Coordination Control of Multiple Mobile Robots Filippo Arrichiello - - PowerPoint PPT Presentation

Coordination Control

• f Multiple Mobile Robots

Filippo Arrichiello

webuser.unicas.it/arrichiello Universit` a degli Studi di Cassino PHILOSOPHIAE DOCTOR in Electrical and Information Engineering November 2006

Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 1/31

Outline

→ Introduction on Multi-Robot Systems → The Null-Space-based Behavioral control (NSB) → NSB for the control of a team of grounded mobile robots → NSB for the control of a fleet of marine surface vessels → NSB for the control of a team of mobile antennas → Conclusions

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Motivations

→ Increasing the mission efficiency → Performing tasks not executable by a single robot → Tolerance to possible vehicles’ faults → Increasing the flexibility of tasks’ execution → Advantages of distributed sensing and actuation

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Applications

→ Explorations → Box-pushing → Localization and Mapping → Rescue Operations → Military Tasks → Entertainment (e.g., Robocup)

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Vehicles’ typologies

→ Grounded Mobile Robots → Marine robots → Aerial Vehicles

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Approcci comportamentali

→ Biological Inspiration → Making the robots

behave like animals

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Behavioral approaches

Composition of the behaviors:

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Behavioral approaches

Composition of the behaviors: Competitive approaches selective activation of the behaviors

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Behavioral approaches

Composition of the behaviors: Competitive approaches selective activation of the behaviors Cooperative approaches the behaviors are combined with proper weights

Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 7/31

Behavioral approaches

Composition of the behaviors: Competitive approaches selective activation of the behaviors Cooperative approaches the behaviors are combined with proper weights Null-Space-Based approach Following the task priority inverse kinematics, a hierarchy-based technique is adopted based on null-space projection

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Behavioral approaches

Composition of the behaviors: Competitive approaches selective activation of the behaviors Cooperative approaches the behaviors are combined with proper weights Null-Space-Based approach Following the task priority inverse kinematics, a hierarchy-based technique is adopted based on null-space projection The NSB behavioral control differs from the other behavioral approaches in the way it combines multiple behaviors

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NSB control

→ The mission is decomposed in elementary behaviors or tasks

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NSB control

→ The mission is decomposed in elementary behaviors or tasks → For each elementary behavior a task function is properly defined σ = f(p1, . . . , pn) ˙ σ =

n

• i=1

∂f(p) ∂pi vi = J(p)v

Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 8/31

NSB control

→ The mission is decomposed in elementary behaviors or tasks → For each elementary behavior a task function is properly defined σ = f(p1, . . . , pn) ˙ σ =

n

• i=1

∂f(p) ∂pi vi = J(p)v

and a motion reference command to each vehicle is elaborated

vd = J† ˙ σd + Λ σ

• σ = σd−σ

Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 8/31

NSB: Merging different tasks

→ To simultaneously handle different, eventually conflicting, tasks the NSB

adopts a singularity-robust task priority inverse kinematics technique

vd = J†

p

• ˙

σp,d + Λp σp

• +
• I − J†

pJp

• J†

s

• ˙

σs,d + Λs σs

• primary

null-Space secondary

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NSB: Merging different tasks

→ To simultaneously handle different, eventually conflicting, tasks the NSB

adopts a singularity-robust task priority inverse kinematics technique

vd = J†

p

• ˙

σp,d + Λp σp

• +
• I − J†

pJp

• J†

s

• ˙

σs,d + Λs σs

• primary

null-Space secondary

→ Three-task example: vi = J†

i

• ˙

σi,d + Λi σi

• (i = 1, 2, 3)

vd = v1 +

• I − J†

1J1

v2 +

• I − J†

2J2

• v3
• Filippo Arrichiello

PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 9/31

Implementation aspects

NSB NSB + Vehicles’ Control

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Multi-robot: elementary behaviors

Definition of the task functions: “Barycenter”

σb = f b (p1, . . . , pn) = 1 n

n

• i=1

pi ˙ σb =

n

• i=1

∂f b (p) ∂pi vi = Jb (p) v Jb = 1 n

 

1 1 . . . 1 1

 

J†

b = nJT b

vb = J†

b

• ˙

σb,d + Λb σb

• Filippo Arrichiello

PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 11/31

Multi-robot: elementary behaviors

Definition of the task functions: “Rigid Formation”

σf =

     

p1 − pb

. . .

pn − pb

     

vf = JfΛf σf Jf =

  A

O O A

 

A =

         

1− 1 n

− 1

n

. . . − 1

n

− 1

n 1− 1 n

. . . − 1

n

. . . . . . ... . . .

