NILPOTENT BASES FOR A CLASS OF NONINTEGRABLE DISTRIBUTIONS WITH APPLICATIONS TO TRAJECTORY GENERATION FOR NONHOLONOMIC SYSTEMS

This paper develops a constructive method for finding a nilpotent basis for a special class of smooth nonholonomic distributions. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior differential systems. The results are applied to the problem of finding a set of nilpotent input vector fields for a nonholonomic control system, which can then be used to construct explicit trajectories to drive the system between any two points. A kinematic model of a rolling penny is used to illustrate this approach. The methods presented here extend previous work using the ''chained form'' and cast that work into a coordinate-free setting.