Geometry of Nonholonomic Systems

Nonholonomic motion planning is best understood with some knowledge of the underlying geometry. In this chapter, we first introduce in Section 1 the basic notions of the geometry associated to control systems without drift. In the following sections, we present a detailed study of an example, the car with n trailers, then some general results on polynomial systems, which can be used to bound the complexity of the decision problem and of the motion planning for these systems.