Path planning on compact Lie groups using a homotopy method. (English) Zbl 1106.93320

Chitour, Y.

Syst. Control Lett. 47, No. 5, 383-391 (2002).

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

MSC:

93C25	Control/observation systems in abstract spaces
53C17	Sub-Riemannian geometry
70F25	Nonholonomic systems related to the dynamics of a system of particles
93C85	Automated systems (robots, etc.) in control theory

Keywords:

Homogeneous control systems; Motion planning; Sub-Riemannian metric; Homotopy method

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