Cooperative mobile robots

Introduction Collaborative robotics Collaborative path planning Control Bibliography Cooperative mobile robots. W. PERRUQUETTI ALIEN INRIA - LNE, LAG...
Author: Preston Jenkins
16 downloads 0 Views 4MB Size
Introduction Collaborative robotics Collaborative path planning Control Bibliography

Cooperative mobile robots. W. PERRUQUETTI ALIEN INRIA - LNE, LAGIS UMR CNRS 8146, Ecole Centrale de Lille, 59650 Villeneuve D’Ascq. [email protected]. Special thanks to : Michael Defoort, Thierry Floquet and Anne Marie K¨ok¨osy.

26 Novembre 2009 W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

OUTLINE

1

Introduction

2

Collaborative robotics

3

Collaborative path planning

4

Control

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Un Robot, c’est quoi ? Robots en r´ eseau

Robotics is a cross fertilizing area which aims at designing and using concrete physical devices with the following capabilities : action, (actuators) perception, (sensors) decision, interaction with the environment, in order to fulfill a task with or without a human. (The case > : human-robot interactions)

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Un Robot, c’est quoi ? Robots en r´ eseau

Classification des robots : Robots mobiles : `a roues, `a chenilles, `a pattes, selon le type de locomotion, a´erien, sous-marin, terrestre ou spatial, avec une attention particuli`ere pour la robotique humano¨ıde Robots fixes : manipulateurs, interface haptique, etc . . .

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

W. Perruquetti

Un Robot, c’est quoi ? Robots en r´ eseau

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

W. Perruquetti

Un Robot, c’est quoi ? Robots en r´ eseau

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

W. Perruquetti

Un Robot, c’est quoi ? Robots en r´ eseau

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

W. Perruquetti

Un Robot, c’est quoi ? Robots en r´ eseau

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Un Robot, c’est quoi ? Robots en r´ eseau

La robotique concerne l’int´egration de quatre composantes : Conception, mod´elisation, analyse : nouveaux besoins Chaine de perception : capteurs qui > les robots d’informations de nature diverse (signaux analogiques, num´eriques (par exemple image), etc . . . ). Chaine d’action et de d´ecision qui comporte plusieurs chainons : cognitif, la planification de tˆaches, la planification de mouvements, la commande et se terminant par les actionneurs. L’interaction avec l’environnement : collaboration robots/robots et/ou hommes et/ou monde physique.

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Un Robot, c’est quoi ? Robots en r´ eseau

R´eseaux informatiques notamment sans fils ont permis d’entrevoir la s´eparation de l’ensemble capteurs-commande-actionneurs (CCA).

Cons´equences : t´el´eop´eration de robots, (nouveaux enjeux). robots en r´eseaux : ce sont des dispositifs robotis´es (manipulateurs, v´ehicules mobiles, robots humano¨ıdes, etc . . . ) qui sont connect´es via un r´eseau de communication tel qu’un r´eseau local (LAN) ou le r´eseau internet (WAN) → faire coop´erer un ensemble de robots. Nouveaux probl`emes : pertes de paquets, retards, QoS etc . . . W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

+ Robocoop project : http ://syner.ec-lille.fr/robocoop Goals Deployment of large scale networks of cooperative mobile robots

to get complex behaviors by using simple agent based behaviors W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

+ Robocoop project : http ://syner.ec-lille.fr/robocoop Goals Deployment of large scale networks of cooperative mobile robots

to get complex behaviors by using simple agent based behaviors W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Applicative fields health (tele-robotics, . . . ) transportation (plane fleet, drones, mobile robots, heterogeneous robots (mobile of different type, planes, underwater robots, . . . ) security (fire, data collection for “spying”, . . . ) ...

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Challenges local information and decision process, constrained communication + delays, large scale system, uncertain and hostile dynamic environnement, ...

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Framework : multidisciplinary research modeling, path planning and control (constraints, nonlinear models, time delays, hierarchical aspects, hybrid system aspect, quantization . . . ) graph theory, communication protocols, logical decision making, scheduling, ...

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Framework : multidisciplinary research modeling, path planning and control (constraints, nonlinear models, time delays, hierarchical aspects, hybrid system aspect, quantization . . . ) graph theory, communication protocols, logical decision making, scheduling, ...

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Framework : multidisciplinary research modeling, path planning and control (constraints, nonlinear models, time delays, hierarchical aspects, hybrid system aspect, quantization . . . ) graph theory, communication protocols, logical decision making, scheduling, ...

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Framework : multidisciplinary research modeling, path planning and control (constraints, nonlinear models, time delays, hierarchical aspects, hybrid system aspect, quantization . . . ) graph theory, communication protocols, logical decision making, scheduling, ...

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Framework : multidisciplinary research modeling, path planning and control (constraints, nonlinear models, time delays, hierarchical aspects, hybrid system aspect, quantization . . . ) graph theory, communication protocols, logical decision making, scheduling, ...

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Snap shot of Robocoop project / Big picture

ROBOTIC CONTROL Non holonomic constraints

Non linear, Hybrid systems, DAE (new challenges)

Under (or Over) actuated systems

Hierarchical aspects – Decision M aking – C ooperative C ontrol

Obstacle avoidance C ooperative path planning

On line time delay identification Observer/ C ontroller for TDS

SENSORS I nverse problem, minimum sensors network structure

Spécification / réalisation / validation

COMMUNICATION

Data fusion Data validation

« QoS » Estimation R edundant architechture for security ?

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Our Goals 4 path planning and path tracking 4 test on benchmarks

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Our Goals 4 path planning and path tracking 4 test on benchmarks

W. Perruquetti

RECAP 2009, Novembre 2009

1

Introduction

Introduction Collaborative robotics

Leader(s) ?

