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Control of stance-leg motion and zero-moment point for achieving perfect upright stationary state of rimless wheel type walker with parallel linkage legs

Published online by Cambridge University Press:  19 September 2024

Fumihiko Asano*
Affiliation:
Graduate School of Advanced Science and Technology, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Japan
Mizuki Kawai
Affiliation:
Graduate School of Advanced Science and Technology, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Japan Shimadzu Corporation, 3-9-4, Hikaridai, Seika-cho, Soraku-gun, Kyoto, Japan
*
Corresponding author: Fumihiko Asano; Email: [email protected]

Abstract

The authors have studied models and control methods for legged robots without having active ankle joints that can not only walk efficiently but also stop and developed a method for generating a gait that starts from an upright stationary state and returns to the same state in one step for a simple walker with one control input. It was clarified, however, that achieving a perfect upright stationary state including zero dynamics is impossible. Based on the observation, in this paper we propose a novel robotic walker with parallel linkage legs that can return to a perfect stationary standing posture in one step while simultaneously controlling the stance-leg motion and zero-moment point (ZMP) using two control inputs. First, we introduce a model of a planar walker that consists of two eight-legged rimless wheels, a body frame, a reaction wheel, and massless rods and describe the system dynamics. Second, we consider two target control conditions; one is control of the stance-leg motion, and the other is control of the ZMP to stabilize zero dynamics. We then determine the control input based on the two conditions with the target control period derived from the linearized model and consider adding a sinusoidal control input with an offset to correct the resultant terminal state of the reaction wheel. The validity of the proposed method is investigated through numerical simulations.

Type
Research Article
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Collins, S., Ruina, A., Tedrake, R. and Wisse, M., “Efficient bipedal robots based on passive-dynamic walkers,” Science 307(5712), 10821085 (2005).CrossRefGoogle ScholarPubMed
Westervelt, E. R., Grizzle, J. W., Chevallereau, C., Choi, J. H. and Morris, B.. Feedback Control of Dynamic Bipedal Robot Locomotion (Boca Raton, FL: CRC Press, Taylor & Francis Group, 2007).Google Scholar
Roussel, L., Canudas-De-Wit, C. and Goswami, A., “Generation of Energy Optimal Complete Gait Cycles for Biped Robots,” In: Proceedings of the IEEE International Conference on Robotics and Automation, (1998) pp. 20362041.Google Scholar
Asano, F. and Xiao, X., “Output Deadbeat Control Approaches to Fast Convergent Gait Generation of Underactuated Spoked Walker,” In: Proceedings of the IEEE/SICE International Symposium on System Integration, (2012) pp. 265270.Google Scholar
Asano, F., “A novel gait generation method independent of target settling-time adjustment for underactuated limit cycle walking,” Multibody Syst Dyn 37(2), 227244 (2016).CrossRefGoogle Scholar
Asano, F., Zheng, Y. and Xiao, X., “Time-scale control approaches to collisionless walking of an underactuated rimless wheel,” J Robot Mechatron 29(3), 471479 (2017).CrossRefGoogle Scholar
Asano, F. and Zheng, Y., “High-speed and energy-efficient collisionless walking of underactuated rimless wheel,” Artif Life Robot 23(4), 523531 (2018).CrossRefGoogle Scholar
Asano, F. and Kawai, M., “Generation of Limit Cycle Gait with Static Standing Posture as Initial and Terminal States,” In: Proceedings of the 6th International Symp. on Swarm Behavior and Bio-Inspired Robotics, (2023) pp. 14811486.Google Scholar
Asano, F., “Stability Principle Underlying Passive Dynamic Walking of Rimless Wheel,” In: Proceedings of the IEEE International Conference on Control Applications, (2012) pp. 10391044.Google Scholar
Narukawa, T., Takahashi, M. and Yoshida, K., “Design and stability analysis of a 3D rimless wheel with flat feet and ankle springs,” J Syst Design Dyn 3(3), 258269 (2009).CrossRefGoogle Scholar
Inoue, R., Asano, F., Tanaka, D. and Tokuda, I., “Passive Dynamic Walking of Combined Rimless Wheel and its Speeding-up by Adjustment of Phase Difference,” In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (2011) pp. 27472752.Google Scholar
Asano, F. and Xiao, X., “Role of Deceleration Effect in Efficient and Fast Convergent Gait Generation,” In: Proceedings of the IEEE International Conference on Robotics and Automation, (2013) pp. 56495654.Google Scholar
Vukobratović, M. and Stepanenko, J., “On the stability of anthropomorphic systems,” Math Biosci 15(1-2), 137 (1972).CrossRefGoogle Scholar
Vukobratović, M. and Borovac, B., “Zero-moment point–thirty five years of its life,” Int J Human Robot 1(1), 157173 (2004).CrossRefGoogle Scholar
Funabashi, H., Horie, M., Tachiya, H. and Tanio, S., “A synthesis of robotic pantograph mechanisms based on working spaces and static characteristic charts,” JSME Int J Series 34(2), 239244 (1991).Google Scholar
Simionescu, P. A. and Tempea, I., “Kinematic and Kinetostatic Simulation of a Leg Mechanism,” In: Proceedings of the tenth World Congress on the Theory of Machines and Mechanisms, (1999) pp. 572577.Google Scholar
Liang, C., Ceccarelli, M. and Takeda, Y., “Operation analysis of a Chebyshev-Pantograph leg mechanism for a single DOF biped robot,” Front Mech Eng 7(4), 357370 (2012).CrossRefGoogle Scholar
Nansai, S., Rojas, N., Elara, M. R., Sosa, R. and Iwase, M., “A novel approach to gait synchronization and transition for reconfigurable walking platforms,” Digital Commun Net 1(2), 141151 (2015).CrossRefGoogle Scholar
Desai, S. G., Annigeri, A. R. and TimmanaGouda, A., “Analysis of a new single degree-of-freedom eight link leg mechanism for walking machine,” Mech Mach Theory 140, 747764 (2019).CrossRefGoogle Scholar
McGeer, T., “Passive dynamic walking,” Int J Robot Res 9(2), 6282 (1990).CrossRefGoogle Scholar
Coleman, M. J., “Dynamics and stability of a rimless spoked wheel: A simple 2D system with impacts,” Dyn Syst 25(2), 215238 (2010).CrossRefGoogle Scholar
Asano, F., Chen, H. and Liu, R., “Ultrahigh-Speed Strict Stealth Walking of Combined Rimless Wheel with 2-DOF Wobbling Mass,” In: Proceedings of the IEEE Int Conference on Robotics and Biomimetics, (2022) pp. 15151520.Google Scholar
Asano, F., “Strict Stealth Walking of Legged Robot Formed by Four Parallelogram Links and Equipped with Wobbling Mass and Reaction Wheel,” In: Preprint of the 12th IFAC Symp. on Nonlinear Control Systems, (2023) pp. 246251.Google Scholar
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