Topological Property of Trajectories Computed Inputs for Nonholonomic Chained Form

This paper deals with nonholonomic motion planning including obstacle avoidance capabilities. We show that the methods developed in absence of obstacles can be extended to the problem of obstacle avoidance, provided that they verify a topological property. This property is proved for the method using sinusoidal inputs applied to chained form systems [9], and illustrated through the Tractor- nailer example.