No CrossRef data available.
Article contents
A Multibody Dynamics Approach to Limit Cycle Walking
Published online by Cambridge University Press: 10 April 2019
Summary
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.
Though significant efforts are made to develop mathematical models of the limit cycle walking (LCW), there is still a lack of a general and efficient framework to study the periodic solution and robustness of a complex model like human with knees, ankles and flat feet. In this study, a numerical framework of the LCW based on general multibody system dynamics is proposed, especially the impacts between the feet and the ground are modeled by Hunt–Crossley normal contact force and Coulomb friction force, and the modeling of the knee locking is presented as well. Moreover, event-based operating strategies are presented to deal with controls for the ground clearance and the knee locking. Importantly, a fast and efficient two-step algorithm is proposed to search for stable periodic gaits. Finally, maximum allowable disturbance is adopted as the index for stability analysis. All these features could be readily implemented in the framework. The presented solution is verified on a compass-like passive dynamic walking (PDW) walker with results in the literature. Based on this framework, a fairly complicated level-walking walkers with ankles and knees under control are analyzed and their periodic gaits are obtained, and surprisingly, double stable periodic gaits with, respectively, low speed and high speed are found.
Information
- Type
- Articles
- Information
- Copyright
- © Cambridge University Press 2019
References
Hobbelen, D. G. E., Limit Cycle Walking (Delft University of Technology, Delft, The Netherlands, 2008).Google Scholar
Koop, D. and Wu, C. Q., “Passive dynamic biped walking – Part I: Development and validation of an advanced model,” J. Comput. Nonlinear Dyn. 8(4), 041007 (2013).CrossRefGoogle Scholar
Gupta, S. and Kumar, A., “A brief review of dynamics and control of underactuated biped robots,” Adv. Robot. 1864(April), 1–17 (2017).Google Scholar
Garcia, M., Chatterjee, A., Ruina, A. and Coleman, M., “The simplest walking model: Stability, complexity, and scaling,” J. Biomech. Eng. 120(2), 281–288 (1998).CrossRefGoogle Scholar
Schwab, A. L. and Wisse, M., “Basin of Attraction of the Simplest Walking Model,” Proceedings of the ASME Design Engineering Technical Conference, Pittsburgh, Pennsylvania vol. 6 (2001) pp. 531–539.Google Scholar
Kwan, M. and Hubbard, M., “Optimal foot shape for a passive dynamic biped,” J. Theor. Biol. 248(2), 331–339 (2007).CrossRefGoogle Scholar
He, J. and Ren, G., “On the stability of passive dynamic walker with flat foot and series ankle spring,” Adv. Mech. Eng. 10(3), 1–12 (2018).CrossRefGoogle Scholar
Zelik, K. E., Huang, T.-W. P., Adamczyk, P. G. and Kuo, A. D., “The role of series ankle elasticity in bipedal walking,” J. Theor. Biol. 346, 75–85 (2014).CrossRefGoogle Scholar
Alghooneh, M. and Wu, C. Q., “Single-support heel-off: A crucial gait event helps realizing agile and energyefficient bipedal walking,” Robotica 34(6), 1335–1350 (2016).CrossRefGoogle Scholar
Wang, Q., Huang, Y. and Wang, L., “Passive dynamic walking with flat feet and ankle compliance,” Robotica 28(3), 413–425 (2010).CrossRefGoogle Scholar
Qi, F., Wang, T. and Li, J., “The elastic contact influences on passive walking gaits,” Robotica 29(5), 787–796 (2011).CrossRefGoogle Scholar
Canudas de Wit, C., Olsson, H., Astrom, K. J. and Lischinsky, P., “A new model for control of systems with friction,” IEEE Trans. Automat. Contr. 40(3), 419–425 (1995).CrossRefGoogle Scholar
