Parametric Study of Model-Based Dynamic Control Methods for Enhancing Locomotion in Underactuated Biped Robots, Case study: Hybrid Zero Dynamics and Proportional-Derivative Feedback

Document Type : Research Article

Authors

1 Shahid Beheshti University

2 Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran.

Abstract

The parametric study of model-based dynamic control methods holds significant importance in biped robot motion control. This research delves into a detailed examination of the parameters of model-based dynamic control methods, specifically the Hybrid Zero Dynamics (HZD) and Proportional-Derivative (PD) feedback control methods, to enhance the locomotion of underactuated biped robots. A three-link underactuated biped robot without a knee joint with three degrees of freedom is used as a case study, and the dynamic equations for this model are extracted in continuous and impact phases. Robot simulations are executed in MATLAB software by comparing and analyzing the control parameters in the two mentioned methods, and the results are compared and discussed. Furthermore, the effect of variations in control parameters in the Proportional-Derivative feedback control method is evaluated and compared. The results indicate that the Hybrid Zero Dynamics method generates more symmetrical and uniformly paced movements than the Proportional-Derivative feedback control method, with lower control effort. Increasing the control parameters in the Proportional-derived feedback control method brings its results closer to those of the hybrid zero dynamics method, accompanied by a reduction in control effort. In addition to presenting results, this study meticulously examines and analyzes control parameters, which can enhance bipedal robot performance.

Keywords

Main Subjects

References

[1] M. Vukobratović, B. Borovac, Zero-moment point—thirty five years of its life, International journal of humanoid robotics, 1(01) (2004) 157-173.
[2] T. McGeer, Dynamics and control of bipedal locomotion, Journal of theoretical biology, 163(3) (1993) 277-314.
[3] T. McGeer, Passive dynamic walking, The international journal of robotics research, 9(2) (1990) 62-82.
[4] T. McGeer, Passive dynamic biped catalogue, 1991, in:  Experimental Robotics II: The 2nd International Symposium, Toulouse, France, June 25–27 1991, Springer, 2005, pp. 463-490.
[5] A. Goswami, B. Espiau, A. Keramane, Limit cycles in a passive compass gait biped and passivity-mimicking control laws, Autonomous Robots, 4 (1997) 273-286.
[6] A. Goswami, B. Thuilot, B. Espiau, Compass-like biped robot part I: Stability and bifurcation of passive gaits, INRIA, 1996.
[7] S. Collins, A. Ruina, R. Tedrake, M. Wisse, Efficient bipedal robots based on passive-dynamic walkers, Science, 307(5712) (2005) 1082-1085.
[8] S.H. Collins, A. Ruina, R. Tedrake, M. Wisse, SUPPORTING ONLINE MATERIAL for Efficient bipedal robots based on passive-dynamic walkers, Mechanical Engineering, University of Michigan,  (2005) 1-8.
[9] S. Gupta, A. Kumar, A brief review of dynamics and control of underactuated biped robots, Advanced Robotics, 31(12) (2017) 607-623.
[10] B. Beigzadeh, S.A. Razavi, Dynamic walking analysis of an underactuated biped robot with asymmetric structure, International Journal of Humanoid Robotics, 18(04) (2021) 2150014.
[11] K. Mitobe, N. Mori, K. Aida, Y. Nasu, Nonlinear feedback control of a biped walking robot, in:  Proceedings of 1995 IEEE International Conference on Robotics and Automation, IEEE, 1995, pp. 2865-2870.
[12] J.W. Grizzle, G. Abba, F. Plestan, Asymptotically stable walking for biped robots: Analysis via systems with impulse effects, IEEE Transactions on automatic control, 46(1) (2001) 51-64.
[13] C. Chevallereau, Y. Aoustin, A. Formal'sky, Optimal walking trajectories for a biped, in:  Proceedings of the First Workshop on Robot Motion and Control. RoMoCo'99 (Cat. No. 99EX353), IEEE, 1999, pp. 171-176.
[14] C. Chevallereau, J.W. Grizzle, C.-L. Shih, Asymptotically stable walking of a five-link underactuated 3-D bipedal robot, IEEE transactions on robotics, 25(1) (2009) 37-50.
[15] J.W. Grizzle, C. Chevallereau, Virtual constraints and hybrid zero dynamics for realizing underactuated bipedal locomotion, arXiv preprint arXiv:1706.01127,  (2017).
[16] E. Westervelt, J. Grizzle, Design of asymptotically stable walking for a 5-link planar biped walker via optimization, in:  Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No. 02CH37292), IEEE, 2002, pp. 3117-3122.
[17] K. Sreenath, H.-W. Park, I. Poulakakis, J.W. Grizzle, A compliant hybrid zero dynamics controller for stable, efficient and fast bipedal walking on MABEL, The International Journal of Robotics Research, 30(9) (2011) 1170-1193.
[18] G.A. Castillo, B. Weng, A. Hereid, Z. Wang, W. Zhang, Reinforcement learning meets hybrid zero dynamics: A case study for rabbit, in:  2019 International Conference on Robotics and Automation (ICRA), IEEE, 2019, pp. 284-290.
[19] E.R. Westervelt, J.W. Grizzle, D.E. Koditschek, Hybrid zero dynamics of planar biped walkers, IEEE transactions on automatic control, 48(1) (2003) 42-56.
[20] E.R. Westervelt, G. Buche, J.W. Grizzle, Experimental validation of a framework for the design of controllers that induce stable walking in planar bipeds, The International Journal of Robotics Research, 23(6) (2004) 559-582.
[21] A. Goo, C.A. Laubscher, J.J. Wiebrecht, R.J. Farris, J.T. Sawicki, Hybrid Zero Dynamics Control for Gait Guidance of a Novel Adjustable Pediatric Lower-Limb Exoskeleton, Bioengineering, 9(5) (2022) 208.
[22] Y. Luo, U.J. Römer, A. Dyck, M. Zirkel, L. Zentner, A. Fidlin, Hybrid Zero Dynamics Control for Bipedal Walking with a Non-Instantaneous Double Support Phase, arXiv preprint arXiv:2303.05165,  (2023).
[23] E.R. Westervelt, J.W. Grizzle, C. Chevallereau, J.H. Choi, B. Morris, Feedback control of dynamic bipedal robot locomotion, CRC press, 2018.
[24] B. Beigzadeh, M.R. Sabaapour, M.R.H. Yazdi, K. Raahemifar, From a 3d passive biped walker to a 3d passivity-based controlled robot, International Journal of Humanoid Robotics, 15(04) (2018) 1850009.
[25] B. Beigzadeh, M.R. Sabaapour, M.R. Hairi Yazdi, Passivity based turning control of 3D biped robot with asymptotical stability, Modares Mechanical Engineering, 16(4) (2016) 205-212.
[26] G.A. Castillo, B. Weng, W. Zhang, A. Hereid, Hybrid zero dynamics inspired feedback control policy design for 3d bipedal locomotion using reinforcement learning, in:  2020 IEEE International Conference on Robotics and Automation (ICRA), IEEE, 2020, pp. 8746-8752.
[27] K.J. Åström, B. Wittenmark, Computer-controlled systems: theory and design, Courier Corporation, 2013.
[28] J.B. Aldrich, Feedback Control of Dynamic Bipedal Robot Locomotion (by Westervelt, ER et al.; 2007)[Book Review], IEEE Transactions on Automatic Control, 53(6) (2008) 1570-1572.
Amirkabir Journal of Mechanical Engineering
Volume 56, Issue 4
2024
Pages 497-516

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