Detail publikačního výsledku

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

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

Originální název

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

Anglický název

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

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

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

Rok RIV

2022

Vydáno

12.07.2021

Nakladatel

MDPI

Místo

BASEL

ISSN

2218-6581

Periodikum

Robotics

Svazek

10

Číslo

3

Stát

Švýcarská konfederace

Strany od

1

Strany do

19

Strany počet

19

URL

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

Plný text v Digitální knihovně

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",
  url="https://www.mdpi.com/2218-6581/10/3/88"
}

Dokumenty

robotics-10-00088-v2