a few examples of different assisting techniquesintroduced so far. As there are some common features betweenspraying in orchards and vineyards, examples of spraying in vine-yards are also considered when appropriate.

Gil et al. (2007) used ultrasonic sensors in vineyards to changespraying flow rate proportionally to estimated canopy volume.They also used a sprayer with individual spraying arms which werefixed due to less pronounced height variations in vine. Ultrasonicsensors were similarly used by Jejcic et al. (2011) for nozzle controlin orchard spraying applications. Nozzle control based on imageprocessing from an RGB camera was presented by Hocevar et al.(2010) together with sprayer upgrades. The orchard sprayer wasupgraded with continuously movable spraying arms. Llorens et al.(2010) continued the work of Gil et al. and in 2011 (based on asimilar experimental set-up) they compared ultrasonic sensors toa laser scanner with regard to vineyard spraying. Before that, laserscanner measurements in orchards were already performed byWalklate et al. in 2002. Apart from these assisting techniques usedfor better spraying, another one makes use of numericalsimulations. Many contributions were presented by Endalew et al.

Fig. 1. Sprayer with sensors and manipulators (1 – laser scanner with protectivehousing, 2 – computer box, 3 – electric box with electronics for hydraulic valves, 4 –electro-hydraulic valves for moving sprayer arms, 5 – sprayer arms and air ducts, 6– trailed air-assisted sprayer, 7 – radial fan).

176 A. Osterman et al. / Computers and Electronics in Agriculture 98 (2013) 175–182

(2010a,b,c) who dealt with air-assisted orchard spraying on thebasis of computational fluid dynamics. Completely different simu-lations were performed by Méndez et al. (2012) who simulated anartificial orchard to estimate the performance of a laser scanner.

The presented assisting techniques deal with key issues suchas consumption of pesticides, proper coverage, and reduction ofundesirable pesticide losses (into soil, air and water). Spraydeposits issues are still relevant as shown by recent publications(Endalew et al., 2010c; Llorens et al., 2011). The relevance is evengreater when considering the commitment of the EU policytowards a reduced pesticide use (Hillocks, 2012). Despite thelarge number of the aforementioned problems, possible solutionscan be found in variable spraying. Such spraying adapts to targetshape (multiple plants, one plant or a part of a plant) with vari-able spraying rate (apart from those mentioned in the previousparagraph also Siegfried et al., 2007; Jeon et al., 2011; Walklateet al., 2011).

However as Cross et al. (2001) showed for air-assisted orchardspraying, the drift is inversely proportional to tree size which leadsto an alternate approach which is to modify sprayer shape accord-ing to target shape. Considering the wide availability of sprayerswith moving spraying geometry (similar to the one presented byHocevar et al. (2010)) our approach was to investigate automaticpositioning of spraying arms with regards to tree canopy shape.Targeted spraying of the crowns in an orchard is expected to atleast partially compensate for the effect of changing tree size andthus contribute to more efficient spray delivery. The following pa-per does not deal with analyses of efficiency or of economic aspectsbut presents in details a positioning algorithm based on laser scan-ner measurements of the canopy. As the proposed positioningalgorithm is intended for real-time application, alternative mea-surement techniques such as 3D laser scanner or stereo visionare not suitable in our case because they are still too slow (Seidelet al., 2011, 2012, Rosell and Sanz, 2012). Compared to aerialmeasurements (Dean et al., 2009) a terrestrial laser scanner waspreferably used because it has been assumed that for more effi-cient spraying not only the height of trees is important but inour case also the positioning of the arms relatively to real contourshape to obtain a more uniform coverage. There are also other dif-ferences between the two approaches. As far as the price of a laserscanner is concerned, access to a database of aerial measurementsmay be cheaper. However, additional costs would arise because ofthe precise positioning equipment (e.g., GPS) needed for a sprayer.On the other hand, our approach ensures a certain level of auton-omy as spraying process would not be dependent on the availabil-ity of aerial data or the degree of how up to date they are(Wellington et al., 2012).

