Topological property for collision-free nonholonomic motion planning: the case of sinusoidal inputs for chained form systems

Deals with nonholonomic motion planning including obstacle avoidance capabilities. We show that the methods developed in the absence of obstacles can be extended to the problem of obstacle avoidance, provided that they verify a topological property. Such steering methods allow us to design exact and complete collision-free path planners for a large family of systems. We show that the steering method using sinusoidal inputs applied to chained form systems fulfills the required conditions, and we illustrate its integration in collision-free path planning schemes through the tractor-trailers example.