✦ LIBER ✦

Path planning on compact Lie groups using a homotopy method

✍ Scribed by Y. Chitour

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 168 KB
Volume: 47
Category: Article
ISSN: 0167-6911
DOI: 10.1016/s0167-6911(02)00235-9

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✦ Synopsis

In this paper, we address the issue of solving the motion planning problems (MPP for short) for a class of left-invariant control systems whose state spaces are semisimple compact Lie groups. The sub-Riemannian metrics induced by the dynamics of admit nontrivial abnormal extremals. This fact a priori represents an obstruction for the procedure we use to tackle the MPP, which consists of a homotopy (or continuation) method. We are however able to provide complete answers for the MPP.