Coordination Control of 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 Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 2/31
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 Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 3/31
Applications → Explorations → Box-pushing → Localization and Mapping → Rescue Operations → Military Tasks → Entertainment (e.g., Robocup) Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 4/31
Vehicles’ typologies → Grounded Mobile Robots → Marine robots → Aerial Vehicles Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 5/31
Approcci comportamentali → Biological Inspiration → Making the robots behave like animals Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 6/31
Behavioral approaches Composition of the behaviors: 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 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 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 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 The NSB behavioral control differs from the other behavioral approaches in the way it combines multiple behaviors Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 7/31
NSB control → The mission is decomposed in elementary behaviors or tasks 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 = f ( p 1 , . . . , p n ) σ n � ∂ f ( p ) ˙ = v i = J ( p ) v σ ∂ p i i =1 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 = f ( p 1 , . . . , p n ) σ n � ∂ f ( p ) ˙ = v i = J ( p ) v σ ∂ p i i =1 and a motion reference command to each vehicle is elaborated v d = J † � � σ d + Λ � ˙ σ = σ d − σ 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 � � � � � � J † I − J † J † = σ p,d + Λ p � ˙ + σ s,d + Λ s � ˙ v d σ p p J p σ s p s � �� � � �� � � �� � primary null-Space secondary Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 9/31
NSB: Merging different tasks → To simultaneously handle different, eventually conflicting, tasks the NSB adopts a singularity-robust task priority inverse kinematics technique � � � � � � J † I − J † J † = σ p,d + Λ p � ˙ + σ s,d + Λ s � ˙ v d σ p p J p σ s p s � �� � � �� � � �� � primary null-Space secondary → Three-task example: � � J † = σ i,d + Λ i � ˙ ( i = 1 , 2 , 3) v i σ i i � � � � � � I − J † I − J † v d = v 1 + 1 J 1 v 2 + 2 J 2 v 3 Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 9/31
Implementation aspects NSB NSB + Vehicles’ Control Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 10/31
Multi-robot: elementary behaviors Definition of the task functions: “Barycenter” n � f b ( p 1 , . . . , p n ) = 1 = σ b p i n i =1 n � ∂ f b ( p ) ˙ = v i = J b ( p ) v σ b ∂ p i i =1 1 0 1 0 1 J † b = n J T = J b . . . b n 0 1 0 1 � � J † ˙ v b = σ b,d + Λ b � σ b b Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 11/31
Multi-robot: elementary behaviors Definition of the task functions: “Rigid Formation” p 1 − p b . . σ f = v f = J f Λ f � σ f . p n − p b 1 − 1 − 1 − 1 . . . n n n − 1 1 − 1 − 1 A O . . . J † n n n J f = A = f = J f . . . ... O A . . . . . . − 1 − 1 1 − 1 . . . n n n 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 J † r T σ o = � p − p o � J o = ˆ o = ˆ σ o,d = d r r = p − p o ˆ p o : obstacle position � p − p o � : unit vector d : safe distance of the obstacle-to-vehicle direction � � v o = J † σ o = λ o d − � p − p o � ˆ o λ o � r r T N ( J o ) = I − ˆ r ˆ Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 11/31
Team of wheeled mobile robots → Platoon of 7 Khepera II → Differential-drive mobile robots → Each robot has a Bluetooth turret Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 12/31
Experimental set-up Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 13/31
Experiments Mission 1: Obstacle-Barycenter-Linear Formation Movie 1 Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 14/31
Experiments Mission 1: Mission steps 150 150 150 150 100 100 100 100 50 50 50 50 0 0 0 0 t = 27.58 t = 28.72 t = 29.93 t = 31.06 −50 −50 −50 −50 0 50 100 150 0 50 100 150 0 50 100 150 0 50 100 150 150 150 150 150 100 100 100 100 50 50 50 50 0 0 0 0 t = 32.29 t = 33.43 t = 34.53 t = 36.1 −50 −50 −50 −50 0 50 100 150 0 50 100 150 0 50 100 150 0 50 100 150 Movie 1 Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 14/31
Experiments Mission 1: Barycenter and rigid formation task function errors 100 100 80 80 60 60 [cm] [cm] 40 40 20 20 0 0 0 10 20 30 0 10 20 30 [s] [s] Movie 1 Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 14/31
Experiments Mission 2: Obstacle-Barycenter-Circular Formation Movie 2 Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 15/31
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 Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 15/31
Experiments Mission 2: Paths of the robots 150 100 Y[cm] 50 0 −50 0 50 100 150 X[cm] Movie 2 Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 15/31
Experiments Mission 2: Barycenter and Rigid Formation task function errors 100 150 80 100 60 [cm] [cm] 40 50 20 0 0 0 20 40 60 0 20 40 60 [s] [s] Movie 2 Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 15/31
Experiments Mission 3: Escorting/Entrapment mission Movie 3 Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 16/31
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