This paper first briefly describes the sprayer with moving spray-ing arms, followed by a description of the laser scanner and themeasurements. The paper continues with a detailed descriptionof the algorithm. Afterwards results present an application of thealgorithm to the measurements along the whole row of trees inan orchard. Discussion covers some aspects of sensitivity analysisfor the main parameters of the algorithm and is followed by somegeneral conclusions.

Fig. 2. Spraying arms with eight degrees of freedom (DF) positioned according tothe shape of a tree canopy in the upper (U), middle (M) and lower (L) zone. Fittedcanopy segments are described with (x, y, H) where x and y are coordinates of themidpoint and H is angle of the normal.

2. Materials and methods

The positioning algorithm is based on the functionality of theprototype sprayer used by Hocevar et al. (2010). Here only a verybrief presentation of the sprayer is given, for more details see thereference. The sprayer (Fig. 1) is an air-assisted sprayer with threehydraulically movable spraying arms for spraying one side of a rowof trees. Each arm covers one height segment of a row. Ends ofarms are equipped with spraying nozzles and air spouts. Moving

of the spraying arms to the desired locations is based on an inversekinematics algorithm which basically provides numerical solutionsfor actuation of hydraulic cylinders of all eight degrees of freedom(Fig. 2). The coordinate system of the spraying arms is Cartesian(moving with the sprayer).

The experiments were done in the research orchard of Brdo priLukovici (46�100N, 14�400E, the Agricultural Institute of Slovenia).The measurements were performed on spindle trained apple treeson cultivars ‘Breaburn’ and ‘Jonagold’, grafted on M.9 rootstock at1.5 m spacing and 3.5 m inter-row distance. The trees were fullyfoliated. They were planted in autumn 2006 and spring 2012, theiraverage height was 3 m (max. 3.5 m).

For the measurements of canopy shape SICK LMS 111 laserscanner (SICK AG Waldkirch, Reute, Germany) was used. It wasconnected to a computer (with the Intel Core i5-3570 processorand a solid-state drive) in a computer box (Fig. 1) via TCP/IP andwas accessed with a NI LabVIEW program (National InstrumentsCorporation, Austin, TX, USA) using a custom driver. Laser scannerdata (raw) are in a cylindrical coordinate system. For the purpose

Fig. 3. Simplified schematic representation of the positioning algorithm.

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of the positioning algorithm they were transformed to a Cartesiancoordinate system of the spraying arms. The laser scanner wasmounted on the sprayer 2.4 m ahead of the spraying arms and2 m from the ground. It has a view of 270� but due to the one-sidedexperimental sprayer design only the measurements from one sideof the sprayer were used (viewing angle of 135�). The measuringplane of the laser scanner was perpendicular to the row and thetractor-sprayer axis. The scanner was operating at 50 Hz acquisi-tion rate with angular resolution of 0.5�. At a distance of 3 m fromthe scanner (which is more than half of the inter-row distance pluscanopy thickness) this gives minimal vertical distance between themeasured points of approx.2.6 cm. During the measurements thespeed of the tractor was chosen in such a way that horizontal dis-placements between consecutive measurements were 2.5 cm andwas equal to 4.5 km/h. The distance-dependent diameter of a mea-sured point is the distance [mm] � 0.015 rad + 8 mm (SICK, 2012).At a distance of 3 m the expanding laser beam has a diameter of53 mm. For our case this means that scanning was without gapsin horizontal and vertical direction. Scanning range for the deviceis dependent on remission of laser light. Remission of 100% is de-fined for perfectly diffuse reflecting white surface. However, upto a distance of 10 m remission of only 3% is needed. Such sensitiv-ity may also be interpreted as reduced target size. For the beamdiameter of 53 mm the correspondingly reduced target size has adiameter of only 9 mm. Due to this laser scanner is able to measurestructures with a high level of detail (Béland et al., 2011, Keightleyand Bawden, 2010). Real remission of targets (leaves, branches,trunks, fruits) varies a lot with their inclination, surface qualityand color but this simple calculation gives an idea of the physicalrepresentation of the measurements. Following on from here an-other aspect related to spatial representation of measurementsshould be considered. Maximum precision of the coordinates ofthe measured objects is half of the beam width. Due to overlappingof beam points it can happen that one relatively small object(smaller than the distance between center points but still big en-ough to be detected) is measured twice. This makes the interpreta-tion of measurements (reconstruction of canopy shape) difficultand only partially reliable. Such conclusions are in accordance withthe lower correlation values obtained in LIDAR simulations byMéndez et al. (2012).

