Publication detail

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

STODOLA, M. RAJCHL, M. BRABLC, M. FROLÍK, S. KŘIVÁNEK, V.

Original Title

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

Type

journal article in Web of Science

Language

English

Original Abstract

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

Authors

STODOLA, M.; RAJCHL, M.; BRABLC, M.; FROLÍK, S.; KŘIVÁNEK, V.

Released

12. 7. 2021

Publisher

MDPI

Location

BASEL

ISBN

2218-6581

Periodical

Robotics

Year of study

10

Number

3

State

Swiss Confederation

Pages from

1

Pages to

19

Pages count

19

URL

https://www.mdpi.com/2218-6581/10/3/88

Full text in the Digital Library

http://hdl.handle.net/11012/203030

BibTex

@article{BUT173085,
  author="Marek {Stodola} and Matej {Rajchl} and Martin {Brablc} and Stanislav {Frolík} and Václav {Křivánek}",
  title="Maxwell Points of Dynamical Control Systems Based on Vertical Rolling Disc-Numerical Solutions",
  journal="Robotics",
  year="2021",
  volume="10",
  number="3",
  pages="1--19",
  doi="10.3390/robotics10030088",
  issn="2218-6581",
  url="https://www.mdpi.com/2218-6581/10/3/88"
}