Authors

Kenji Fujimoto, Satoru Sakai, Toshiharu Sugie

Abstract

This paper is concerned with state and output feedback stabilization of a class of port-Hamiltonian systems with nonholonomic constraints. First we study canonical forms for port-Hamiltonian systems with nonholonomic constraints. Second, we give a new state feedback stabilization method by using non-smooth Hamiltonian functions via generalized canonical transformations. Third, we propose a dynamic output feedback stabilization method without measuring the velocity based on the corresponding state feedback result. Numerical examples demonstrate the effectiveness of the proposed method.

Keywords

Port-Hamiltonian systems; Nonholonomic systems; Stabilization

Citation

BibTeX

@article{Fujimoto_2012,
  title={{Passivity based control of a class of Hamiltonian systems with nonholonomic constraints}},
  volume={48},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2012.08.032},
  number={12},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Fujimoto, Kenji and Sakai, Satoru and Sugie, Toshiharu},
  year={2012},
  pages={3054--3063}
}

Download the bib file

References

  • Arimoto, (1996)
  • Astolfi, A. Discontinuous control of nonholonomic systems. Systems & Control Letters vol. 27 37–45 (1996) – 10.1016/0167-6911(95)00041-0
  • 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
  • Fierro, R. & Lewis, F. L. Control of a nonholonomic mobile robot: backstepping kinematics into dynamics. Proceedings of 1995 34th IEEE Conference on Decision and Control vol. 4 3805–3810 – 10.1109/cdc.1995.479190
  • Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica vol. 39 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005
  • 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
  • Fujimoto, K. & Sugie, T. Iterative learning control of hamiltonian systems: I/O based optimal control approach. IEEE Transactions on Automatic Control vol. 48 1756–1761 (2003) – 10.1109/tac.2003.817908
  • JIANGdagger, Z.-P. & NIJMEIJER, H. Tracking Control of Mobile Robots: A Case Study in Backstepping**This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Alberto Isidori under the direction of Editor Tamer Başar. Automatica vol. 33 1393–1399 (1997) – 10.1016/s0005-1098(97)00055-1
  • Kelly, A simple set point robot controller by using only position measurements. (1993)
  • Khalil, (1996)
  • Khennouf, Quasi-continuous exponential stabilizers for nonholonomic systems. (1996)
  • Developments in nonholonomic control problems. IEEE Control Systems vol. 15 20–36 (1995) – 10.1109/37.476384
  • Macchelli, A. & Melchiorri, C. Control by interconnection of mixed port Hamiltonian systems. IEEE Transactions on Automatic Control vol. 50 1839–1844 (2005) – 10.1109/tac.2005.858656
  • Maschke, B. M., van der Schaft, A. J. & Breedveld, P. C. An intrinsic Hamiltonian formulation of the dynamics of LC-circuits. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications vol. 42 73–82 (1995) – 10.1109/81.372847
  • Murray, R. M. & Sastry, S. S. Nonholonomic motion planning: steering using sinusoids. IEEE Transactions on Automatic Control vol. 38 700–716 (1993) – 10.1109/9.277235
  • Nijmeijer, (1990)
  • Ortega, R., Loria, A., Kelly, R. & Praly, L. On passivity‐based output feedback global stabilization of euler‐lagrange systems. International Journal of Robust and Nonlinear Control vol. 5 313–323 (1995) – 10.1002/rnc.4590050407
  • Ortega, (1998)
  • Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Transactions on Automatic Control vol. 47 1218–1233 (2002) – 10.1109/tac.2002.800770
  • Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
  • Takegaki, M. & Arimoto, S. A New Feedback Method for Dynamic Control of Manipulators. Journal of Dynamic Systems, Measurement, and Control vol. 103 119–125 (1981) – 10.1115/1.3139651
  • van der Schaft, (2000)
  • 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
  • Van der schaft, A. J. & Maschke, B. M. Mathematical Modeling of Constrained Hamiltonian Systems. IFAC Proceedings Volumes vol. 28 637–642 (1995) – 10.1016/s1474-6670(17)46900-x