Authors

Joel Ferguson, Alejandro Donaire, Richard H. Middleton

Abstract

In this paper we present an energy shaping control law for set-point regulation of the Chaplygin sleigh. It is well known that nonholonomic mechanical systems cannot be asymptotically stabilised using smooth control laws as they do no satisfy Brockett’s necessary condition for smooth stabilisation. Here, we propose a discontinuous control law that can be interpreted as a potential energy shaping and damping injection controller. The proposed controller is shown to be robust against the parameters of both the inertia matrix and the damping structure of the open-loop system.

Keywords

Nonholonomic systems; port-Hamiltonian systems; discontinuous control; robust control

Citation

  • Journal: IFAC-PapersOnLine
  • Year: 2018
  • Volume: 51
  • Issue: 3
  • Pages: 211–216
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.ifacol.2018.06.056
  • Note: 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018

BibTeX

@article{Ferguson_2018,
  title={{Discontinuous energy shaping control of the Chaplygin sleigh}},
  volume={51},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2018.06.056},
  number={3},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Ferguson, Joel and Donaire, Alejandro and Middleton, Richard H.},
  year={2018},
  pages={211--216}
}

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References