The laser scanner measurements used for the development andanalysis of the positioning algorithm were obtained with orchardmeasurements under the same conditions as in real spraying (thelaser scanner was mounted on a trailed sprayer which was spray-ing the canopy). Based on this the algorithm itself was developedin an artificial orchard environment in MATLAB.

3. Positioning algorithm

It is important to distinguish between the so-called inversekinematics algorithm and the positioning algorithm. It can be saidthat the positioning algorithm gives the coordinates of the spray-ing arms and the inclinations of the nozzles (answers Where?)while the inverse kinematics algorithm is there to reach them(answers How?). Therefore the inverse kinematics algorithm isspecific for each sprayer design while the positioning algorithmcan be applied more generally. In this way different variable-geom-etry sprayer designs could operate using the same positioningalgorithm which is why we believe this algorithm is of a widerinterest.

The algorithm is schematically shown in Fig. 3. At a given posi-tion along the row, measured points are sent from the laser scan-ner to the computer and are imported (big arrow at the top) intothe main spraying program and further into the positioningalgorithm module (square block). To simplify the terms, from

now on all measured points from one position along the row(one set) are referred to as one ‘measurement’. Inside the blockseveral steps of the algorithm are listed which will be describedshortly. After the points are consolidated, the outer contour ofthe canopy is determined. Then the contour is approximated withlinear segments corresponding to the number of the spraying armsand for each segment a normal is calculated. Next, the algorithmcalculates two possible positions for each spraying arm. Based onspray angle the first position is calculated for optimum coverageof the canopy segment. The second position is calculated so thatthere is no possibility of contact between the spraying arm andthe canopy. As regards the positioning of the spraying arm, thearm that is chosen is the one for which its distance to the fit islarger. Final step of the algorithm deals with smoothing of theconsecutive required positions to facilitate real movements of thespraying arms. The output of the spraying algorithm appears atthe bottom of the block and represents smoothed positions ofthe spraying arms. These positions are used as an input for inversekinematics algorithm that for example sends controls to the elec-tro-hydraulic valves for movements of spraying arms cylinders.

The required time of the positioning algorithm to processmeasurements for one position is around 5 ms and is estimatedto be suitable for real-time spraying application. Due to simplemathematical functions used in it, the algorithm can be easilytranslated/applied to other programming languages. The algorithmtreats all arms equally and therefore the number of arms in differ-ent sprayer designs can be easily adjusted (increased).

3.1. Determination of the canopy contour

After transformation of measured points from cylindrical toCartesian coordinates the points that are out of interest are elimi-nated. Such points are for example measurements of protectivenetting above the trees or other rows behind the one currentlybeing sprayed. As pesticide deposit gets smaller with distance froma sprayer (Walklate et al., 2011), the algorithm can for simplicityreasons take into account only points from the closest half of therow, having regard that the other half is sprayed from the otherside. This distance (from the laser scanner to the middle of the can-opy) can be determined continuously with extrapolation from themeasured trunks (points between the lowest branches and groundvegetation) or set constant for a whole row as an approximation(e.g., half of the inter-row distance). Both approaches are suitable

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as the algorithm extracts the canopy contour from the nearestpoints while the points from the middle of the row are normallyfurther.

The remaining points are grouped in bands by height. The bandshave constant width and from each band a point with the smallestx-coordinate (row depth) is chosen for the contour. In Fig. 4, threeexamples for different band heights (0.05, 0.2 and 0.5 m) areshown. While the contour of 0.5 m-bands is clearly not representa-tive for the measured canopy (circles), the one from 0.2 m-bandsalready gives some idea about the canopy shape. For the algorithm,bands of 0.05 m are chosen which give very detailed contours. Fur-ther reduction in the band width does not make sense because0.05 m is already at the level of individual leaves (and branches)and close to the spatial resolution of the scanner.

