A port-Hamiltonian formulation of mechanical systems with switching contact constraints

Authors

Thomas O’Brien, Joel Ferguson, Alejandro Donaire

Abstract

In this paper, a port-Hamiltonian approach to modelling of mechanical systems subject to switching contact constraints is presented. It is well known that a class of constrained systems can be represented as port-Hamiltonian systems without Lagrange multipliers by considering a reduced momentum space. Here, we revisit the modelling of these systems for the purpose of demonstrating that the discrete dynamics associated with switching constraints can be obtained directly through the process of mapping between reduced-order continuous systems. The modelling framework is illustrated by applying it to the compass-like biped robot, and the obtained port-Hamiltonian model is used to derive a passivity-based controller.

Citation

• Journal: 2025 European Control Conference (ECC)
• Year: 2025
• Volume:
• Issue:
• Pages: 1918–1924
• Publisher: IEEE
• DOI: 10.23919/ecc65951.2025.11187143

BibTeX

@inproceedings{O_Brien_2025,
  title={{A port-Hamiltonian formulation of mechanical systems with switching contact constraints}},
  DOI={10.23919/ecc65951.2025.11187143},
  booktitle={{2025 European Control Conference (ECC)}},
  publisher={IEEE},
  author={O’Brien, Thomas and Ferguson, Joel and Donaire, Alejandro},
  year={2025},
  pages={1918--1924}
}

Download the bib file

References

• Duindam, V., Macchelli, A., Stramigioli, S. & Bruyninckx, H. Modeling and Control of Complex Physical Systems. (Springer Berlin Heidelberg, 2009). doi:10.1007/978-3-642-03196-0 – 10.1007/978-3-642-03196-0
• Ferguson, Robust Control of Port-Hamiltonian Systems. Ph.D. thesis (2018)
• O’Brien, T., Ferguson, J. & Donaire, A. Exponentially Stable Regulation of Mechanical Systems to a Path. IFAC-PapersOnLine 56, 6801–6806 (2023) – 10.1016/j.ifacol.2023.10.389
• Brogliato, B. Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives. Annual Reviews in Control 55, 297–337 (2023) – 10.1016/j.arcontrol.2022.12.002
• Duindam, Port-Based Modelling and Control for Efficient Bipedal Walking Robots. Ph.D. thesis (2006)
• Ascher, U. M. & Petzold, L. R. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. (1998) doi:10.1137/1.9781611971392 – 10.1137/1.9781611971392
• Todorov, E. Convex and analytically-invertible dynamics with contacts and constraints: Theory and implementation in MuJoCo. 2014 IEEE International Conference on Robotics and Automation (ICRA) (2014) doi:10.1109/icra.2014.6907751 – 10.1109/icra.2014.6907751
• Van Der Schaft, A. J. & Maschke, B. M. On the Hamiltonian formulation of nonholonomic mechanical systems. Reports on Mathematical Physics 34, 225–233 (1994) – 10.1016/0034-4877(94)90038-8
• McGeer, T. Passive Dynamic Walking. The International Journal of Robotics Research 9, 62–82 (1990) – 10.1177/027836499000900206
• Goebel, R., Sanfelice, R. G. & Teel, A. R. Hybrid Dynamical Systems. (2012) doi:10.23943/princeton/9780691153896.001.0001 – 10.23943/princeton/9780691153896.001.0001
• Westervelt, E. R., Grizzle, J. W. & Koditschek, D. E. Hybrid zero dynamics of planar biped walkers. IEEE Trans. Automat. Contr. 48, 42–56 (2003) – 10.1109/tac.2002.806653
• Haddad, W. M., Nersesov, S. G. & Chellaboina, V. Energy-based control for hybrid port-controlled Hamiltonian systems. Automatica 39, 1425–1435 (2003) – 10.1016/s0005-1098(03)00113-4
• van der Schaft, A. J. & Schumacher, J. M. Complementarity modeling of hybrid systems. IEEE Trans. Automat. Contr. 43, 483–490 (1998) – 10.1109/9.664151
• Maschke, B. M. & van der Schaft, A. J. A Hamiltonian approach to stabilization of nonholonomic mechanical systems. Proceedings of 1994 33rd IEEE Conference on Decision and Control vol. 3 2950–2954 – 10.1109/cdc.1994.411344
• Hurmuzlu, Y. & Marghitu, D. B. Rigid Body Collisions of Planar Kinematic Chains With Multiple Contact Points. The International Journal of Robotics Research 13, 82–92 (1994) – 10.1177/027836499401300106
• Sadeghian, H., Ott, C., Garofalo, G. & Cheng, G. Passivity-based control of underactuated biped robots within hybrid zero dynamics approach. 2017 IEEE International Conference on Robotics and Automation (ICRA) 4096–4101 (2017) doi:10.1109/icra.2017.7989471 – 10.1109/icra.2017.7989471
• Ames, A. D., Galloway, K., Sreenath, K. & Grizzle, J. W. Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics. IEEE Trans. Automat. Contr. 59, 876–891 (2014) – 10.1109/tac.2014.2299335