Wilfrid et Annemarie Collaborative path planning Graph Hierarchical structure This paper focuses on the problemControl of autonomous navigation of a swarm of mobile robots which naviga Bibliography in a partially known or unknown environment with obstacles. The swarm must navigate between know initial and final points without collision. In order to be able to move autonomously, the robot needs to kno at each moment its localization on the map and information about the obstacles on its neighborhood. Th software architecture of each robot of the swarm proposed in this paper is depicted in figure 1. 6

Physical constraints Intermediate goals

 ?

?

6

Constraint parameters STRATEGY

Constraints

?? ?

6

?

6

PATH PLANNING

-

COMMUNICATION PERCEPTION Desired trajectory

SENSORS

?

-

6

TRACKING LOCALISATION

Desired Velocities

?

? To other robots

ACTUATORS FEEDBACK

? Robot motion ?

-

Fig. 1. Software architecture for an autonomous mobile robot

The blocks ”Perception” and ”Localisation” receive information from the proprioceptive and exteroce W. ”Localisation” Perruquetti RECAPthe 2009, Novembre 2009 tive sensors of the robot. In the block, information is processed in order to obtain th

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Leader or not ? Within a group of mobile robots, some of them may play a particular role : leaders. Distinguish between fleets : 1

with leader : the leader drive the whole fleet or a part of it.

2

without leader : need of a local/global coordination : decision rules must use local informations (most of the time neighbors) or global informations

Questions + How to collect such informations ? + What happen if this robot dedicated to data collection is out of order, destroy, or not reliable ?

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Leader or not ? Within a group of mobile robots, some of them may play a particular role : leaders. Distinguish between fleets : 1

with leader : the leader drive the whole fleet or a part of it.

2

without leader : need of a local/global coordination : decision rules must use local informations (most of the time neighbors) or global informations

Questions + How to collect such informations ? + What happen if this robot dedicated to data collection is out of order, destroy, or not reliable ?

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Leader or not ? Within a group of mobile robots, some of them may play a particular role : leaders. Distinguish between fleets : 1

with leader : the leader drive the whole fleet or a part of it.

2

without leader : need of a local/global coordination : decision rules must use local informations (most of the time neighbors) or global informations

Questions + How to collect such informations ? + What happen if this robot dedicated to data collection is out of order, destroy, or not reliable ?

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Introduction General framework Collaborative robotics Path PlanningCollaborative for networkedpath mobile robots planning TrajectoryControl tracking Bibliography Bibliography

Leader(s) ? Leader(s) Graph ? Graph Hierarchical structure Hierarchical Models structure

Communicationsgraph graphGGc c Communications R0 = L R2 R1

R3

R7 R5

R4

W.Perruquetti Perruquetti W.

R6

SSIR 2006, 2006 2009 RECAP 2009, July Novembre

Introduction Introduction General framework Collaborative robotics Path Planning forCollaborative networked mobile robots path planning Trajectory tracking Control Bibliography Bibliography

Leader(s) ? Leader(s) ? Graph Graph Hierarchical structure Hierarchical structure Models

Formation Formationgraph graph GGff R0 = L

d02 R2

d01

d23

d12

d(R0 , R7) = d07 > 0

R1

d25

d17

R3

d15 d35

R5

R7 d57

d34 d45

d56

R4

d67 R6

W. W.Perruquetti Perruquetti

SSIR 2006, JulyNovembre 2006 RECAP 2009, 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Questions + How to extract from a graph a minimal representation ensuring some properties (communications, geometric forms of the formation, . . . ) ? + According to some mission how to choose an initial graph which induces some good properties ? + These graphs are time varying (dynamical graphs) :

Open questions : analyse, how to control ? . . .

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Hierarchical structure To achieve computational tractability : “Strategic layer” (higher level) : goal planning (for example choose an appropriate functional cost), task scheduling (for example use a petri net for description), “Tactical layer” (mid level) : guidance, navigation “Reflexive layer” (low level) : (control) state observation or estimation, trajectory tracking, . . . Questions How can we get an “integrated layer” ? + Solve an optimisation problem which integrate some of these facts (gives a path) and then use a good “trajectory tracking” W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Hierarchical structure To achieve computational tractability : “Strategic layer” (higher level) : goal planning (for example choose an appropriate functional cost), task scheduling (for example use a petri net for description), “Tactical layer” (mid level) : guidance, navigation “Reflexive layer” (low level) : (control) state observation or estimation, trajectory tracking, . . . Questions How can we get an “integrated layer” ? + Solve an optimisation problem which integrate some of these facts (gives a path) and then use a good “trajectory tracking” W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Hierarchical structure To achieve computational tractability : “Strategic layer” (higher level) : goal planning (for example choose an appropriate functional cost), task scheduling (for example use a petri net for description), “Tactical layer” (mid level) : guidance, navigation “Reflexive layer” (low level) : (control) state observation or estimation, trajectory tracking, . . . Questions How can we get an “integrated layer” ? + Solve an optimisation problem which integrate some of these facts (gives a path) and then use a good “trajectory tracking” W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Hierarchical structure To achieve computational tractability : “Strategic layer” (higher level) : goal planning (for example choose an appropriate functional cost), task scheduling (for example use a petri net for description), “Tactical layer” (mid level) : guidance, navigation “Reflexive layer” (low level) : (control) state observation or estimation, trajectory tracking, . . . Questions How can we get an “integrated layer” ? + Solve an optimisation problem which integrate some of these facts (gives a path) and then use a good “trajectory tracking” W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Leader(s) ? Graph Hierarchical structure

Hierarchical structure To achieve computational tractability : “Strategic layer” (higher level) : goal planning (for example choose an appropriate functional cost), task scheduling (for example use a petri net for description), “Tactical layer” (mid level) : guidance, navigation “Reflexive layer” (low level) : (control) state observation or estimation, trajectory tracking, . . . Questions How can we get an “integrated layer” ? + Solve an optimisation problem which integrate some of these facts (gives a path) and then use a good “trajectory tracking” W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