− 1

n

− 1

n

. . .

1− 1 n

         

J†

f = Jf

Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 11/31

Multi-robot: elementary behaviors

Definition of the task functions: “Obstacle Avoidance” The obstacle avoidance task function is built individually to each vehicle, i.e., it is not an aggregate task function

σo = p − po σo,d = d Jo = ˆ rT J†

• = ˆ

r po: obstacle position d: safe distance ˆ r= p−po

p−po: unit vector

• f the obstacle-to-vehicle direction

vo = J†

• λo

σo = λo

• d − p−po
• ˆ

r N(Jo) = I − ˆ rˆ rT

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Team of wheeled mobile robots

→ Platoon of 7 Khepera II → Differential-drive mobile robots → Each robot has a Bluetooth turret

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Experimental set-up

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Experiments

Mission 1: Obstacle-Barycenter-Linear Formation

Movie 1

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Experiments

Mission 1: Mission steps

50 100 150 −50 50 100 150 t = 27.58 50 100 150 −50 50 100 150 t = 28.72 50 100 150 −50 50 100 150 t = 29.93 50 100 150 −50 50 100 150 t = 31.06 50 100 150 −50 50 100 150 t = 32.29 50 100 150 −50 50 100 150 t = 33.43 50 100 150 −50 50 100 150 t = 34.53 50 100 150 −50 50 100 150 t = 36.1

Movie 1

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Experiments

Mission 1: Barycenter and rigid formation task function errors

10 20 30 20 40 60 80 100 [s] [cm] 10 20 30 20 40 60 80 100 [s] [cm]

Movie 1

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Experiments

Mission 2: Obstacle-Barycenter-Circular Formation

Movie 2

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Experiments

Mission 2: Mission steps

t = 0 t = 5.9 t = 12.17 t = 18.49 t = 24.99 t = 31.19 t = 37.56 t = 43.46 t = 49.58 t = 55.69 t = 61.83 t = 67.84

Movie 2

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Experiments

Mission 2: Paths of the robots

50 100 150 −50 50 100 150 X[cm] Y[cm]

Movie 2

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Experiments

Mission 2: Barycenter and Rigid Formation task function errors

20 40 60 20 40 60 80 100 [s] [cm] 20 40 60 50 100 150 [s] [cm]

Movie 2

Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 15/31

Experiments

Mission 3: Escorting/Entrapment mission

Movie 3

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Feet of marine vessels

→ Navigation in formation → Autonomous navigation systems → Harbor operations

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Guidance system

→ Supervisor: Null-Space-based Behavioral control → Maneuvering control

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Single-vessel modelling

Kinematics

n e U ψ u v χ β

{B}

ν = ( u v r )T linear and

angular velocity in surge-sway- yaw BODY components

η = ( n e ψ )T position and

• rientation in the NE-plane

˙ η=R(ψ) ν

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Single-vessel modelling

Dynamics

M ˙ ν + N(ν)ν = τ + RT(ψ) w

Inertial Parameters Hydrodynamic Effects Environmental Disturbances:

• Wind
• Waves
• Current

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Single-vessel modelling

Actuation System → Two main thrusters → One tunnel thruster (for low-speed maneuvers)

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Single-vessel modelling

Actuation System

Main Propellers Tunnel thrusters F1 F2 F3 {BODY }

1 2 3 1 2 3 4 x 10

4

b

u τ2,max

Fully-Actuated Under-Actuated

τ =

     

F1 + F2 F3 τ3(F1, F2, F3)

     

τ =

     

F1 + F2 τ3(F1, F2)

     

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Maneuvering control

τ = M ˙ α + Nα − RT ˆ w − hk1z1 − K2z2

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Maneuvering control

τ = M ˙ α + Nα − RT ˆ w − hk1z1 − K2z2 α =

  

UNSB cos(βNSB) α2 ˙ ψNSB−z1

  

