Minimum Wheel-Rotation Paths for Differential-Drive Mobile Robots

The shortest paths for a mobile robot are a fundamental property of the mechanism, and may also be used as a family of primitives for motion planning in the presence of obstacles. This paper characterizes 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 the Pontryagin Maximum Principle and other tools, we derive the set of optimal paths, and we give a representation of the extremals in the form of finite automata. It turns out that minimum time for the Reeds—Shepp car is equal to minimum wheel-rotation for the differential-drive, and minimum time curves for the convexified Reeds—Shepp car are exactly the same as minimum wheel-rotation paths for the differential-drive. It is currently unknown whether there is a simpler proof for this fact.

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