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The Markov-Dubins Problem with Angular Acceleration Control

Authors: Hector J. Sussmann

Published: 1997 (Conference Paper)

Source: Proceedings of the 36th IEEE Conference on Decision and Control

Algorithm: Markov-Dubins Path

DOI: 10.1109/CDC.1997.657778

Summary

Studies a second-order variant of the Markov-Dubins minimum-length path problem where angular acceleration is the control rather than angular velocity, finding that optimal trajectories exclude bang-bang/singular junctions but may exhibit the Fuller phenomenon of infinite control chattering in Pontryagin extremals.

Abstract

We study a modified version of the well known Markov-Dubins problem, in which the control is angular acceleration rather than angular velocity. We show that an optimal trajectory cannot contain a junction of a bang-bang and a singular piece, and use the results of Zelikin and Borisov (1994) to show that there are Pontryagin extremals involving infinite chattering.

Primary

Paper doi.org

Standard

DOI 10.1109/CDC.1997.657778

Tags

  • Dubins path

  • optimal control

  • angular acceleration

  • bang-bang control

  • singular control

  • path planning

  • Pontryagin maximum principle