/Extremal Trajectories for Bounded Velocity Mobile Robots

Extremal Trajectories for Bounded Velocity Mobile Robots

Devin Balkcom and Matthew T. Mason
Conference Paper, ICRA, May, 2002

Copyright notice: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author’s copyright. These works may not be reposted without the explicit permission of the copyright holder.


Previous work has presented the time optimal trajectories for three classes of non-holonomic mobile robots: steered cars that can only go forwards, steered cars that go forwards or backwards, and differential drives. Each of the vehicles is modelled as a rigid body in the plane with velocity and angular velocity controls. The systems are differentiated only by the bounds on the controls, but the optimal trajectories are qualitatively different for each system. We explore this difference by considering the effect that control bounds have on the extremal trajectories of bounded velocity vehicles, where the extremal trajectories are defined to be the set of trajectories that satisfy Pontryagin’s Maximum Principle, a necessary condition for optimality.

BibTeX Reference
author = {Devin Balkcom and Matthew T. Mason},
title = {Extremal Trajectories for Bounded Velocity Mobile Robots},
booktitle = {ICRA},
year = {2002},
month = {May},
keywords = {time optimal trajectories, mobiile robots, Pontryagin, Extremal trajectories, kinematics models of mobile robots},