Sepulchre, Rodolphe[Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Proceedings of the 47th IEEE Conference on Decision and Control
47th IEEE Conference on Decision and Control
IEEE / CSS
[en] Coordinated motion ; Lie groups ; formation control
[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).