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Mobile Robotics and Group Coordination
Dra. America B. Morales Dıaz
Hugo Gutierrez FloresFlabio Dario Mirelez DelgadoHector Manuel Perez Villeda
Robotics and advanced manufacturing
April 30, 2014
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Outline1 Introduction
Aim2 Coordination of an unicycle robot group
Simulation controlExperiments
3 Different topologies analysisAnalysisExperiments
4 Collision avoidance strategyDefinitionSimulationsExperiments
5 Delay problem analysis6 Conclusions and future trends
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 2 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Aim
Main purposes
To keep a robot group in a formation.
To merge and remove robots.
To test different topologies in an robot group.
Collision avoidance.
The delay effect.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 3 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Simulation controlExperiments
Fig. 1 : The actual and desired coordinates of the unicycle eq. (1).
xi = vi cos(θi)
yi = vi sin(θi) (1)
θi = ωi
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 4 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Simulation controlExperiments
xei = cosθi(xri − xi) + sinθi(yri − yi)
yei = −sinθi(xri − xi) + cosθi(yri − yi) (2)
θei = θri − θi
xei = ωiyei − vi + vricosθei
yei = −ωixei + vrisinθei (3)
θei = ωri − ωi
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 5 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Simulation controlExperiments
Fig. 2 : A formation composed of 4 vehicles with a known virtualcenter.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 6 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Simulation controlExperiments
all-to-all syncronization control
vi = vri cos θei + Kxi
[xei +
n∑j=1
C xij (xei − xej )
](4)
ωi = ωri + Kθiθei + vrisin θeiKCyi
θeiαi+[
yei +n∑
j=1
C yij (y e
i − y ej )
]; for i 6= j (5)
with αi =√
K 2 + (xei)2 + (yei)2 +∑n
j=1 [(xei − xej)2 + (yei − yej)2]
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 7 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Simulation controlExperiments
−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8
−0.4
−0.2
0
0.2
0.4
0.6
xri,x
i
yr i,y
i
x
1(0),y
1(0)
Robot1
x2(0),y
2(0)
Robot2
x3(0),y
3(0)
Robot3
Trajectory
Fig. 3 : Tracking evolution with control (4) and (5) for three robotsswarm.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 8 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Simulation controlExperiments
0 5 10 15 20 25 30 35 40 45 50−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
time (seconds)
x ei,
x ei−
x ej
Tracking and coupling errors
x
e1
xe2
xe3
xe1
−xe2
xe1
−xe3
xe2
−xe3
0 5 10 15 20 25 30 35 40 45 50
−0.5
0
0.5
1
time (seconds)
y ei,
y ei−
y ej
y
e1
ye2
ye3
ye1
−ye2
ye1
−ye3
ye2
−ye3
Fig. 4 : Evolution of cartesian and angular tracking and coupling errorsfor three coupling robots with control.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 9 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Simulation controlExperiments
−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
xri,x
i
yri,
yi
Cartesian trajectories
x1(0),y
1(0)
Robot1
x2(0),y
2(0)
Robot2
x3(0),y
3(0)
Robot3
Trajectory
Fig. 5 : Entrance of a new element in the formation.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 10 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Simulation controlExperiments
−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
xri, x
i
yri, y
i
Cartesian trajectories
x
1(0),y
1(0)
Robot1
x2(0),y
2(0)
Robot2
x3(0),y
3(0)
Robot3
Fig. 6 : Three robots synchronized in experiments: entrance of robot 2.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 11 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Simulation controlExperiments
0 50 100 150 200−1
−0.5
0
0.5
1
1.5
2
time (seconds)
i (
rad/s
)
Angular velocity
Robot 1
Robot 2
Robot 3
DisturbanceRobot 2
DisturbanceRobot 1
Disturbance inRobot 1
Disturbance inRobot 2 Robot 2
enters to theformation
Fig. 7 : Angular velocity for control in experiments: entrance of robot2.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 12 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Simulation controlExperiments
−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
xri, x
i
yri, y
i
Cartesian trajectories: multiple merging
x
1(0),y
1(0)
Robot1
x2(0),y
2(0)
Robot2
x3(0),y
3(0)
Robot3
x4(0),y
4(0)
Robot4
x5(0),y
5(0)
Robot5
x6(0),y
6(0)
Robot6
merging ofnew robots
Fig. 8 : Incorporation of several robots with controller in experiments:XY coordinates.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 13 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
AnalysisExperiments
all-to-all syncronization control
Position and coupling errorsconverge to zero in the faceof a perturbation.
Each individual robotcontroller needs the stateinformation of all the othersrobots.
The computation timeincreases with the number ofrobots.
The transient has aunderdamped behavior.
