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.
Original language | English (US) |
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Pages (from-to) | 66-80 |
Number of pages | 15 |
Journal | International Journal of Robotics Research |
Volume | 28 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2009 |
Externally published | Yes |
Keywords
- Differential drive
- Mobile robot
- Nonholonomic constraints
- Optimal control
- Shortest paths (or geodesics)
ASJC Scopus subject areas
- Software
- Modeling and Simulation
- Mechanical Engineering
- Electrical and Electronic Engineering
- Artificial Intelligence
- Applied Mathematics