Although in Fig. 3 it is indicated that the algorithm starts with asingle measurement from which canopy contour is later deter-mined, it is in practice determined from several consecutive mea-surements. Such approach was chosen to minimize the effect ofholes in the canopy that occur between individual branches.Consistently very good results (e.g., measurements in Fig. 4) wereobtained for 5 measurements which cover about 15 cm of the can-opy length.

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Fig. 5. Positions of the spraying arms for a given contour shape and a spray angle of135�.

3.2. Contour fitting and positions of the spraying arms

In the next step the contour is divided in three height zoneseach corresponding to one spraying arm. In Fig. 5 zone limits arepresented with continuous horizontal lines. The lowest limit is

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Fig. 4. Comparison of canopy contours based on bands of different heights.

set to 0.5 m as no direct spraying was intended below that height.The limit of 0.5 m is chosen because it is expected that few lowertargets will be nevertheless adequately covered with spray dueto the surrounding turbulent air flow and spray drift. Alternativelythe lowest limit can be set to zero (ground height) or can be deter-mined from laser scanner measurements similarly as the height ofthe trees. Zones are equally high. Their heights are determinedwith regard to the current tree height. Points of the contour (mark-ers in a diamond shape) in each zone are approximated with a lin-ear fit based on the least-squares method. These fits are presentedin Fig. 5 with dashed lines.

For efficient spraying it is assumed that the best results areachieved if air flow with pesticide droplets is blown directly tothe canopy. It is so because of many factors. First, penetration ofthe air flow through the canopy is better. Secondly, the effect ofdrift is reduced when spray travels shorter distance. Thirdly, orien-tation of leaves can be regarded as isotropic so as far as they areconcerned there is no preferable direction for spraying that wouldcontradict the arguments mentioned before. Consequently airspouts and pesticide nozzles should be directed towards the can-opy in such a way that their orientation is normal to the canopysurface.

Let us continue with the description of Fig. 5: perpendicularly tothe fits are normals (represented with arrows). The normals repre-sent spray directions and split the spray angle. Each normal isgoing through a point on the fit in the middle of the zone height(end points of arrows). For each zone the appropriate position ofthe spraying arm (referring to its end with an air spout and a noz-zle) from the fit is calculated on the basis of two conditions. Thefirst condition is that it lies on the normal and the second conditionis that the angle defined with an intersection of the fit with theupper zone limit, the spraying arm position and the intersectionof the fit with the lower zone limit matches the spray angle.

Parallel to the linear fits (dashed lines) are the so-calledcorrected fits (continuous lines). They have the same inclination

A. Osterman et al. / Computers and Electronics in Agriculture 98 (2013) 175–182 179

but are moved to the edge of the canopy. They are chosen to limitthe positions of the spraying arms so that they never come into thecanopy. For example, in Fig. 5 the fit in the upper zone is in themiddle deeply inside the canopy. To illustrate the use of thecorrected fit, a spray angle of 135� is chosen. For this angle the re-quired position of the spraying arm is on the right side of the cor-rected fit. Generally this means that it can be inside of the canopy.To prevent potential contact and damage, the final position of theupper arm (start point of the upper arrow marked with a star) ispositioned on the intersection between the normal and the cor-rected fit. In the middle and lower zone the required positionsbased on the spray angle are on the left side of the corrected fitsand are therefore preserved.

To summarize the positioning of the spraying arms, only geo-metrical parameters for one zone are shown in Fig. 6. Starting withh1 and h2 that mark the lower and upper height limits of the zone,a fit f is calculated for contour points between h1 and h2. A cor-rected fit cf presents the fit f shifted in such a way that it onlytouches a contour c. Point P1 lies on the fit f in the middle of h1and h2. A normal n to the fit f is chosen so that it goes throughP1. Point P2 is defined where the normal n intersects the correctedfit cf. Based on a known spray angle a point P3 is located on thenormal n (splitting a) at a distance from P1 which is such thatthe arms of the angle go through intersections between the heightlimits h1 and h2 and the fit f (points A and B). If the distance P3P1 isgreater than the distance P2P1, P3 is chosen as the spraying armposition, otherwise it is P2.

