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Motion planning of rolling surfaces

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2 Author(s)
A. Chelouah ; Lab. des Signaux et Systemes, CNRS, Gif sur Yvette, France ; Y. Chitour

In this paper, we address the issues of controllability and motion planning for the control system SR that results from the rolling without slipping nor spinning of a two dimensional Riemmanian manifold M1 onto another one M2. In the first part of the paper, we describe precisely the control system under consideration together with its Lie algebraic structure. This leads to a recovery of the result of Agrachev and Sachkov (1999) who provided a necessary and sufficient condition on the manifolds for complete controllability of SR. In the main part of the paper, we present two procedures to tackle the motion planning problem when M1 is a plane and M2 a convex surface. The first approach is based on differential algebra. We show that SR is a Liouvillian system and if M2 has a symmetry of revolution, we compute a maximal linearizing output. The second technic consists of the use of a continuation method to attack the motion planning problem. Even though SR admits nontrivial abnormal extremals, we are still able to successfully apply the continuation method if M2 admits a stable periodic geodesic

Published in:

Decision and Control, 2001. Proceedings of the 40th IEEE Conference on  (Volume:1 )

Date of Conference:

2001