Minimum wheel-rotation paths for differential-drive mobile robots

Hamidreza Chitsaz, Steven M Lavalle, Devin J. Balkcom, Matthew T. Mason

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)66-80
Number of pages15
JournalInternational Journal of Robotics Research
Issue number1
StatePublished - Jan 1 2009
Externally publishedYes


  • 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


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