On the way to integration Philosophy integrated layer : “Strategic layer” (goal planning) + “Tactical layer” (guidance, navigation) + “Reflexive layer” (obstacle avoidance) Solution + Generate and execute a (sub)-optimal path planning which satisfy : geometric formation and communications constraints, obstacle avoidance constraints, given boundary conditions, other constraints : time constraints (rescue missions), energy constraints (batteries duration, . . . ) W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

On the way to integration Philosophy integrated layer : “Strategic layer” (goal planning) + “Tactical layer” (guidance, navigation) + “Reflexive layer” (obstacle avoidance) Solution + Generate and execute a (sub)-optimal path planning which satisfy : geometric formation and communications constraints, obstacle avoidance constraints, given boundary conditions, other constraints : time constraints (rescue missions), energy constraints (batteries duration, . . . ) W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

On the way to integration Philosophy integrated layer : “Strategic layer” (goal planning) + “Tactical layer” (guidance, navigation) + “Reflexive layer” (obstacle avoidance) Solution + Generate and execute a (sub)-optimal path planning which satisfy : geometric formation and communications constraints, obstacle avoidance constraints, given boundary conditions, other constraints : time constraints (rescue missions), energy constraints (batteries duration, . . . ) W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

On the way to integration Philosophy integrated layer : “Strategic layer” (goal planning) + “Tactical layer” (guidance, navigation) + “Reflexive layer” (obstacle avoidance) Solution + Generate and execute a (sub)-optimal path planning which satisfy : geometric formation and communications constraints, obstacle avoidance constraints, given boundary conditions, other constraints : time constraints (rescue missions), energy constraints (batteries duration, . . . ) W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

On the way to integration Philosophy integrated layer : “Strategic layer” (goal planning) + “Tactical layer” (guidance, navigation) + “Reflexive layer” (obstacle avoidance) Solution + Generate and execute a (sub)-optimal path planning which satisfy : geometric formation and communications constraints, obstacle avoidance constraints, given boundary conditions, other constraints : time constraints (rescue missions), energy constraints (batteries duration, . . . ) W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

General constraints We would like to include in the path planning the following constraints : 1

some constraints due to physics (energy limitation, maximal velocity and acceleration of the robots)

2

obstacle avoidance,

3

collision avoidance with the robots and other mobile objects,

4

distances between robots (communications),

5

geometry of the formation

6

...

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Somme settings Group of Ni a mobile robots related to the ith mobile robot evolving in a partially known space with No obstacles. each obstacle Om (m ∈ {1, . . . , No }) is covered by a disc o ) with radius r o (if complex geometry use centered at (xom , ym m a covering of discs). IN the set {1, . . . , N },

the nth ∈ IN mobile robot denoted by An and located at (xn , yn ) occupies a space modeled by a disc of radius rn centered at (xn , yn ). robot An : Xn and Un denotes respectively the state variables and the control variables. a. Index i (dropped sometimes) will refer to some properties or known objects linked to the ith mobile robot. N = Ni ! W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Robot de type unicycle Non Holonomy (Admissible path)

Kinematic constraint : a robot should not be reduced to a single point (x, y). W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Types of models : see [5] “Theory of Robot Control”, C. Canudas de Wit, B. Siciliano and G. Bastin (Eds). 1

Kinematic model (take into account non holonomic constraints)

Posture =(x, y, θ) in most of the case.

2

Dynamical model (KM + dynamics induced by actuators (most of the time electrical motors))

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Kinematic model is enough Kinematic model which includes non holonomic constraints this is non integrable constraints of the form q˙ = B(q)u,

(1)

where u ∈ Rm , q ∈ Rn (n > m). + If not under-actuated (with respect to the mobility degree) then one can perform a feedback linearization : J(q)u˙ + C(q, u)u + G(q) = B T (q)D(q)Γ, leads to u˙ = v  −1 by using Γ = B T (q)D(q) (J(q)v + C(q, u)u + G(q)). W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Kinematic model : flatness is the key point Flatness (see works from M. Fliess, J.L´evine, Ph.Martin, et P.Rouchon details in [11, 12, 13, 15, 16])

x˙ = f (x, u), x ∈ Rn , u ∈ Rm flat ⇔ il existe m fonctions qui param´etrisent tout !

Donc fixer ces fonctions c’est fixer le comportement dynamique du syst`eme !

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Kinematic model : flatness is the key point + Thus the PKM and PDM are flat. + Thus it implies that they are controllable. + But from Brockett’s theorem (see [4]) they are not stabilizable by a continuous static time-invariant state feedback.

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Kinematic model : flatness is the key point 1

Unicycle mobile robot (type (2,0)) x˙ = v cos θ y˙ = v sin θ θ˙ = w

2

(2)

Car-like mobile robot (type (1,1)) x˙ = v cos θ y˙ = v sin θ tan(φ) θ˙ = v l ˙ φ=w W. Perruquetti

RECAP 2009, Novembre 2009

(3)

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Kinematic model : flatness is the key point Flat Outputs : (x, y). Indeed : 1

2

 

p , v = ± x˙ 2 + y˙ 2 ,w =   p for (3) : θ = arctan xy˙˙ , v = ± x˙ 2 + y˙ 2 , φ =   ˙ y −y¨ ˙x ˙ , w = φ. arctan l 2x¨ 3/2 2 for (2) : θ = arctan

y˙ x˙

(x˙ +y˙ )

W. Perruquetti

RECAP 2009, Novembre 2009

x¨ ˙ y −y¨ ˙x x˙ 2 +y˙ 2

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Path planning for a single robot Motion planning Computation of an executable collision-free trajectory for a robot between an initial given configuration and a finalReview given configuration INTRODUCTION - Path Planning Trajectory planning

