Coordination on Lie groups

Sarlette, Alain; Bonnabel, Silvère; Sepulchre, Rodolphe

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Coordination on Lie groups

Sarlette, Alain; Bonnabel, Silvère; Sepulchre, Rodolphe

2008 • In Proceedings of the 47th IEEE Conference on Decision and Control

Peer reviewed

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https://hdl.handle.net/2268/9499

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Keywords :

Coordinated motion; Lie groups; formation control

Abstract :

[en] This paper studies the coordinated motion of a group of agents evolving on a Lie group. Left- or right-invariance with respect to the absolute position on the group lead to two different characterizations of relative positions and two associated definitions of coordination (fixed relative positions). Conditions for each type of coordination are derived in the associated Lie algebra. This allows to formulate the coordination problem on Lie groups as consensus in a vector space. Total coordination occurs when both types of coordination hold simultaneously. The discussion in this paper provides a common geometric framework for previously published coordination control laws on SO(3), SE(2) and SE(3). The theory is illustrated on the group of planar rigid motion SE(2).

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Sarlette, Alain ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation

Bonnabel, Silvère; Ecole des Mines de Paris > Centre de Robotique

Sepulchre, Rodolphe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation

Language :

English

Title :

Coordination on Lie groups

Publication date :

December 2008

Event name :

47th IEEE Conference on Decision and Control

Event organizer :

IEEE / CSS

Event place :

Cancun, Mexico

Audience :

International

Main work title :

Proceedings of the 47th IEEE Conference on Decision and Control

Pages :

1275-1279

Peer reviewed :

Peer reviewed

Available on ORBi :

since 24 March 2009

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Scopus citations^®
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