Article (Scientific journals)
Coordinated motion design on Lie groups
Sarlette, Alain; Bonnabel, Silvere; Sepulchre, Rodolphe
2010In IEEE Transactions on Automatic Control, 55 (5), p. 1047-1058
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Keywords :
Cooperative systems; Distributed control; Motion planning; Lie groups; Geometric control
Abstract :
[en] The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics. It thereby shows that coordination can be studied in a systematic way once the Lie group geometry of the configuration space is well characterized. Applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds. A link with Brockett's double bracket flows is also made. The concepts are illustrated on SO(3) , SE(2) and SE(3).
Research center :
Systems and Modeling
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, Silvere;  Mines ParisTech > Centre de robotique
Sepulchre, Rodolphe ;  Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation
Language :
English
Title :
Coordinated motion design on Lie groups
Publication date :
May 2010
Journal title :
IEEE Transactions on Automatic Control
ISSN :
0018-9286
Publisher :
IEEE, Piscataway, United States - New Jersey
Volume :
55
Issue :
5
Pages :
1047-1058
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Available on ORBi :
since 07 May 2010

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