The Markov-Dubins Problem with Angular Acceleration Control

Authors

Hector J. Sussmann

Year

1997

Conference Paper

Algorithm

Markov-Dubins Path

Source

Proceedings of the 36th IEEE Conference on Decision and Control

Identifiers

DOI 10.1109/CDC.1997.657778

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.

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.