The Dubins Car and Other Arm-Like Mobile Robots

Devin Balkcom1, Andrei Furtuna1, Weifu Wang2

  • 1Dartmouth College
  • 2University at Albany, SUNY

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Interactive Session

Sessions

10:30 - 13:00 | Tue 22 May | podG | TuA@G

Motion Planning 1

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Abstract

This paper investigates the connection between the kinematics of robots arms and the shortest paths for mobile robots. Lagrange multipliers are used to show that the shortest paths are equivalent to arms in configurations that balance an external force, while applying equal torques and forces at each joint. Analysis of the arm Jacobian yields a further geometric interpretations of optimal paths, constraining the locations of rotation centers and the directions of translations that may occur along optimal paths.

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Summary

A few trajectories for a Reeds-Sheep car, and corresponding robot arms.

  • Motion of rigid bodies under constant controls can be described as a kinematic robot arm.
  • Shortest paths for mobile robots including the Dubins car can be studied in terms of arms.
  • Shortest paths correspond to configurations of the arm in static force-torque balance.
  • This provides an alternate perspective on Dubins and Reeds-Sheep curves, using only simple calculus.