Model reduction of a flexible-joint robot: a port-Hamiltonian approach
Authors
H. Jardón-Kojakhmetov, M. Muñoz-Arias, Jacquelien M.A. Scherpen
Abstract
In this paper we explore the methodology of model order reduction based on singular perturbations for a flexible-joint robot within the port-Hamiltonian framework. We show that a flexible-joint robot has a port-Hamiltonian representation which is also a singularly perturbed ordinary differential equation. Moreover, the associated reduced slow subsystem corresponds to a port-Hamiltonian model of a rigid-joint robot. To exploit the usefulness of the reduced models, we provide a numerical example where an existing controller for a rigid robot is implemented.
Citation
- Journal: IFAC-PapersOnLine
- Year: 2016
- Volume: 49
- Issue: 18
- Pages: 832–837
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2016.10.269
- Note: 10th IFAC Symposium on Nonlinear Control Systems NOLCOS 2016- Monterey, California, USA, 23—25 August 2016
BibTeX
@article{Jard_n_Kojakhmetov_2016,
title={{Model reduction of a flexible-joint robot: a port-Hamiltonian approach}},
volume={49},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2016.10.269},
number={18},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Jardón-Kojakhmetov, H. and Muñoz-Arias, M. and Scherpen, Jacquelien M.A.},
year={2016},
pages={832--837}
}
References
- Canudas-de Wit, (1996)
- De Luca, Flexible Robots. (2014)
- Dirksz, D. A. & Scherpen, J. M. A. On Tracking Control of Rigid-Joint Robots With Only Position Measurements. IEEE Transactions on Control Systems Technology vol. 21 1510–1513 (2013) – 10.1109/tcst.2012.2204886
- Duindam, (2009)
- Fenichel, N. Geometric singular perturbation theory for ordinary differential equations. Journal of Differential Equations vol. 31 53–98 (1979) – 10.1016/0022-0396(79)90152-9
- Fujimoto, K. & Sugie, T. Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters vol. 42 217–227 (2001) – 10.1016/s0167-6911(00)00091-8
- Jones, C. K. R. T. Geometric singular perturbation theory. Lecture Notes in Mathematics 44–118 (1995) doi:10.1007/bfb0095239 – 10.1007/bfb0095239
- Kaper, T. J. An introduction to geometric methods and dynamical systems theory for singular perturbation problems. Proceedings of Symposia in Applied Mathematics 85–131 (1999) doi:10.1090/psapm/056/1718893 – 10.1090/psapm/056/1718893
- Kokotović, P. V. Applications of Singular Perturbation Techniques to Control Problems. SIAM Review vol. 26 501–550 (1984) – 10.1137/1026104
- Kokotovic, (1986)
- Kokotovic, P. V., O’Malley, R. E., Jr. & Sannuti, P. Singular perturbations and order reduction in control theory — An overview. Automatica vol. 12 123–132 (1976) – 10.1016/0005-1098(76)90076-5
- Murray, (1994)
- Ortega, (1998)
- Polyuga, R. V. & van der Schaft, A. Structure preserving model reduction of port-Hamiltonian systems by moment matching at infinity. Automatica vol. 46 665–672 (2010) – 10.1016/j.automatica.2010.01.018
- Scherpen, A structure preserving minimal representation of a nonlinear port-hamiltonian system. In Decision and Control, 2008. CDC 2008. 47th IEEE Conference on (2008)
- Spong, (2006)
- Spong, M. W. Modeling and Control of Elastic Joint Robots. Journal of Dynamic Systems, Measurement, and Control vol. 109 310–318 (1987) – 10.1115/1.3143860
- van der Schaft, (2000)
- van der Schaft, Structure-preserving model reduction of complex physical systems. Proceedings of the 48th IEEE Conference on Decision and Control (2009)
- Verhulst, (2005)
- Viola, G., Ortega, R., Banavar, R., Acosta, J. A. & Astolfi, A. Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes. IEEE Transactions on Automatic Control vol. 52 1093–1099 (2007) – 10.1109/tac.2007.899064