Extension of Reeds & Shepp Paths to a Robot with Front and Rear Wheel Steer

This paper presents an algorithm for extending RS paths for a robot with both front and rear wheel steer. We call such robots as FR steer. The occurrence of such paths is due to the additional maneuver possible in such a robot which we call parallel steer, in addition to the ones already present in a vehicle with only front wheel steering. Hence we extend the optimal path set Λ, containing only a single element to a set Ω, containing n elements, thereby extending its configuration set along the optimal path from the initial to the final configuration. This extension of the set Λ to set Ω is made possible by introducing a special set, which we call the Parallel Steer (PS) Set. Such an extension of the configuration set would increase the size of the final configuration set achievable by a path that is optimal in free space. In the following discussion, we shall term all paths whose length is equal to an RS path as optimal. Index Terms Reeds and Shepp (RS) Paths, Parallel steer, FR steer, motion planning