Maxwell Points of Dynamical Control Systems Based on Vertical Rolling Disc-Numerical Solutions

We study two nilpotent affine control systems derived from the dynamic and control of a vertical rolling disc that is a simplification of a differential drive wheeled mobile robot. For both systems, their controllable Lie algebras are calculated and optimal control problems are formulated, and their Hamiltonian systems of ODEs are derived using the Pontryagin maximum principle. These optimal control problems completely determine the energetically optimal trajectories between two states. Then, a novel numerical algorithm based on optimisation for finding the Maxwell points is presented and tested on these control systems. The results show that the use of such numerical methods can be beneficial in cases where common analytical approaches fail or are impractical.

Keywords

differential drive wheeled mobile robot, geometric control theory, Lie algebra, non-holonomics mechanics, nilpotent approximation, optimal control, Maxwell points, nonlinear optimisation, numerical solver

Citation

Robotics. 2021, vol. 10, issue 3, p. 1-19.
https://www.mdpi.com/2218-6581/10/3/88

Document type

Peer-reviewed

Document version

Published version

Language of document

en

Document licence

Creative Commons Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/