Uniform Global Exponential Stabilizing Passivity-Based Tracking Controller Applied to Planar Biped Robots
Authors
Pierluigi Arpenti, Alejandro Donaire, Fabio Ruggiero, Vincenzo Lippiello
Abstract
This paper presents a novel control approach, based on the interconnection and damping-assignment passivity-based control (IDA-PBC), to achieve stable and periodic walking for underactuated planar biped robots with one degree of underactuation. The system’s physical structure is preserved by assigning a target port-Hamiltonian dynamics to the closed-loop system, which also ensures passivity. The control design ensures that the tracking error to the desired periodic gait converges exponentially to zero, and the convergence rate can be adjusted via gain tuning. Besides, through the hybrid zero dynamics, the stability of the full-order system can be retrieved from the stability of the orbit created in a lower-dimensional manifold. The proposed approach is the first example of a tracking controller based on the IDA-PBC applied to underactuated biped robots. Numerical simulations on a five-link planar biped robot with unactuated ankles validate the approach and show the performance of the closed-loop system.
Citation
- Journal: 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- Year: 2022
- Volume:
- Issue:
- Pages: 6739–6745
- Publisher: IEEE
- DOI: 10.1109/iros47612.2022.9981206
BibTeX
@inproceedings{Arpenti_2022,
title={{Uniform Global Exponential Stabilizing Passivity-Based Tracking Controller Applied to Planar Biped Robots}},
DOI={10.1109/iros47612.2022.9981206},
booktitle={{2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}},
publisher={IEEE},
author={Arpenti, Pierluigi and Donaire, Alejandro and Ruggiero, Fabio and Lippiello, Vincenzo},
year={2022},
pages={6739--6745}
}
References
- Arpenti, P., Donaire, A., Ruggiero, F. & Lippiello, V. Energy pumping-and-damping for gait robustification of underactuated planar biped robots within the hybrid zero dynamics framework. 2020 IEEE-RAS 20th International Conference on Humanoid Robots (Humanoids) 415–421 (2021) doi:10.1109/humanoids47582.2021.9555787 – 10.1109/humanoids47582.2021.9555787
- Arpenti, P., Ruggiero, F. & Lippiello, V. A Constructive Methodology for the IDA-PBC of Underactuated 2-DoF Mechanical Systems with Explicit Solution of PDEs. International Journal of Control, Automation and Systems vol. 20 283–297 (2022) – 10.1007/s12555-020-0839-1
- Ferguson, J., Donaire, A. & Middleton, R. H. Kinetic-Potential Energy Shaping for Mechanical Systems With Applications to Tracking. IEEE Control Systems Letters vol. 3 960–965 (2019) – 10.1109/lcsys.2019.2919842
- Romero, J. G., Ortega, R. & Sarras, I. A Globally Exponentially Stable Tracking Controller for Mechanical Systems Using Position Feedback. IEEE Transactions on Automatic Control vol. 60 818–823 (2015) – 10.1109/tac.2014.2330701
- Holm, J. K. & Spong, M. W. Kinetic energy shaping for gait regulation of underactuated bipeds. 2008 IEEE International Conference on Control Applications 1232–1238 (2008) doi:10.1109/cca.2008.4629638 – 10.1109/cca.2008.4629638
- Arpenti, P., Ruggiero, F. & Lippiello, V. Interconnection and Damping Assignment Passivity-Based Control for Gait Generation in Underactuated Compass-Like Robots. 2020 IEEE International Conference on Robotics and Automation (ICRA) 9802–9808 (2020) doi:10.1109/icra40945.2020.9196598 – 10.1109/icra40945.2020.9196598
- de-León-Gómez, Ví., Santibañez, V. & Sandoval, J. Interconnection and damping assignment passivity-based control for a compass-like biped robot. International Journal of Advanced Robotic Systems vol. 14 172988141771659 (2017) – 10.1177/1729881417716593
- Westervelt, E. R., Grizzle, J. W. & Koditschek, D. E. Hybrid zero dynamics of planar biped walkers. IEEE Transactions on Automatic Control vol. 48 42–56 (2003) – 10.1109/tac.2002.806653
- Grizzle, J. W., Chevallereau, C., Sinnet, R. W. & Ames, A. D. Models, feedback control, and open problems of 3D bipedal robotic walking. Automatica vol. 50 1955–1988 (2014) – 10.1016/j.automatica.2014.04.021
- Branicky, M. S. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control vol. 43 475–482 (1998) – 10.1109/9.664150
- Garofalo, G., Ott, C. & Albu-Schaffer, A. Orbital stabilization of mechanical systems through semidefinite Lyapunov functions. 2013 American Control Conference 5715–5721 (2013) doi:10.1109/acc.2013.6580733 – 10.1109/acc.2013.6580733
- westervelt, Feedback Control of Dynamic Bipedal Robot Locomotion (2007)
- Westervelt, E. R., Buche, G. & Grizzle, J. W. Experimental Validation of a Framework for the Design of Controllers that Induce Stable Walking in Planar Bipeds. The International Journal of Robotics Research vol. 23 559–582 (2004) – 10.1177/0278364904044410
- 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
- ortega, Putting energy back into control. IEEE Control Syst Mag (2001)
- 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
- westervelt, Feedback Control of Dynamic Bipedal Robot Locomotion (2007)
- Isidori, A. Nonlinear Control Systems. Communications and Control Engineering (Springer London, 1995). doi:10.1007/978-1-84628-615-5 – 10.1007/978-1-84628-615-5
- 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 Transactions on Automatic Control vol. 59 876–891 (2014) – 10.1109/tac.2014.2299335