Local planner

Latombe 1991 Laumond 1997

Global planner

Optimal control Pontryagin et al. 1962 Bryson et Ho 1975 Bobrow 1988

Potential fields Khatib 1986 Borenstein et Koren 1991 Barraqunad et al. 1992 Rimon et Koditschek 1992

Dynamic window

Fox 1997

Flatness Fliess et al. 1995

Cell decompostion

Visibility graph

Voronoï graph

Chazelle et Guibas 1989

Choset 1996

W. Perruquetti

Agrawal et al. 1996 Murray et al. 2001 Milam 2003

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Motion planning for a single robot : problem setup

− → j

− → j

Obstacle area Oi (1s)

zone obstacle Oi (0)

yi (1s)

Detection range of sensors

yi (0)

Detection range of sensors O

xi (0)

− → i

W. Perruquetti

O

xi (1s)

RECAP 2009, Novembre 2009

− → i

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Single robot : off-line algorithm Dynamic optimisation based on flatness Flatness

Optimal control

Dynamic optimization based on flatness

Criteria R tf :inal J = tinitial Li (qi , ui , t)dt wrt : ∀t ∈ [tinitial , tf inal ], q˙i (t) = fi (qi (t), ui (t))  q (t ) = qi,initial    i initial qi (tf inal ) = qi,f inal ui (tinitial ) = ui,initial    ui (tf inal ) = ui,f inal ui (t) ∈ Ui ∀Omi ∈ Oi (tinitial ) d(qi (t), Omi ) ≥ ρi + rmi W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Single robot : off-line algorithm Dynamic optimisation based on flatness Flatness

Optimal control

Dynamic optimization based on flatness

Criteria R tf :inal J = tinitial Li (qi , ui , t)dt wrt : ∀t ∈ [tinitial , tf inal ], q˙i (t) = fi (qi (t), ui (t))  q (t ) = qi,initial    i initial qi (tf inal ) = qi,f inal ui (tinitial ) = ui,initial    ui (tf inal ) = ui,f inal ui (t) ∈ Ui ∀Omi ∈ Oi (tinitial ) d(qi (t), Omi ) ≥ ρi + rmi W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Single robot : off-line algorithm Dynamic optimisation based on flatness Flatness

Optimal control

Dynamic optimization based on flatness

Criteria R tf :inal J = tinitial Li (qi , ui , t)dt wrt : ∀t ∈ [tinitial , tf inal ], q˙i (t) = fi (qi (t), ui (t))  q (t ) = qi,initial    i initial qi (tf inal ) = qi,f inal ui (tinitial ) = ui,initial    ui (tf inal ) = ui,f inal ui (t) ∈ Ui ∀Omi ∈ Oi (tinitial ) d(qi (t), Omi ) ≥ ρi + rmi W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Single robot : off-line algorithm Dynamic optimisation based on flatness Flatness

Optimal control

Dynamic optimization based on flatness

Criteria R tf :inal J = tinitial Li (qi , ui , t)dt wrt : ∀t ∈ [tinitial , tf inal ], q˙i (t) = fi (qi (t), ui (t))  q (t ) = qi,initial    i initial qi (tf inal ) = qi,f inal ui (tinitial ) = ui,initial    ui (tf inal ) = ui,f inal ui (t) ∈ Ui ∀Omi ∈ Oi (tinitial ) d(qi (t), Omi ) ≥ ρi + rmi W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Single robot : off-line algorithm Dynamic optimisation based on flatness Flatness

Optimal control

Dynamic optimization based on flatness

Criteria R tf :inal J = tinitial Li (qi , ui , t)dt wrt : ∀t ∈ [tinitial , tf inal ], q˙i (t) = fi (qi (t), ui (t))  q (t ) = qi,initial    i initial qi (tf inal ) = qi,f inal ui (tinitial ) = ui,initial    ui (tf inal ) = ui,f inal ui (t) ∈ Ui ∀Omi ∈ Oi (tinitial ) d(qi (t), Omi ) ≥ ρi + rmi W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Single robot : off-line algorithm Dynamic optimisation based on flatness Flatness

Optimal control

Dynamic optimization based on flatness

Criteria R tf :inal J = tinitial Li (qi , ui , t)dt wrt : ∀t ∈ [tinitial , tf inal ], q˙i (t) = fi (qi (t), ui (t))  q (t ) = qi,initial    i initial qi (tf inal ) = qi,f inal ui (tinitial ) = ui,initial    ui (tf inal ) = ui,f inal

 qi = ϕ1 (zi , z˙ i , z ¨i ) ui = ϕ2 (zi , z˙ i , z ¨i )

ui (t) ∈ Ui ∀Omi ∈ Oi (tinitial ) d(qi (t), Omi ) ≥ ρi + rmi W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Single robot : off-line algorithm Dynamic optimisation based on flatness Flatness

Optimal control Criteria R tf :inal J = tinitial Li (qi , ui , t)dt wrt : ∀t ∈ [tinitial , tf inal ],

Dynamic optimization based on flatness

Criteria R tf inal : J = ¨i ), ϕ2 (zi , z˙i , z¨i ), t)dt tinitial Li (ϕ1 (zi , z˙i , z wrt : ∀t ∈ [tinitial , tf inal ],

q˙i (t) = fi (qi (t), ui (t))  q (t ) = qi,initial    i initial qi (tf inal ) = qi,f inal ui (tinitial ) = ui,initial    ui (tf inal ) = ui,f inal ui (t) ∈ Ui

...  ϕ1 (zi (tinitial ), z¨i (tinitial )) = qi,initial    ϕ1 (zi (tf inal ), z¨i (tf inal )) = qi,f inal ϕ2 (zi (tinitial ), z¨i (tinitial )) = ui,initial    ϕ2 (zi (tf inal ), z¨i (tf inal )) = ui,f inal etc.