Fig. 9 : Mutual couplings graph.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 14 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
AnalysisExperiments
different conectivities
Fig. 10 : Different couplings between robots.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 15 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
AnalysisExperiments
Experimental setup
Fig. 11 : Setup Arena. Fig. 12 : E-puck robots.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 16 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
AnalysisExperiments
Experimental formation example
Fig. 13 : Square formation.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 17 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
AnalysisExperiments
Accumulated errors
Etrack =1
T
n∑i=1
exi +n∑
i=1
eyi
n∑i=1
eθi (6)
Ecoup =1
T
n∑i=1
ecxi +n∑
i=1
ecyi
n∑i=1
ecθi (7)
Etotal = Etrack + Ecoup (8)
where exi , eyi , eθi are the position errors, ecxi , ecyi are the couplingerrors and T is the sampling time.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 18 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
AnalysisExperiments
Results: configuration A and F
0 20 40 60 80 100 1200
5
10Accumulated tracking error
0 20 40 60 80 100 1200
0.2
0.4Accumulated coupling error
0 20 40 60 80 100 1200
5
10Total acumulated error
Time (seg)
Fig. 14 : Accum. errors, config.A.
0 20 40 60 80 100 1200
5
Accumulated tracking error
0 20 40 60 80 100 1200
0.2
0.4Accumulated coupling error
0 20 40 60 80 100 1200
5
Total accumulated error
Time (seg)
Fig. 15 : Accum. errors, config.F.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 19 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
DefinitionSimulationsExperiments
Collision avoidance strategy
Fig. 16 : AvoidanceRegions.
dij =√
(xi − xj)2 + (yi − yj)2
Ω =([xy ] : (x , y) ∈ R2, dij ≤ r
)Γ =
([xy ] : (x , y) ∈ R2, r < dij ≤ R
)
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 20 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
DefinitionSimulationsExperiments
Definition of regions
Fig. 17 : Potential function.
f ci = 1− 1
1000 exp(−50dij)
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 21 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
DefinitionSimulationsExperiments
Change on the reference trajectory
New position on the local frame
p′yi = pyi + δi fci (9)
Velocities on the inertial frame
x ′ri = xri − δi fci sin θri − δi fci ∗ ωri cos(θri) (10)
y ′ri = yri − δi fci cos θri + δi fci ∗ ωri sin(θri) (11)
Accelerations on the inertial frame
x ′ri = xri − (δi fci − δi fciω2ri) sin(θri) + (2δi fciωri ...
−δi fci ωri) cos(θri) (12)
y ′ri = yri + (δi fci − δi fciω2
ri) cos(θri) + (2δi fciωri ...
−δi fci ωri) sin(θri) (13)Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 22 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
DefinitionSimulationsExperiments
Simulation: two robots
Two robots in the same path, opposite directions.
−0.5 0 0.5
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
1 2
Cartesian coordinates
xri, xi
yri,y
i
x1(0),y
1(0)
Robot1
Reference
x2(0),y
2(0)
Robot2
Fig. 18 : Cooperative collision avoidance betweeen two robots.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 23 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
DefinitionSimulationsExperiments
Results: errors
0 20 40 60 80 100 120−0.1
0
0.1X errors
me
ters
0 20 40 60 80 100 120−0.1
0
0.1Y errors
me
ters
0 20 40 60 80 100 120−0.2
0
0.2theta errors
rad
time(sec)
Fig. 19 : Data acquisition for our collision avoidance strategy.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 24 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
DefinitionSimulationsExperiments
Simulation: Two formations
Two formations in the same path, opposite directions.
−1 −0.5 0 0.5 1−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
1 23
4
5
6
Cartesian coordinates
xri, xi
yri,yi
Robot1
Robot2
Robot3
Robot4
Robot5
Robot6
Fig. 20 : Cooperative collision avoidance betweeen two formations
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 25 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
DefinitionSimulationsExperiments
Experiments: Implementation
Fig. 21 : Data acquisition for our collision avoidance strategy.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 26 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
DefinitionSimulationsExperiments
Inertial data adquisition
Fig. 22 : Microcontroller Arduino board with embedded IMU.Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 27 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
DefinitionSimulationsExperiments
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 28 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
DefinitionSimulationsExperiments
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 29 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
DefinitionSimulationsExperiments
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 30 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
DefinitionSimulationsExperiments
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 31 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 32 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 33 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 34 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 35 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 36 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Conclusions and future trends
Group coordination in a robot group is an interesting topic that hasbeen receive a lot of attention the las decade.
Many applications have been done: drones, surveillance, maprecognition, exploration, in the fuel company, among others.
Future trends can be encountered in:
Automated highways (AHDA see:https://www.youtube.com/watch?v=4pMO475heog)Manufacturing systems (see Kiva Systems,https://www.youtube.com/watch?v=lWsMdN7HMuA).
In the future trends we have coordination in unstructuredenvironments for service robot at home and also in the industry ingeneral for un identical robots.
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 37 / 38
IntroductionCoordination of an unicycle robot group
Different topologies analysisCollision avoidance strategy
Delay problem analysisConclusions and future trends
Thanks!, questions?
america.morales,hugo.gutierrez,hector.perez,[email protected]
Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 38 / 38