βNSB = χNSB − ψ α2 =

UNSB sin(βNSB) [FA] tale che τ2 =0 [UA]

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Maneuvering control

τ = M ˙ α + Nα − RT ˆ w − hk1z1 − K2z2 α =

  

UNSB cos(βNSB) α2 ˙ ψNSB−z1

  

βNSB = χNSB − ψ α2 =

UNSB sin(βNSB) [FA] tale che τ2 =0 [UA]

z1 = ψ−ψNSB k1 > 0 z2 = ν−α K2 > 0 ˙

• w = Γ R z2

Γ =Γ T > 0 h =

  

1

  

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Case studies

Mission 1

−200 200 400 600 800 1000 −500 −400 −300 −200 −100 100 200 300 400 500 e[m] n[m] −200 200 400 600 800 1000 −500 −400 −300 −200 −100 100 200 300 400 500 e[m] n[m] −200 200 400 600 800 1000 −500 −400 −300 −200 −100 100 200 300 400 500 e[m] n[m] −200 200 400 600 800 1000 −500 −400 −300 −200 −100 100 200 300 400 500 e[m] n[m]

Simulation 1

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Case studies

Mission 1

200 400 600 800 1000 −150 −100 −50 50 100 150 σf t[s] d 500 1000 1500 2000 −10 10 20 30 40 σb t[s] c 200 400 600 800 1000 −5 5 10 15 20 25 30 σo t[s] b 500 1000 −500 500 e[m] n[m] a

Simulation 1

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Case studies

Mission 1

500 1000 1500 2000 2500 −3 −2 −1 1 2 3 x 10

4

t[s] τ [N] a) 500 1000 1500 2000 2500 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 t[s] θ [rad] b)

Simulation 1

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Case studies

Mission 2

−200 200 400 600 800 1000 −500 −400 −300 −200 −100 100 200 300 400 500 e[m] n[m] −200 200 400 600 800 1000 −500 −400 −300 −200 −100 100 200 300 400 500 e[m] n[m] −200 200 400 600 800 1000 −500 −400 −300 −200 −100 100 200 300 400 500 e[m] n[m] −200 200 400 600 800 1000 −500 −400 −300 −200 −100 100 200 300 400 500 e[m] n[m]

Simulation 2

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Case studies

Mission 2

200 400 600 800 1000 −60 −40 −20 20 40 60 σf t[s] d 500 1000 1500 2000 −20 −15 −10 −5 5 10 15 σb t[s] c 200 400 600 800 1000 5 10 15 20 25 30 σo t[s] b 500 1000 −500 500 e[m] n[m] a

Simulation 2

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Case studies

Mission 2

500 1000 1500 2000 2500 −3 −2 −1 1 2 3 4 5 x 10

4

t[s] τ [N] a) 500 1000 1500 2000 2500 −3 −2 −1 1 2 t[s] θ [rad] b)

Simulation 2

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Team of mobile antennas

base station mobile antennas agent

→ Mobile Ad-hoc NETworks (MANET) → To guarantee coverage of an autonomous vehicle → Platoon of robots carrying repeater antennas

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MANET

antenna dmin dmax rmax

→ Each antenna has a maximum communication range equal to rmax → Each antenna needs to be in a range [dmin, dmax] from the other

antennas

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MANET

The task function aimed at ensuring connection of the chain is:

σc =

n

• i=1

σc,i σc,i =

      

r

if r≤dmin if dmin <r<dmax with r = pi−pi−1

r

if r≥dmax

Jc,i =

if σc,i =0

rT

• therwise .

σd,i =

      

dmin

if r≤dmin if dmin <r<dmax

dmax

if r≥dmax .

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MANET

The tasks are organized in priorities :

• 1. avoid the obstacles;
• 2. keep the next antenna in the coverage area;
• 3. keep the previous antenna in the coverage area.

