Minimum Wheel-Rotation Paths for Differential-Drive Mobile Robots

Authors:
Hamidreza Chitsaz;Steven M. Lavalle;Devin J. Balkcom;Matthew T. Mason
Affiliations:
201 N Goodwin Ave Urbana Illinois United States 61801,;201 N Goodwin Ave Urbana Illinois United States 61801,;Dartmouth Computer Science Department Sudikoff Lab:HB 6211 Hanover, NH 03755 USA;Carnegie Mellon University, School of Computer Science5000 Forbes Avenue Pittsburgh PA 15213-3891
Venue:
International Journal of Robotics Research
Year:
2009

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Abstract

The shortest paths for a mobile robot are a fundamentalproperty of the mechanism, and may also be used as a family ofprimitives for motion planning in the presence of obstacles. Thispaper characterizes shortest paths for differential-drive mobilerobots, with the goal of classifying solutions in the spirit ofDubins curves and Reeds-Shepp curves for car-like robots. To obtaina well-defined notion of shortest, the total amount ofwheel-rotation is optimized. Using the Pontryagin Maximum Principleand other tools, we derive the set of optimal paths, and we give arepresentation of the extremals in the form of finite automata. Itturns out that minimum time for the Reeds-Shepp car is equal tominimum wheel-rotation for the differential-drive, and minimum timecurves for the convexified Reeds-Shepp car are exactly the same asminimum wheel-rotation paths for the differential-drive. It iscurrently unknown whether there is a simpler proof for thisfact.