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The International Journal of Robotics Research
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Minimum Wheel-Rotation Paths for Differential-Drive Mobile Robots

Hamidreza Chitsaz

201 N Goodwin Ave Urbana Illinois United States 61801, Chitsaz{at}cs.uiuc.edu

Steven M. LaValle

201 N Goodwin Ave Urbana Illinois United States 61801, lavalle{at}cs.uiuc.edu

Devin J. Balkcom

Dartmouth Computer Science Department Sudikoff Lab: HB 6211 Hanover, NH 03755 USA, devin{at}cs.dartmouth.edu

Matthew T. Mason

Carnegie Mellon University, School of Computer Science 5000 Forbes Avenue Pittsburgh PA 15213-3891, matt.mason{at}cs.cmu.edu

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.

Key Words: optimal control • nonholonomic constraints • shortest paths (or geodesics) • differential drive • mobile robot

The International Journal of Robotics Research, Vol. 28, No. 1, 66-80 (2009)
DOI: 10.1177/0278364908096750
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