Hobbelen, D. G. E. and Wisse, M., “A disturbance rejection measure for limit cycle walkers: The gait sensitivity norm,” IEEE T. Robot. 23(6), 1213–1224 (2007).CrossRefGoogle Scholar
Hürmüzlü, Y. and Moskowitz, G. D., “The role of impact in the stability of bipedal locomotion,” Dynam. Stabil. Syst. 1(3), 217–234 (1986).CrossRefGoogle Scholar
Shabana, A. A., “Flexible multibody dynamics: Review of past and recent developments,” Multibody Syst. Dyn. 1(2), 189–222 (1997).CrossRefGoogle Scholar
Peng, Y., Zhao, Z., Zhou, M., He, J., Yang, J. and Xiao, Y., “Flexible multibody model and the dynamics of the deployment of mesh antennas,” J. Guid. Control Dyn. 40(6), 1499–1510 (2017).CrossRefGoogle Scholar
Bauchau, O. A., “Flexible multibody dynamics,” Solid Mech. Appl. 176(4), 543–564 (2011).Google Scholar
Goldstein, H., Poole, C. and Safko, J., Classical Mechanics, 3rd ed. (Pearson Education, Essex, England, 2011).Google Scholar
Shabana, A., Dynamics of Multibody Systems (Cambridge University Press, Cambridge, UK, 2005).CrossRefGoogle Scholar
Hunt, K. H. and Crossley, F. R. E., “Coefficient of restitution interpreted as damping in vibroimpact,” J Appl. Mech. 42(2), 440–445 (1975).CrossRefGoogle Scholar
Wu, J., Zhao, Z. and Ren, G., “Multibody analysis of the force in deploying booms,” J. Guid. Control Dyn. 36(6), 1881–1886 (2013).CrossRefGoogle Scholar
Hairer, E. and Wanner, G., Solving Ordinary Differential Equations II: Stiff and Differential-algebraic Problems (Springer, Berlin, 1996).CrossRefGoogle Scholar
Ning, L., Junfeng, L. and Tianshu, W., “The effects of parameter variation on the gaits of passive walking models: Simulations and experiments,” Robotica 27(4), 511–528 (2009).CrossRefGoogle Scholar
Gan, Z., Yesilevskiy, Y., Zaytsev, P. and Remy, C. D., “All common bipedal gaits emerge from a single passive model,” J R Soc Interface 15(146), (in press) (2018).CrossRefGoogle Scholar
Kim, M. and Collins, S. H., “Once-per-step control of ankle push-off work improves balance in a threedimensional simulation of bipedal walking,” IEEE T. Robot. 33(2), 406–418 (2017).CrossRefGoogle Scholar
Bregman, D. J. J., Van Der Krogt, M. M., De Groot, V., Harlaar, J., Wisse, M. and Collins, S. H., “The effect of ankle foot orthosis stiffness on the energy cost of walking: A simulation study,” Clin. Biomech. 26(9), 955–961 (2011).CrossRefGoogle Scholar
Anderson, F. C. and Pandy, M. G., “A dynamic optimization solution for vertical jumping in three dimensions,” Comput. Methods Biomech. Biomed. Eng. 2(3), 201–231 (1999).CrossRefGoogle Scholar
Sherman, M. A., Seth, A. and Delp, S. L., “Simbody: Multibody dynamics for biomedical research,” Procedia IUTAM 2, 241–261 (2011).CrossRefGoogle Scholar
Grieve, D. W., “Gait patterns and the speed of walking,” Biomed. Eng. 3, 119–122 (1968).Google Scholar
Nelder, J. A. and Mead, R., “A simplex method for function minimization,” Comput. J. 7(4), 308–313 (1965).CrossRefGoogle Scholar
Wright, M. H., Direct Search Methods: Once Scorned, Now Respectable (Addison-Wesley, Boston, MA, 1996) pp. 191–208.Google Scholar
Collins, S., Ruina, A., Tedrake, R. and Wisse, M., “Efficient bipedal robots based on passive-dynamic walkers,” Science 307(5712), 1082–1085 (2005).CrossRefGoogle Scholar
Kuo, A. D., “A simple model of bipedal walking predicts the preferred speed-step length relationship,” J. Biomech. Eng. 123(3), 264–269 (2001).CrossRefGoogle Scholar
He and Ren supplementary material
He and Ren supplementary material 1
Video
3.7 MB
He and Ren supplementary material
He and Ren supplementary material 2
Video
1.5 MB
He and Ren supplementary material
He and Ren supplementary material 3
Video
2.2 MB
You have
Access
- 8
- Cited by