∀Omi ∈ Oi (tinitial ) d(qi (t), Omi ) ≥ ρi + rmi W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Single robot : off-line algorithm Dynamic optimisation based on flatness Optimal control

Flatness

Dynamic optimization based on flatness

Resolution of optimal control problems + Transformation into a nonlinear programming problem, using B-spline functions in order to approximate the trajectory of the flat output + Computation of optimal control points using an optimisation procedure (CFSQP) + Computation of the corresponding control inputs using the flatness properties of the system

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Single robot : on-line algorithm

Main Principle

Legend:

Tp

+ To relax the constraint that the final point is reached during the planning horizon, allowing the use of an on-line receding horizon motion planner

Computed trajectory Reference Trajectory

Tp (> 0) : planning horizon Tc (> 0) : update period τk (k ∈ N, τk = tinitial + kTc ) : updates

W. Perruquetti

Tc τk

RECAP 2009, Novembre 2009

τk+1

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Single robot : on-line algorithm Implementation + initialisation step : computations before the movement of the robot + step of iterative computations : computations over any interval [τk−1 , τk ) Legend: Computed trajectory Reference trajectory

qi,ref (t, τk )

qi,ref (t, τk+1 )

qi,ref (t, τk−1 )

Comput. of qi,ref (t, τk+1 )

Comput. of qi,ref (t, τk ) τk

τk+1

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Single robot : on-line algorithm Implementation + initialisation step : computations before the movement of the robot + step of iterative computations : computations over any interval [τk−1 , τk ) Legend: Computed trajectory Reference trajectory

qi,ref (t, τk )

qi,ref (t, τk+1 )

qi,ref (t, τk−1 )

Comput. of qi,ref (t, τk+1 )

Comput. of qi,ref (t, τk ) τk

τk+1

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination Objective + To generate a (sub) optimal trajectory for each robot which satisfy : terminal constraints physical constraints (nonholonomic, maximum velocities, . . . ) obstacle avoidance minimum distances between robots (collision avoidance) maximum distances between robots (respect of the broadcasting Communication graph (N , A, S) range) Robots N = {1, . . . , Na } Edges A ⊂ N × N  communication links Constraints of the edges di,com ∈ R+ : broadcasting range of robot i

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination Objective + To generate a (sub) optimal trajectory for each robot which satisfy : terminal constraints physical constraints (nonholonomic, maximum velocities, . . . ) obstacle avoidance minimum distances between robots (collision avoidance) maximum distances between robots (respect of the broadcasting Communication graph (N , A, S) range) Robots N = {1, . . . , Na } Edges A ⊂ N × N  communication links Constraints of the edges di,com ∈ R+ : broadcasting range of robot i

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination Objective + To generate a (sub) optimal trajectory for each robot which satisfy : terminal constraints physical constraints (nonholonomic, maximum velocities, . . . ) obstacle avoidance minimum distances between robots (collision avoidance) maximum distances between robots (respect of the broadcasting Communication graph (N , A, S) range) Robots N = {1, . . . , Na } Edges A ⊂ N × N  communication links Constraints of the edges di,com ∈ R+ : broadcasting range of robot i

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination Objective + To generate a (sub) optimal trajectory for each robot which satisfy : terminal constraints physical constraints (nonholonomic, maximum velocities, . . . ) obstacle avoidance minimum distances between robots (collision avoidance) maximum distances between robots (respect of the broadcasting Communication graph (N , A, S) range) Robots N = {1, . . . , Na } Edges A ⊂ N × N  communication links Constraints of the edges di,com ∈ R+ : broadcasting range of robot i

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

INTRODUCTION - Multi-robot Planning and Control Review

Multi-robots coordination Trajectory planning: multirobot framework

Without cooperation

Worst case approach Tomlin et al., 1998

With cooperation

Centralized approach Loizou et Kyriakopoulos, 2002, Olfati-Saber et al., 2003, Tanner et al., 2003 Ogren, 2003 Dunbar et Murray, 2002 W. Perruquetti

Decentralized approach Guo et Parker, 2002 Gazi et Passino, 2004 Gennaro et Jadbabaie, 2006, Keviczky et all, 2006 Kuwata et al. 2006

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : centralized approach

Limitation to direct extension via a supervisor 1

Prohibitive computation time (centralized approche))

2

Problems due to the supervisor (if destroyed ...)

Solution to 1

Step of simplification of the initial problem : + Motion planning of a virtual robot which is located at the centre of gravity of the formation

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : centralized approach

Limitation to direct extension via a supervisor 1

Prohibitive computation time (centralized approche))

2

Problems due to the supervisor (if destroyed ...)

Solution to 1

Step of simplification of the initial problem : + Motion planning of a virtual robot which is located at the centre of gravity of the formation

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach Desired objectives low computation time high performances use of available local information no supervisor Solution Distributed optimisation based on local information . Each vehicle i only takes into account the intentions of the robots belonging to the conflict set Ci (τk ) (may produce a collision Ci,collision (τk ) or may lost the communication Ci,com (τk ))

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach Desired objectives low computation time high performances use of available local information no supervisor Solution Distributed optimisation based on local information . Each vehicle i only takes into account the intentions of the robots belonging to the conflict set Ci (τk ) (may produce a collision Ci,collision (τk ) or may lost the communication Ci,com (τk ))

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach Desired objectives low computation time high performances use of available local information no supervisor Solution Distributed optimisation based on local information . Each vehicle i only takes into account the intentions of the robots belonging to the conflict set Ci (τk ) (may produce a collision Ci,collision (τk ) or may lost the communication Ci,com (τk ))

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach Desired objectives low computation time high performances use of available local information no supervisor Solution Distributed optimisation based on local information . Each vehicle i only takes into account the intentions of the robots belonging to the conflict set Ci (τk ) (may produce a collision Ci,collision (τk ) or may lost the communication Ci,com (τk ))

