Discontinuous energy shaping control of the Chaplygin sleigh
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}
}
References
- Astolfi, Discontinuous control of nonholonomic systems. Systems & Control Letters (1996)
- Astolfi, A., Ortega, R. & Venkatraman, A. A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints. Automatica vol. 46 182–189 (2010) – 10.1016/j.automatica.2009.10.027
- Bloch, (2003)
- Bloch, A. M., Reyhanoglu, M. & McClamroch, N. H. Control and stabilization of nonholonomic dynamic systems. IEEE Transactions on Automatic Control vol. 37 1746–1757 (1992) – 10.1109/9.173144
- Brockett, Asymptotic stability and feedback stabilization. (1983)
- Fujimoto, K., Sakai, S. & Sugie, T. Passivity based control of a class of Hamiltonian systems with nonholonomic constraints. Automatica vol. 48 3054–3063 (2012) – 10.1016/j.automatica.2012.08.032
- Goldstein, (1980)
- Gómez-Estern, F. & Van der Schaft, A. J. Physical Damping in IDA-PBC Controlled Underactuated Mechanical Systems. European Journal of Control vol. 10 451–468 (2004) – 10.3166/ejc.10.451-468
- Lee, D. Passivity-Based Switching Control for Stabilization of Wheeled Mobile Robots. Robotics: Science and Systems III (2007) doi:10.15607/rss.2007.iii.008 – 10.15607/rss.2007.iii.008
- Lieb, (2001)
- Tian, Y.-P. & Li, S. Exponential stabilization of nonholonomic dynamic systems by smooth time-varying control. Automatica vol. 38 1139–1146 (2002) – 10.1016/s0005-1098(01)00303-x
- Van Der Schaft, A. J. & Maschke, B. M. On the Hamiltonian formulation of nonholonomic mechanical systems. Reports on Mathematical Physics vol. 34 225–233 (1994) – 10.1016/0034-4877(94)90038-8