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Effect of circular arc feet on a control law for a biped

Published online by Cambridge University Press:  01 July 2009

T. Kinugasa ,
C. Chevallereau  and
Y. Aoustin
T. Kinugasa*
Affiliation:
Okayama University of Science, 1-1, Ridai-cho, Okayama, 700-0005, Japan
C. Chevallereau
Affiliation:
IRCCyN, Ecole Centrale de Nantes, CNRS, Université de Nantes BP 92101, 1, rue de la Noë, 44321 Nantes cedex 3, France
Y. Aoustin
Affiliation:
IRCCyN, Ecole Centrale de Nantes, CNRS, Université de Nantes BP 92101, 1, rue de la Noë, 44321 Nantes cedex 3, France
*
*Corresponding author. E-mail: kinugasa@mech.ous.ac.jp
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Summary

The purpose of our research is to study the effects of circular arc feet on the biped walk with a geometric tracking control. The biped studied is planar and is composed of five links and four actuators located at each hip and each knee thus the biped is underactuated in single support phase. A geometric evolution of the biped configuration is controlled, instead of a temporal evolution. The input-output linearization with a PD control law and a feed forward compensation is used for geometric tracking. The controller virtually constrains 4 degrees of freedom (DoF) of the biped, and 1 DoF (the absolute orientation of the biped) remained. The temporal evolution of the remained system with impact events is analyzed using Poincaré map. The map is given by an analytic expression based on the angular momentum about the contact point. The effect of the radii of the circular arc feet on the stability is studied. As a result, the speed of convergence decreases when the radii increases, if the radius is larger than the leg length the cyclic motion is not more stable. Among the stable cyclic motion, larger radius broadens the basin of attraction. Our results agree with those obtained for passive dynamic walking on stability, even if the biped is controlled through the geometric tracking.

Keywords

under-actuated bipedcircular arc feetnonlinear controlstability analysis
Type
Article
Information
Robotica , Volume 27 , Issue 4 , July 2009 , pp. 621 - 632
Copyright
Copyright © Cambridge University Press 2008

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References

1.Aoustin, Y. and Formal'sky, A. M., “Design of Reference Trajectory to Stabilize Desired Nominal Cyclic Gait of a Biped,” Proceedings of the International Workshop on Robot Motion and Control, ROMOCO'99, (1999) pp. 159–165.Google Scholar
2.Grizzle, J., Abba, G. and Plestan, F., “Asymptotically stable walking for biped robots: Analysis via systems with impulse effects,” IEEE Trans. Automat. Contr. 46 (1), 51–64 (2001).CrossRefGoogle Scholar
3.Aoustin, Y. and Formal'sky, A. M., “Control design for a biped reference trajectory based on driven angles as functions of the undriven Angle,” J. Comput. Syst. Sci. Int. 42 (4), 159–176 (2003).Google Scholar
4.Chevallereau, C., Abba, G., Aoustin, Y., Plestan, F., Westervelt, E. R., Canudas-De-Wit, C. and Grizzle, J. W., “Rabbit: A test bed for advanced control theory,” IEEE Contr. Syst. Mag. 23 (5), 57–79 (Oct. 2003).Google Scholar
5.Furusho, J., Moritsuka, H. and Masubuchi, M., “Low order modeling of biped locomotion system using local feedback,” Trans. Soc. Instrum. Contr. Eng. 17 (5), 596–601, (1981) in Japanese.Google Scholar
6.Kajita, S. and Tani, K., “Study of Dynamic Biped Locomotion on Rugged Terrain – Derivation and Application of the Linear Inverted Pendulum Mode,” Proceedings of IEEE International Conference on Robotics and Automation (1991) pp. 1405–1411.Google Scholar
7.Westervelt, E. R., Buche, G. and Grizzle, J. W., “Experimental validation of a framework for the design of controllers that induce stable walking in planar bipeds,” Int. J. Robot. Res. 24 (6), 559–582 (2004).CrossRefGoogle Scholar
8.McGeer, T., “Passive dynamic walking,” Int. J. Robot. Res. 9, 62–82 (1990).CrossRefGoogle Scholar
9.Kinugasa, T., Hashimoto, Y. and Fushimi, H., “Passive Walking of Biped Emu with Attitude Control of Body,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (2003) pp. 346–359.Google Scholar
10.Kinugasa, T., Osuka, K. and Miwa, S., “Biped walking by variations of knee lengths and attitude control of a body and its frequency Analysis,” J. Robot. Soc. Japan 25 (3), (2007) in Japanese.CrossRefGoogle Scholar
11.Kinugasa, T., Miwa, S. and Yoshida, K., “Frequency analysis for biped walking via length variation of legs,” J. Robot. Mech. 20 (1), 98–105 (2008).CrossRefGoogle Scholar
12.Chevallereau, C. and Djoudi, D., “Feet can Improve the Stability Property of a Control Law for a Walking Robot,” Proceedings of International Conference on Robotics and Automation, (2006) pp. 1206–1212.Google Scholar
13.Chevallereau, C., Djoudi, D. and Grizzle, J. W., “Stable bipedal walking with foot rotation through direct regulation of the zero moment point,” IEEE Trans. Robot. 24 (2), 390–401 (2008).CrossRefGoogle Scholar
14.Wisse, M. and Frankenhuyzen, J. van, “Design and Construction of Mike; A 2D Autonomous Biped based on Passive Dynamic Walking,” Proceedings of Conference on Adaptive Motion of Animals and Machines WeP-I-1, Springer, Tokyo (2003).Google Scholar
15.Wisse, M., Schwab, A. L., Linde, R. Q. van der and Helm, F. C. T. van der, “How to keep from falling forward: Elementary swing leg action for passive dynamic walkers,” IEEE Trans. Robot. 21 (3), 393–401 (2005).CrossRefGoogle Scholar
16.Wisse, M., Hobbelen, D. G. E., Rotteveel, R. J. J., Anderson, S. O. and Zeglin, G. J., “Ankle Springs Instead of Arc-shaped Feet for Passive Dynamic Walkers,” Proceedings of Humanoids 2006, (2006) pp. 110–116.Google Scholar
17.Asano, F. and Luo, Z. W, “On Energy-Efficient and High-Speed Dynamic Biped Locomotion with Semicircular Feet,” Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, (2006) pp. 5901–5906.Google Scholar
18.Asano, F. and Luo, Z. W., “The Effect of Semicircular Feet on Energy Dissipation by Heel-strike in Dynamic Biped Locomotion,” Proceedings of IEEE International Conference on Robotics and Automation, (2007) pp. 3976–3981.Google Scholar
19.Adamczyk, P. G., Collins, S. H. and Kuo, A. D., “The advantages of a rolling foot in human walking,” J. Exp. Biol. 209, 3953–3963 (2006).CrossRefGoogle ScholarPubMed
20.Morris, B. and Grizzle, J. W., “A Restricted Poincare Map for Determining Exponentially Stable Periodic Orbits in Systems with Impulse Effects: Application to Bipedal Robots,” Proceedings of IEEE Conference on Decision and Control, (2005) pp. 419 9–4206.Google Scholar
21.Kuo, A. D., “Energetics of actively powered locomotion using the simplest walking model,” J. Biomech. Eng. 124, 113–120 (2001).CrossRefGoogle Scholar
22.Chevallereau, C., Formal'sky, A. and Djoudi, D., “Tracking of a joint path for the walking of an underactuated biped,” Robotica 22, 15–28, (2004).CrossRefGoogle Scholar