LCP method for a planar passive dynamic walker based on an event-driven scheme
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The main purpose of this paper is to present a linear complementarity problem (LCP) method for a planar passive dynamic walker with round feet based on an event-driven scheme. The passive dynamic walker is treated as a planar multi-rigid-body system. The dynamic equations of the passive dynamic walker are obtained by using Lagrange’s equations of the second kind. The normal forces and frictional forces acting on the feet of the passive walker are described based on a modified Hertz contact model and Coulomb’s law of dry friction. The state transition problem of stick-slip between feet and floor is formulated as an LCP, which is solved with an event-driven scheme. Finally, to validate the methodology, four gaits of the walker are simulated: the stance leg neither slips nor bounces; the stance leg slips without bouncing; the stance leg bounces without slipping; the walker stands after walking several steps.
KeywordsPassive dynamic walker Non-smooth dynamics Dry friction Linear complementarity problem Stick-slip
The project was supported by the National Natural Science Foundation of China (Grants 11372018, 11772021).
- 3.Walsh, C.J., Paluska, D., Pasch, K., et al.: Development of a lightweight, underactuated exoskeleton for load-carrying augmentation. In: IEEE International Conference on Robotics and Automation, ICRA 2006, May 15–19, Orlando, Florida, USA, 3485–3491 (2006)Google Scholar
- 6.Alexander, M.N.: Walking made simple. Science 308, 58–59 (2005)Google Scholar
- 16.Asano, F., Saka, T., Fujimoto, T.: Passive dynamic walking of compass-like biped robot on slippery downhill. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Hamburg, Germany, 4113–4118 (2015)Google Scholar
- 17.Asano, F., Saka, T., Harata, Y.: 3-DOF passive dynamic walking of compass-like biped robot with semicircular feet generated on slippery downhill. In: IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, 3570–3575 (2016)Google Scholar
- 18.Asano, F., Seino, T., Tokuda, I., et al.: A novel locomotion robot that slides and rotates on slippery downhill. In: IEEE International Conference on Advanced Intelligent Mechatronics (AIM), Banff, Alberta, Canada, 425–430 (2016)Google Scholar
- 29.Duan, W., Wang, Q., Wang, T.: Simulation research of a passive dynamic walker with round feet based on non-smooth method. Lixue Xuebao/Chin. J. Theor. Appl. Mech. 43, 765–774 (2011)Google Scholar
- 30.Johnson, K.L.: One hundred years of Hertz contact. Proc. Inst. Mech. Eng. 196, 363–378 (1982)Google Scholar
- 31.Johnson, K.L.: Contact mechanics. J. Tribol. 108, 464 (1985)Google Scholar
- 37.Glocker, C.: Set-Valued Force Laws: Dynamics of Non-Smooth Systems. In: Lecture Notes in Applied & Computational Mechanics, Vol. 1, Springer-Verlag Berlin Heidelberg (2001)Google Scholar