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach Conflicts with robot 1 : C1,collision (τk ) = {2} C1,com (τk ) = {4} L´egende :

Zone d’accessibilit´e Port´ee de diffusion des informations d1,com

Robot 4

R1 (τk ) Robot 1

Robot 2

Robot 3

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach Difficulties

Knowledge of the intentions of robots p ∈ Ci (τk ) uniqueness of the presumed trajectory

coherence between the presumed trajectory and the optimal planned trajectory Solution

+ Decomposition of the algorithm into 2 steps : ? determination of the presumed trajectory (which only satisfy the individual constraints) ? determination of the optimal planned trajectory from the exchanged information between robots belonging to the subset Ci (τk ) W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach Difficulties

Knowledge of the intentions of robots p ∈ Ci (τk ) uniqueness of the presumed trajectory

coherence between the presumed trajectory and the optimal planned trajectory Solution

+ Decomposition of the algorithm into 2 steps : ? determination of the presumed trajectory (which only satisfy the individual constraints) ? determination of the optimal planned trajectory from the exchanged information between robots belonging to the subset Ci (τk ) W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach Difficulties

Knowledge of the intentions of robots p ∈ Ci (τk ) uniqueness of the presumed trajectory

coherence between the presumed trajectory and the optimal planned trajectory Solution

+ Decomposition of the algorithm into 2 steps : ? determination of the presumed trajectory (which only satisfy the individual constraints) ? determination of the optimal planned trajectory from the exchanged information between robots belonging to the subset Ci (τk ) W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach Difficulties

Knowledge of the intentions of robots p ∈ Ci (τk ) uniqueness of the presumed trajectory

coherence between the presumed trajectory and the optimal planned trajectory Solution

+ Decomposition of the algorithm into 2 steps : ? determination of the presumed trajectory (which only satisfy the individual constraints) ? determination of the optimal planned trajectory from the exchanged information between robots belonging to the subset Ci (τk ) W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach Difficulties

Knowledge of the intentions of robots p ∈ Ci (τk ) uniqueness of the presumed trajectory

coherence between the presumed trajectory and the optimal planned trajectory Solution

+ Decomposition of the algorithm into 2 steps : ? determination of the presumed trajectory (which only satisfy the individual constraints) ? determination of the optimal planned trajectory from the exchanged information between robots belonging to the subset Ci (τk ) W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach Difficulties

Knowledge of the intentions of robots p ∈ Ci (τk ) uniqueness of the presumed trajectory

coherence between the presumed trajectory and the optimal planned trajectory Solution

+ Decomposition of the algorithm into 2 steps : ? determination of the presumed trajectory (which only satisfy the individual constraints) ? determination of the optimal planned trajectory from the exchanged information between robots belonging to the subset Ci (τk ) W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach

Few notations of robot i Intuitive horizon Td ∈ R+

Planning horizon Tp ∈ R+ (Tp ≤ Td ) Update horizon Tc ∈ R+ (Tc ≤ Tp )

qbi (t, τk ), u bi (t, τk ) : presumed trajectory of robot i beginning at τk with t ∈ [τk , τk + Td ] and corresponding control inputs

qi,ref (t, τk ), ui,ref (t, τk ) : optimal planned trajectory of robot i beginning at τk with t ∈ [τk , τk + Tp ] and corresponding control inputs

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach

Few notations of robot i Intuitive horizon Td ∈ R+

Planning horizon Tp ∈ R+ (Tp ≤ Td ) Update horizon Tc ∈ R+ (Tc ≤ Tp )

qbi (t, τk ), u bi (t, τk ) : presumed trajectory of robot i beginning at τk with t ∈ [τk , τk + Td ] and corresponding control inputs

qi,ref (t, τk ), ui,ref (t, τk ) : optimal planned trajectory of robot i beginning at τk with t ∈ [τk , τk + Tp ] and corresponding control inputs

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach Reach neighborhood of qi,f inal

YES

Stop of comput.

Initialization step (before robot’s movement) NO (qi,ref (t, τ0 ), ui,ref (t, τ0 )) ∀t ∈ [τ0 , τ0 + Tc ] Computation step over [τk−1 , τk−1 + Tc )

(qi,ref (t, τk ), ui,ref (t, τk ))

W. Perruquetti

∀t ∈ [τk , τk + Tc ]

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : decentralized approach D´etermination des param`etres initiaux YES

Reach of neighborhood qi,f inal

Arret des calculs

Oi (τ0 )

R´esolution du probl`eme Pbi (τ0 )

(b qi (t, τ0 ), ubi (t, τ0 ))

Initialization step (before robot’s Phasemovement) d’initialisation NO

(qi,ref (t, τ0 ), ui,ref (t, τ0 )) ∀t ∈ [τ0 , τ0 + Tc ] Computation step over [τk−1 , τOUI k−1 + Tc )

(qi,ref (t, τk ), ui,ref (t, τk ))

Ci,com (τ0 ) Ci,collision (τ0 ) Echange de donn´ees localement ∀p ∈ Ci (τ0 )

Arret des calculs

(b q p (t, τ0 ), ubp (t, τ0 ))

∀t ∈ [τk , τk + Tc ]

NON W. Perruquetti

∀t ∈ [τ0 , τ0 + Td ]

Calcul des ensembles de conflit

(avant d´eplacement des robots)

atteinte voisinage de qi, f inal

(qi (τ0 ), ui (τ0 ))

∀t ∈ [τ0 , τ0 + Tp ]

R´esolution du probl`eme Pi∗ (τ0 ) et stockage

(q

(t, τ ), u

(t, τ ))

0 Novembre 02009 i,re f 2009, i,re f RECAP

∀t ∈ [τ0 , τ0 + Tc ]

atteinte voisinage de qi, f inal

OUI

Arret Introduction Collaborativedes robotics calculs Collaborative path planning Control Bibliography

Goal and philosophy q p (t, τ0 ), ubp (t, τ0 )) ∀t Models(b Path planning for a single robot Multi-robots coordination

∈ [τ0 , τ0 + Tp ]

R´esolution du probl`eme Pi∗ (τ0 ) et stockage

Multi-robots approach NON coordination : decentralized (q (t, τ ), u (t, τ )) ∀t ∈ [τ , τ + T ] i,re f

0

i,re f

0

0

0

c

Mise a` jour zone obstacle Reach neighborhood of qi,f inal

YES

Stop of comput.

