A motion planning algorithm for the rolling-body problem

In this paper, we consider the control system ¿ defined by the rolling of a strictly convex surface S on a plane without slipping or spinning. It is well known that ¿ is completely controllable. The purpose of this paper is to present the numerical implementation of a constructive planning algorithm for ¿, which is based on a continuation method. The performances of that algorithm, both in robustness and convergence speed, are illustrated through two examples: rolling of a flattened ball and an egg on the plane.