We describe an approach for motion planning for nonholo-nomic systems without drift based on a combination of (a) earlier work of Sussmann and Laaerriere and (b) some recent results on approximation of trajectories, based on extensions of theorems of Kurzweil and Jarnik about limits of trajectories for highly oscillatory inputs.

We describe some recent new approaches for motion planning for nonholonomic systems without drift, developed in joint work of with G. Laaerriere and W. Liu. The main idea is to relate the trajectories of the given system to those of a \Lie bracket extension," and to seek ways to obtain trajectories of the original system that achieve the same eeect as a trajectory of the extended system.

This paper addresses the problem of path planning for a free-flying object in a (threedimensional) environment that contains both obstacles and so-called dangerzones. The path should (obviously) avoid collisions with the obstacles. The path is allowed to intersect with the dangerzones but this should be avoided as much as possible. We show that, under some mild conditions, a path always exists ...