Initialization step (before robot’s movement) NO

Phase de calculs sur [τk−1 , τk−1 + Tc ) (qi,ref (t, τ0 ), ui,ref (t, τ0 )) ∀t ∈ [τ0 , τ0 + Tc ] Computation step over [τk−1 , τk−1 + Tc )

(qi,ref (t, τk ), ui,ref (t, τk ))

∀t ∈ [τk , τk + Tc ]

W.1Perruquetti

Oi (τk ) R´esolution du probl`eme Pbi (τk )

(b qi (t, τk ), ubi (t, τk ))

∀t ∈ [τk , τk + Td ]

Calcul des ensembles de conflit Ci,com (τk ) Ci,collision (τk )

Echange de donn´ees localement ∀p ∈ Ci (τk ) (b q p (τk ), ubp (τk ))

∀t ∈ [τk , τk + Tp ]

R´esolution du probl`eme Pi∗ (τk ) et stockage

), u Novembre (t, τ ))2009 ∀t ∈ [τ , τ + T ] (qRECAP (t, τ2009,

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : comparative results (2) 

1

K



2

U

3

K U



5

4 Figure 1:

Number of robots Na Maximum linear velocity vi,max Maximum angular velocity vi,max Radius of robot ρi Broadcasting range di,com Planning horizon Tp Update horizon Tc Intuitive horizon Td Maximum deformation ξ W. Perruquetti

5 0.5m/s 5rad/s 0.2m 2.5m 2s 0.5s 2.5s 0.25

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Multi-robots coordination : comparative results (2) Approach Maxi time of conflict resolution Exchanged Info. Implem. Time reaching goal

Cent.

Leader/Follower

Weakly decent.

Strongly decent.

2050ms

313ms

703ms

121ms

global

local

local

local

−−

++ sequential resolution

− if conflict with a lot of robots

+

39s

36s

36.5s

if Na  1 35s

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Strongly decentralized

Video W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Goal and philosophy Models Path planning for a single robot Multi-robots coordination

Strongly decentralized

Video W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Challenges Nonlinear dynamics, Presence of perturbations (unmodelled dynamics, sensor noise, external disturbances) How deal with the stabilization problem at low or zero velocity ? How to integrate cooperation into the control design ? Leader or not ?

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Facts : 90 percent of the job is done by nominal control (path planning from which the open loop control is obtained thanks to differential flatness), 10 by feedback !

Several solutions were proposed, a challenging problem being control design taking into account cooperation.

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Nouvelle architechture de commande (robots communicants) : nouveaux pb en Automatique (pr´esence de retards variables, effet de quantification des donn´ees, aspects distribu´es de la commande . . . ) partage des capteurs ext´eroceptifs (une cam´era associ´ee `a un robot, un t´el´em`etre `a un second, un compteur Geiger-M¨ uller `a un troisi`eme, etc.) : traitement de l’information (conditionnement des signaux, fusion de donn´ees, etc...)

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Quelques points durs : la conception et la commande de robots mobiles via des r´eseaux : dynamiques limit´ees (quelques m/s) ; capteurs distants : pbs li´es `a une identification performante + mesure temps r´eel pr´ecise de l’´etat du r´eseaux (perturbations ´electromagn´etiques, pertes d’informations, gigue, retards, etc.) ; les QoS (actuelles) sur des r´eseaux h´et´erog`enes asynchrones filaires et/ou sans fil ne sont pas adapt´ees en termes de temps de r´eponse, d’acc`es au m´edium pour la commande de processus ; les architectures de commandes logicielles et mat´erielles temps r´eel devront ˆetre adapt´ees `a des syst`emes communicants et distribu´es dont les syst`emes d’exploitations seront certainement h´et´erog`enes ainsi que les supports mat´eriels. W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

La conclusion pour RECAP .... voici un nouveau terrain de jeux o` u les capteurs “bougent” et donnent naissance `a de nouveaux probl`emes pour la communaut´e scientifique topologie du r´eseau change dans le temps et l’espace, les entit´es qui bougent sont plus ou moins connues (mod`eles cin´ematique + dynamique : on peut avec les techniques de l’automatique estimer certaines variables).... il faut utiliser ces connaissances, il y a d´ej`a eu, du temps des RTP, des interaction automatique/ informatique (commande `a travers les r´eseaux, commande pour la gestion de congestion etc...) : let’s do it again... ces probl`emes d’optimisations en d´ecentralis´e ne peuvent-ils pas r´epondre `a d’autres probl`emes de RECAP ? W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Bibliography

A. Astolfi, “Discontinuous control of nonholonomic systems”, Systems and Control Letters, 27(1), pp. 37–45, 1996. M. Bennani and P. Rouchon (1995),“Robust stabilization of flat and chained systems”, in Proceedings of the ECC, Rome, Italie. C.D. Boor, “A practical guide to splines ”, Springer, 1978. R. Brockett, “Asymptotic stability and feedback stabilization”, in R.W. Brockett, R.S. Millman, and H.J. Sussmann (eds.), Differential geometric control theory (Boston, MA : Birkhauser), pp. 181–195, 1983.

