Minimum Wheel-Rotation Paths for Differential-Drive Robots
Abstract
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.
BibTeX
@article{Chitsaz-2009-10155,author = {Hamidreza Chitsaz and Steven M. LaValle and Devin J. Balkcom and Matthew T. Mason},
title = {Minimum Wheel-Rotation Paths for Differential-Drive Robots},
journal = {International Journal of Robotics Research},
year = {2009},
month = {January},
volume = {28},
number = {1},
pages = {66 - 80},
}