On optimal nonholonomic paths in a limited space

This work addresses the problem of finding the shortest path for a vehicle (say, a mobile robot or a car) moving in a limited workspace. The proposed approach makes use of a tool dubbed the reflective unfolding operator which has a clear geometric interpretation and provides an interesting means for solving other trajectory design problems. The authors' previously reported result (1997) which relates to the special case of a car maneuvering within a disc-shaped area, is extended here to the general case of an arbitrarily shaped area. The approach is illustrated by computer simulations.