Such positioning of spraying arms is also inherently suitable forcases when canopy is wider in some part because the fit of thesection above or below the one that is wider always leans towardsit. This causes greater overlapping of spraying inside the widersection which is consequently sprayed more (at the expense ofthinner sections).

3.3. Smoothing of positions

The obtained positions of the spraying arms are justified by theprevious steps of the positioning algorithm based on measure-ments and contours but in practice they may not be reachabledue to physical limitations of the sprayer. If a distance betweentwo consecutive positions is too large it cannot move the sprayingarm from one position to another in a time step between two con-secutive measurements. Let us consider an abrupt change in a treerow (e.g., one younger tree planted within a row of mature trees)requiring an arm displacement of 0.5 m in a time step of 50 ms.

Fig. 6. Geometry model for positioning of the spraying arm.

This requires a mean speed of 10 m/s. If such movement is a uni-formly accelerated motion it results in accelerations and decelera-tions of 800 m/s2. Not only that it is impossible for any existingdrive to move spraying arms in such a way, even much smalleraccelerations would damage the sprayer and the measuring equip-ment (e.g., the laser scanner has vibration resistance of 5 g RMS at10 Hz). Although not an optimal response of the sprayer to suchchanges in a row may be accepted because they are not sofrequent, other unavoidable large displacements still remain. Theirorigin is in changing of the inclination of consecutive fits combinedwith changes of contour shapes between individual trees. Thesedisplacements increase with the growing distance of the arms fromthe fit (increases with smaller spray angle). Therefore smoothing ofcalculated positions is necessary to enable proper functioning ofthe sprayer. In the positioning algorithm smoothing is done sepa-rately for x and y coordinates (depth and height) and is based ona moving average. For the moving average a central numericalscheme is used meaning that for a certain smoothed positionprevious and also subsequent primary positions are needed. Thisapproach is better than the one using only past positions becausesuch smoothed signal better matches primary signal (without adelay). This kind of smoothing was possible because the laser scan-ner is mounted before the spraying arms (2.4 m). During the timeneeded for the spraying arms to travel along the row to a positioncorresponding to the position of the laser scanner some new mea-surements can be made. However, some of these measurementsare already needed for contour determination for which the centralscheme is also preferably used.

Fig. 7. Comparison of positions of spraying arms with regard to the canopy shape.Primary positions are marked with ‘x’, smoothed positions are marked with ‘+’.Spray angle is 80�.

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180 A. Osterman et al. / Computers and Electronics in Agriculture 98 (2013) 175–182

After the smoothing process displacements of the arms aregenerally within a centimeter range. Differences between primaryand smoothed positions at a certain position are presented inFig. 7. The measurements are the same as in Fig. 5 but a more real-istic spray angle of 80� is used. For each nozzle a spray is shown asa gray triangle. Spray is directed towards the canopy in the direc-tion indicated with the arrow. Smoothed positions of the nozzlesare marked with ‘+’ (larger arrowhead, continuous line). The otherarrows (starting from ‘x’, dashed, smaller arrowhead) show sprayorigin and direction without smoothing. The biggest difference isin the upper zone which is due to variations in the height of trees.Fig. 7 also shows good coverage of the left side of the canopy.

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Fig. 9. Lower arm x-coordinates for a segment of primary (black) and smoothed(gray) signal.

