Path planning on compact Lie groups using a homotopy method

Abstract In this paper, we address the issue of solving the motion planning problems (MPP for short) for a class of left-invariant control systems Σ whose state spaces are semisimple compact Lie groups. The sub-Riemannian metrics induced by the dynamics of Σ 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.

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