A supervisor is in charge of detecting when the moving robot is going outside the maximum MANET coverage and, eventually, modifying the tasks’ priorities

• r adding/removing tasks

The virtual chain is organized at each sampling time Simulations: Obstacles building

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Conclusions

→ Introduction to multi-robot systems → Description of the Null-Space-based Behavioral (NSB) control for the

control of a generic multi-robot system

→ Implementation of the NSB to control a team wheeled mobile robots

performing several formation control missions with collision avoidance

→ The NSB has been test in simulative case studies while controlling a fleet

• f marine surface vessels with a particular actuation system and a team
• f mobile antennas

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Conclusioni

→ The experimental and simulative results prove the effectiveness and

flexibility of the approach

→ The NSB is well suitable to control several typologies of vehicles

performing different missions

→ The NSB results robust to sensor noise, external disturbances and

non-static environment

→ The NSB results dynamically scalable to the adding or removing a vehicle

from the team during the mission

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Publications

Journal Papers: 1.

• G. Antonelli, F

. Arrichiello, S. Chiaverini, The Null-Space-Based Behavioral Control for Autonomous Robotic Systems, Journal of Intelligent Service Robotics,in press 2007 2.

• G. Antonelli, F

. Arrichiello, S. Chiaverini and R. Setola, Coordinated control of mobile antennas for ad-hoc networks, International Journal of Modelling, Identification and Control, Special/Inaugural issue on Intelligent Robot Systems, Vol. 1, No. 1, pp.63-71, 2006 Book Chapters 1. F . Arrichiello, S. Chiaverini and T.I. Fossen, Formation Control of Marine Surface Vessels using the Null-Space-Based Behavioral Control, In Group Coordination and Cooperative Control (K.Y.Pettersen, T.Gravdahl, and H.Nijmeijer, Eds.). Lecture Notes in Control and Information Systems series, Springer-Verlag, pp.1-19, 2006

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Publications

International Conference Papers (with review):

• 11. G. Antonelli, F

. Arrichiello, S. Chakraborty and S. Chiaverini, Experiences of formation control of multi-robot systems with the Null-Space-based Behavioral Control, Proceedings 2007 IEEE International Conference on Robotics and Automation, Rome, I, 2007.

• 10. F

. Arrichiello, S. Chiaverini and T.I. Fossen, Formation Control of Underactuated Surface Vessels using the Null-Space-Based Behavioral Control, Proceedings 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, 2006

• 9. G. Antonelli, F

. Arrichiello, S. Chiaverini and K.J. Rao, Preliminary Experiments of Formation Control using the Null-Space-Based Behavioral Control, 8th IFAC Symposium on Robot Control, Bologna, I, 2006

• 8. G. Antonelli, F

. Arrichiello, S. Chiaverini, Experiments of Formation Control with Collisions Avoidance using the Null-Space-Based Behavioral Control, 14th Mediterranean Conference on Control and Automation, Ancona, I, 2006

• 7. F

. Arrichiello, S. Chiaverini, A simulation package for coordinated motion control of a fleet of under-actuated surface vessels, 5th MATHMOD Conference, Vienna, Austria, 2006

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Publications

• 6. G. Antonelli, F

. Arrichiello, S. Chiaverini and R. Setola, Coordinated control of mobile antennas for ad-hoc networks in cluttered environments, 9th International Conference on Intelligent Autonomous Systems, Tokyo, J,2006

• 5. G. Antonelli, F

. Arrichiello, S. Chiaverini and R. Setola, A Self-Configuring MANET for Coverage Area Adaptation through Kinematic Control of a Platoon of Mobile Robots, IEEE/RSJ International Conference on Intelligent Robots and Systems, Edmonton, CA, pp.1332-1337, 2005

• 4. G. Antonelli, F

. Arrichiello and S. Chiaverini, The Null-Space-Based Behavioral Control for Soccer-Playing Mobile Robots, 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Monterey, CA, pp.1257-1262, 2005

• 3. G. Antonelli, F

. Arrichiello and S. Chiaverini, Experimental kinematic comparison of behavioral approaches for mobile robots, 16th IFAC World Congress, Praha, CZ, 2005

• 2. G. Antonelli, F

. Arrichiello and S. Chiaverini, The Null-Space-Based behavioral control for mobile robots, IEEE International Symposium on Computational Intelligence in Robotics and Automation, Espoo, Finland, pp.15-20, 2005

• 1. F

. Arrichiello, S. Gerbino, How to investigate constraints and motions in assemblies by screw theory,

• Proc. of 4th CIRP ICME’04 Int. Conf., Sorrento, I, 2004

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