4. Results and discussion

The beginning of this section partially continues with the pre-sentation of some of the already mentioned aspects of the position-ing algorithm, although it now focuses on a larger scale (a row oftrees). Therefore an application of the positioning algorithm on asection of a row is presented. First, Fig. 8 demonstrates the resultsof smoothing for displacements calculated from consecutive posi-tions of the lower arm. Displacements computed from primarypositions (black) are compared to displacements computed fromsmoothed positions (gray). Smoothing was done with a width ofthe moving average of 5 measurements. Before smoothing, primary(before smoothing) displacements (black) are often larger than0.2 m and exceeding 0.4 m on three occasions (around measure-ment 3500). In comparison with the primary signal, displacementsof the smoothed signal (gray) are greatly reduced. They are practi-cally under 0.1 m with only one displacement exceeding 0.2 m(measurement 3500).

Fig. 9 presents x-coordinates of the lower arm in detail. Labels ofmeasurements match those in Fig. 8. It can be seen that the courseof the smoothed coordinates (gray circles) very much resemblesthe course of the primary coordinates (black crosses). Consideringthat the same smoothing algorithm was used for x and y coordi-nates these results imply that smoothed positions are very closeto primary positions. Thiscould be contrary to the expectationsbased on the greatly reduced displacements but can be explainedwith a slope of the course which is much better resolved aftersmoothing. The greatest differences in courses can be seen at ex-treme positions (peaks and valleys). They are within the range ofa few centimeters. Differences at the extremes can be reduced with

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Fig. 8. Lower arm displacements for primary (black) and smoothed (gray) signal.

a weighed moving average at the expense of slightly increaseddisplacements.

At this point a general conclusion about smoothing can be thatit represents a suitable approach for the adjustment of theoreticalpositioning results to real working conditions. In next paragraphsthe effects of some parameters of the positioning algorithm onthe displacements of the spraying arms are presented. The follow-ing parameters are considered: number of measurements for con-tour determination, spray angle and number of measurementsused for smoothing.

Considering first the number of laser scanner measurementsused for determination of canopy contour (Fig. 10, left diagram)it can be regarded as another form of averaging. Increased numberof measurements taken for contour determination causes a signif-icant decrease in size of the required displacements of the sprayingarms. Both mean value of displacements (continuous line) andtheir standard deviation (light gray, dashed line) are reduced (for50% and 44%, respectively) when number of measurements is in-creased from 5 to 20. Shapes of both curves also indicate thatincreasing of the number of measurements has a diminishing effectas these numbers get higher. Practically the maximal number ofmeasurements is limited by the acquisition and processing rate,the speed of a tractor and the distance between the spraying armsand the laser scanner. When measurements are distributed be-tween contour determination and smoothing of the spraying armspositions, smoothing should have a priority.

Another parameter that has a similar effect on displacements isspray angle (Fig. 10, right diagram). The spray angle can differ witha spout, a nozzle and operating pressure. When different sprayingangles can be chosen (mainly depending on the choice of a nozzleand a spout while operating pressure should often remain thesame for the same quality of a spray), larger spray angles are favor-able for the positioning algorithm. A comparison between calcu-lated displacements for different spray angles shows that for a100� angle their mean is 38% lower than for a 60� angle. A similardecrease is obtained for standard deviation values. These findingsconfirm a statement mentioned previously that displacements in-crease with an increasing distance of the spraying arms from thefit. In practice the algorithm is also suitable for hollow-cone noz-zles because their pattern is predominantly altered by the air flowfrom the spouts which flattens it in horizontal direction. Theemerging spray is thus consistent with the algorithm.

A similar analysis was done for the effect of a number of mea-surements used for smoothing of consecutive spraying arms posi-tions. In addition to displacements Fig. 11 also presents deviationsbetween primary and smoothed positions. They have the same

Fig. 10. Displacement of spraying arms between consecutive time steps as a function of the number of measurements for contour (left) and nozzle spray angle (right).

Fig. 11. Displacement of spraying arms between consecutive time steps anddeviation with regard to primary positions as a function of the number ofmeasurements used for smoothing.

