Nonholonomic distance to polygonal obstacles for a car-like robot of polygonal shape

This paper shows how to compute the nonholonomic distance between a polygonal car-like robot and polygonal obstacles. The solution extends previous work of Reeds and Shepp by finding the shortest path to a manifold (rather than to a point) in configuration space. Based on optimal control theory, the proposed approach yields an analytic solution to the problem. Index Terms--Car-like robots, nonholonomic distance, optimal control theory, shortest paths.