A Motion-Planning Algorithm for the Rolling-Body Problem

摘要

In this paper, we consider the control system $Sigma$ defined by the rolling of a strictly convex surface $S$ of $I!! R^3$ on a plane without slipping or spinning. The purpose of this paper is to present the numerical implementation of a constructive planning algorithm for $Sigma$, which is based on a continuation method. The performances of that algorithm, both in robustness and convergence speed, are illustrated through several examples.