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Asymptotically stable biped gait generation based on stability principle of rimless wheel

Published online by Cambridge University Press:  06 March 2009

Fumihiko Asano  and
Zhi-Wei Luo
Fumihiko Asano*
Affiliation:
School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, JAPAN
Zhi-Wei Luo
Affiliation:
Department of Computer Science and Systems Engineering, Faculty of Engineering, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, JAPAN.
*
*Corresponding author. E-mail: fasano@jaist.ac.jp
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Summary

We investigated and identified the conditions necessary for stable dynamic gait generation in biped robots from the mechanical energy balance point of view. The equilibrium point at impact in a dynamic gait is uniquely determined by two conditions; keeping the restored mechanical energy constant and settling the relative hip-joint angle to the desired value before impact. The generated gait then becomes asymptotically stable around the equilibrium point determined by these conditions. This is shown by a simple recurrence formula of the kinetic energy immediately before impact. We verified this stability theorem using numerical simulation of virtual passive dynamic walking. The results were compared with those for a rimless wheel and an inherent stability principle was derived. Finally, we derived a robust control law using a reference mechanical energy trajectory and demonstrated its effectiveness numerically.

Keywords

Gait generationBiped robotAsymptotic stabilityMechanical energy balanceVirtual passive dynamic walking

Information

Type
Article
Information
Robotica , Volume 27 , Issue 6 , October 2009 , pp. 949 - 958
Copyright
Copyright © Cambridge University Press 2009

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References

1.McGeer, T., “Passive dynamic walking,” Int. J. Rob. Res. 9 (2), 62–82 (Apr. 1990).CrossRefGoogle Scholar
2.Gubina, F., Hemami, H. and McGhee, R. B., “On the dynamic stability of biped locomotion,” IEEE Trans. Biomed. Eng. BME-21 (2), 102–108 (Mar. 1974).CrossRefGoogle ScholarPubMed
3.Katoh, R. and Mori, M., “Control method of biped locomotion giving asymptotic stability of trajectory,” Automatica 20 (4), 405–414 (Jul. 1984).CrossRefGoogle Scholar
4.Miura, H. and Shimoyama, I., “Dynamic walk of a biped,” Int. J. Rob. Res. 3 (2), 60–74 (Jun. 1984).CrossRefGoogle Scholar
5.Goswami, A., Thuilot, B. and Espiau, B., “A study of the passive gait of a compass-like biped robot: Symmetry and chaos,” Int. J. Rob. Res. 17 (12), 1282–1301 (Dec. 1998).CrossRefGoogle Scholar
6.Asano, F., Luo, Z.-W. and Yamakita, M., “Biped gait generation and control based on a unified property of passive dynamic walking,” IEEE Trans. Rob. 21 (4), 754–762 (Aug. 2005).CrossRefGoogle Scholar
7.Garcia, M., Chatterjee, A., Ruina, A. and Colema, M., “The simplest walking model: Stability, complexity, and scaling,” ASME J. Biomech. Eng. 120 (2), 281–288 (Apr. 1998).CrossRefGoogle ScholarPubMed
8.Hosoe, S., Takeichi, K., Kumai, S. and Ito, M., “Analysis of stability of dynamic biped locomotion with high gain feedback (in Japanese),” Trans. Soc. Instr. Control Engineers 22 (9), 948–954 (Sep. 1986).CrossRefGoogle Scholar
9.Grizzle, J. W., Abba, G. and Plestan, F., “Asymptotically stable walking for biped robots: Analysis via systems with impulse Effects,” IEEE Trans. Automat. Control 46 (1), 51–64 (Jan. 2001).CrossRefGoogle Scholar
10.Ikemata, Y., Sano, A. and Fujimoto, H., “A stability mechanism of the fixed point in passive walking (in Japanese),” J. Rob. Soc. Jpn 23 (7), 73–80 (Oct. 2005).Google Scholar
11.Wisse, M., Atkeson, C. G. and Kloimwieder, D. K., “Swing leg retraction helps biped walking stability,” Proceedings of the IEEE-RAS International Conference on Humanoid Robots, Tsukuba, Japan (Dec. 2005) pp. 295–300.Google Scholar
12.Hyon, S.-H. and Emura, T., “Symmetric walking control: Invariance and global stability,” Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, Spain (Apr. 2005) pp. 1455–1462.Google Scholar
13.Tazaki, Y. and Imura, J., “A study of the energy-saving effect of foot shape on planar passive bipedal walking (in Japanese),” J. Rob. Soc. Jpn 23 (1), 131–138 (Jan. 2005).CrossRefGoogle Scholar
14.Coleman, M., “A stability study of a three-dimensional passive-dynamic model of human gait,” Ph.D. Thesis (Cornell University, Feb. 1998).Google Scholar
15.Asano, F. and Luo, Z.-W., “The effect of semicircular feet on energy dissipation by heel-strike in dynamic biped locomotion,” Proceedings of the IEEE International Conference on Robotics and Automation, Roma, Italy (Apr. 2007) pp. 3976–3981.CrossRefGoogle Scholar