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Bibliography

C. Canudas de Wit, B. Siciliano and G. Bastin (Eds), “Theory of Robot Control”, Communications and control engineering series, Springer-verlag, Berlin Heidelberg New-York, 1996. M. Defoort, T. Floquet, W. Perruquetti, A. K¨ ok¨ osy, “Tracking of a unicycle-type mobile robot using integral sliding mode”, ICINCO, Barcelone, Espagne, 2005. M. Defoort, T. Floquet, A. K¨ ok¨ osy, W. Perruquetti, “Commande coop´erative d’une formation de robots mobiles”, in proc. IEEE CIFA 2006, Bordeaux, France, 30 mai – 1er juin, 2006.

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Bibliography M. Defoort, T. Floquet, A. K¨ ok¨ osy, W. Perruquetti, “Integral sliding mode control for trajectory tracking of a unicycle type mobile robot”, textitInt. Journal of Integrated Computer Aided Engeneering, to appear, 2006. J. Desai, J. Ostrowski and V. Kumar, “Modeling and control of formation of nonholonomic mobile robots”, IEEE Robotics and Automation, 17(6) pp. 905–308, 2001. S.V. Drakunov, T. Floquet and W. Perruquetti, “Stabilization and tracking control for an extended Heisenberg system with a drift”, Systems ans control Letters 54 (2005), pp. 435–445. M. Fliess, J.L´evine, Ph.Martin, et P.Rouchon. “Sur les syst`emes non lin´eaires diff´erentiellement plats”, C.R. Acad. Sci. Paris, I–315, pp. 619–624, 1992. W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Bibliography

M. Fliess, J. L´evine, Ph. Martin et P. Rouchon, “Lin´earisation par bouclage dynamique et transformations de Lie-B¨acklund.”, C.R. Acad. Sci. Paris, I 317, pp. 981–986, 1993. M. Fliess, J. L´evine, Ph. Martin and P. Rouchon, “Flatness and defect of nonlinear systems : introductory theory and examples”, Int. J. Control, Vol. 61 (6), pp. 1327–1361, 1995. M. Fliess, J. L´evine, Ph. Martin and P. Rouchon, “Design of trajectory stabilizing feedback for driftless flat systems”, in proc. ECC 95, Rome, Italie, pp. 1882–1887, 1995.

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Bibliography

M. Fliess, J.L´evine, Ph.Martin, et P.Rouchon. “A lie- b¨acklund approach to equivalence and flatness of nonlinear systems”, IEEE Trans Automatic Control, 44, pp. 922–937, 1999. Michel Fliess et Richard Marquez. “Continuous-time linear predictive control and flatness : a module-theoretic setting with examples”, International Journal of Control, 73(7) :606, 2000. T. Floquet, J.-P. Barbot and W. Perruquetti, “Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems”, Automatica, 39(6), pp. 1077–1083, 2003.

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Bibliography J.P. Hespanha, D. Liberzon and A.S. Morse, “Logic-based switching control of a nonholonomic system with parametric modeling uncertainty ”, Systems and Control Letters, 38, pp. 167–177, 1999. ZP. Jiang and H. Nijmeijer, “Tracking control of mobile robots : a case study in backsteeping”, Automatica, 33, No 7, pp. 1393-1399, 1997. J.P. Laumond, “La robotique mobile”, Herm`es, Trait´e IC2 INformation – Commande – Communication. P. Martin, P. Rouchon, “Feedback linearization and driftless systems”, Mathematics of Control, Signals and Systems, Vol. 7, pp. 235–254, 1994. P. Martin, P. Rouchon, “Any controllable driftless systems with 3 W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Bibliographie P. Martin, P. Rouchon, “Any controllable driftless systems with m inputs and m + 2 states is flat”, Proc. IEEE CDC, New Orleans, LA, pp. 167–175, 1995. M. B. Milam, N. Petit, and R. M. Murray, “Constrained trajectory generation for microsatellite formation flying”, In Proceedings of the AIAA Guidance, Navigation and Control Conference, pp. 328–333, 2001. R. Murray and S. Sastry, “Nonholonomic Motion Planning : Steering Using Sinusoids”, IEEE Trans. on Automatic Control, 38(5), pp. 700–716, 1993.

W. Perruquetti

RECAP 2009, Novembre 2009

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Bibliography J. Pomet, “Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift”, Systems and Control Letters, 18(2), pp. 147–158, 1992. C. Samson, “Control of chained systems : Application to path following and time-varying point-stabilization of mobile robots”, IEEE Trans. on Automatic Control, 40, pp. 64–77, 1995. Herbert G. Tanner and Amit Kumar,“Towards Decentralization of Mutli-robot Navigation Functions”, IEEE International Conference on Robotics and Automation, Barcelona, Spain, pp. 4143–4148, 2005. Herbert G. Tanner and Amit Kumar, “Formation Stabilization of Multiple Agents Using Decentralized Navigation Functions”, Robotics : Science and Systems I, S. Thrun, G. Sukhatme, S. W. Perruquetti RECAP pp 2009,49–56, Novembre 2009 Schaal and O. Brock (eds), MIT Press, 2005.

Introduction Collaborative robotics Collaborative path planning Control Bibliography

Bibliography

Z.-P. Jiang, E. Lefeber and H. Nijmeijer, “Saturated stabilization and track control of a nonholonomic mobile robot”, Systems and Control Letters, 42, pp. 327–332, 2001. Z.P. Jiang, “Robust exponential regulation of nonholonomic systems with uncertainties”, Automatica 36, pp. 189–209, 2000. Z.P. Jiang and H. Nijmeijer, “A recursive technique for tracking control of nonholonomic systems in chained form”, IEEE Transactions on Automatic Control, Vol. 44, No 2, pp. 265–279, 1999.

W. Perruquetti

RECAP 2009, Novembre 2009

Suggest Documents