Canonical nilpotent approximation of control systems: application to nonholonomic motion planning

This paper deals with the applications of the nilpotentization techniques developed by the author (1992) to motion planning for nonholonomic system. We show how to transform any controllable system into a canonical form corresponding to a nilpotent system approximating the original one. Its special triangular form allows to apply sinusoidal inputs to steer the system locally. Moreover, we show how to derive from the proposed canonical form an estimation of the metrics induced by the shortest feasible paths. This estimation holds at regular points as well as at singular points. All these results are illustrated by the example of a mobile robot with trailers