Publication detail

Numerical Experiment on Optimal Control for the Dubins Car Model

FROLÍK, S. RAJCHL, M. STODOLA, M.

Original Title

Numerical Experiment on Optimal Control for the Dubins Car Model

Type

conference paper

Language

English

Original Abstract

This paper deals with optimal control of the Dubins car model, whose configuration space is three dimensional smooth manifold. There are computed vector fields that generate solvable Lie algebra isomoprhically equivalent to tangent space in each point of the manifold. Then an otpimal control problem for finding the shortest curve between two points on the manifold is formulated. The problem is analytically solved for the nilpotent approximation of the fields and fixed points of the symmetries are found. To these fixed points multiple optimal trajectories can lead. The problem is also solved by using numerical simulations and these are compared with the analyticla solutions.

Keywords

Dubins car model, Lie algebra, Optimal control problem, Pontryagin maximum principle, Nilpotent algebra, Numerical simulations

Authors

FROLÍK, S.; RAJCHL, M.; STODOLA, M.

Released

5. 3. 2021

ISBN

978-3-030-70739-2

Book

Modelling and Simulation for Autonomous Systems

ISBN

1611-3349

Periodical

Lecture Notes in Computer Science

Number

12619

State

Republic of Italy

Pages from

111

Pages to

122

Pages count

11

BibTex

@inproceedings{BUT183064,
  author="Stanislav {Frolík} and Matej {Rajchl} and Marek {Stodola}",
  title="Numerical Experiment on Optimal Control for the Dubins Car Model",
  booktitle="Modelling and Simulation for Autonomous Systems",
  year="2021",
  journal="Lecture Notes in Computer Science",
  number="12619",
  pages="111--122",
  doi="10.1007/978-3-030-70740-8\{_}7",
  isbn="978-3-030-70739-2",
  issn="1611-3349"
}