Presentacion Robótica

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




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.






Fig. 1 : The actual and desired coordinates of the unicycle eq. (1).

xi = vi cos(θi)

yi = vi sin(θi) (1)

θi = ωi






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






Fig. 2 : A formation composed of 4 vehicles with a known virtualcenter.






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]






−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.






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.






−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.






−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.






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.






−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.





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.





AnalysisExperiments

different conectivities

Fig. 10 : Different couplings between robots.





AnalysisExperiments

Experimental setup

Fig. 11 : Setup Arena. Fig. 12 : E-puck robots.





AnalysisExperiments

Experimental formation example

Fig. 13 : Square formation.





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.





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.





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

)






Definition of regions

Fig. 17 : Potential function.

f ci = 1− 1

1000 exp(−50dij)






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





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.






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.






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






Experiments: Implementation

Fig. 21 : Data acquisition for our collision avoidance strategy.






Inertial data adquisition

Fig. 22 : Microcontroller Arduino board with embedded IMU.Dra. America Morales (CINVESTAV Saltillo) April 30, 2014 27 / 38












































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.


https://www.youtube.com/watch?v=4pMO475heog

https://www.youtube.com/watch?v=lWsMdN7HMuA




Thanks!, questions?

america.morales,hugo.gutierrez,hector.perez,[email protected]


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Presentacion Robótica