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units as displacements therefore in Fig. 11 they both share thesame vertical axis. First thing to note is that the standard deviation(dashed lines) follows a similar course as the mean values (contin-uous lines) and so the rest of the discussion will concentrate onmean values. At first, the increasing number of measurementshas great effect on reducing the size of displacements (continuousline with diamonds). Later on this effect is reduced. At the sametime deviations between primary and smoothed positions (contin-uous line with triangles) increase faster than displacements arereduced (the slope is steeper). Intersection of the curves for themean values is approx. at 6 (the standard deviation curves inter-sect at 4). The results shown in previous figures were obtainedwith 5 measurements used for smoothing. This may be regardedas a suitable choice especially if considered with not only increas-ing deviations in view but also the number of available measure-ments before the spraying arms travel to the correspondingposition of the laser scanner measurements.

Some remarks should be given about additional algorithm fea-tures based on the laser scanner measurements. They act as logicalconstraints for outputs to valves that control the opening and clos-ing of pesticide nozzles. First example is when a gap in a row (e.g.,missing tree due to illness) is detected. In that case, all nozzles areclosed. The same happens at the end of the row. Similarly at thebeginning of the row the nozzles are not opened until the sprayingarms are next to trees. Second example when some nozzles areclosed is when trees are too small. Generally, height is divided intothirds. Below a certain threshold level height is only split in half,the upper nozzle is closed and the upper arm is not activated.For tree heights further below there is a second threshold level.When it is applied (for spraying of the smallest trees) only thelowest nozzle is open.

Regarding the evaluation of spray efficacy and drift reductionthis paper relies on previous work published in 2010 by Hocevar

et al. who used the same sprayer. Considering the results from apart of their experiment where the spraying arms were manuallypositioned, they achieved an increase of up to 67% in both coverageand number of impacts with regard to a simple vertical positioningof the spraying arms. Without the expense of using one of the var-ious experimental techniques for direct drift measurements (Crosset al., 2001; Felsot, 2005), at the same consumption these resultsclearly indicate a significant drift reduction. With the positioningalgorithm presented in the present paper the spraying arms canbetter and continuously adapt to a canopy shape and thereforethe same or better drift reduction can be reasonably expected.

5. Conclusions

The paper presents the positioning algorithm used for an up-grade of the experimental air-assisted orchard sprayer. The sprayerhas a variable geometry of spraying arms and the algorithm is usedfor automatic positioning of three hydraulically movable sprayingarms with regard to real-time laser scanner measurements so thatthey follow the shape of a sprayed canopy. In this way sprayingnozzles located at the ends of the arms are optimally positioned.The laser scanner is mounted on the sprayer in front of the spray-ing arms. The algorithm is basically platform-independent becauseit uses simple arithmetical operations. As such it is also robust andfast which is necessary for real orchard conditions and real-timeoperation.

The algorithm calculates the optimal position of the threespraying arms corresponding to the three height segments of a treecanopy so that each segment is properly covered (sprayed) by onearm. First from the closest measurements a simplified contour isextracted for one side of a row of trees (the one that is sprayed).At the same time canopy height is measured and the canopy is di-vided into three equally high segments. Inside the height segmentsparts of the contour are simplified with a linear approximationusing the least-squares method. Spraying arms are directed nor-mally to the linear fit at distances that ensure complete coverageof the tree segments. These distances are calculated according tothe spray angle. In the next step of the positioning algorithm suc-cessively calculated positions are smoothed with an unweightedmoving average. This is done to facilitate or even enable propermovements of spraying arms. Analysis of smoothed positions alongthe row shows decrease in the amplitude of required movementsof the spraying arms. At the same time the smoothed positions stillstrongly match primary calculated positions and are therefore suit-able for the desired positioning of the spraying arms relatively tothe canopy shape. In the last part of the paper some variations ofthe main parameters of the algorithm are considered. The benefi-cial effect of averaging on the reduction of displacements is shown.In a similar way reduced displacements can be obtained byincreasing the spray angle.

182 A. Osterman et al. / Computers and Electronics in Agriculture 98 (2013) 175–182

Acknowledgments

This work was funded by the EU as a part of the 7 FP researchproject CROPS (Grant Agreement Number 246252). The authorsare also grateful to the technician and tractor driver Toni Gjergekand the head of the experimental orchard Roman Mavec.

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