Minimum wheel-rotation paths for differential-drive mobile robots

Characterizing optimal paths for mobile robots is an interesting, important, and challenging endeavor. Not only they are interesting with respect to the optimized criteria, but also they offer a family of motion primitives that can be used for motion planning in the presence of obstacles. This paper presents characterization of shortest paths for differential-drive mobile robots, with the goal of classifying solutions in the spirit of Dubins curves and Reeds-Shepp curves for car-like robots. To obtain a well-defined notion of shortest., the total amount of wheel rotation is optimized. Using Pontryagin maximum principle and other tools, we establish the existence of optimal trajectories, and derive the set of optimal paths. Some Reeds-Shepp curves appear in the set of optimal paths, whereas there are optimal paths which are different from Reeds-Shepp curves. To the best of our knowledge, this is the first progress on the problem