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Measurement of robustness for biped locomotion using a linearized Poincaré map*

Published online by Cambridge University Press:  09 March 2009

M. -Y. Cheng  and
C. -S. Lin
M. -Y. Cheng
Affiliation:
Department of Electrical and Computer Engineering, University of Missouri-Columbia, Columbia, MO65211 (USA)
C. -S. Lin
Affiliation:
Department of Electrical and Computer Engineering, University of Missouri-Columbia, Columbia, MO65211 (USA)
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Summary

Many studies on control of dynamic biped walking have been done in the past two decades. While the biped dynamics is highly nonlinear, the stability analysis, if done, is usually based on a linearized model. The validity of the linearized model may become questionable if the walking involves states that are too far away from the operating point. In this paper, an approach for evaluating the robustness based on the linearized Poincare map is suggested and examined. The Poincare map is a useful tool to investigate the periodic motion of a dynamic system. Using the Poincare“ map, one can study an associated discrete time map instead of studying the continuous time system directly. Investigation of stability of a periodic motion can be reduced to the study of the stability of a fixed point of the Poincaré map. The computational method that results in a measurement for evaluating the robustness of biped locomotion is developed. Our simulation study has verified that the suggested measurement is a good indicator.

Keywords

Biped locomotionPoincare mapLinearized model
Type
Article
Information
Robotica , Volume 14 , Issue 3 , May 1996 , pp. 253 - 259
Copyright
Copyright © Cambridge University Press 1996

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References

1.Vukobratovic, M., Frank, A. A. and Juricic, D.. “On the Stability of Biped Locomotion” IEEE Trans on Bio-Med Engr. BME-17, No. 1. 25–36 (01, 1970).Google Scholar
2.Gubina, F., Hemami, H. and McGhee, R. B., “On the Dynamic Stability of Biped Locomotion” IEEE Trans on Bio-Med Engr. BME-21, No. 2. 102–108 (03, 1974).CrossRefGoogle Scholar
3.Hemami, H. and Wyman, B. F.. “Modeling and Control of Constrained Dynamic Systems with Application to Biped Locomotion in the Frontal Plane” IEEE Trans on Automatic Control AC-24, 526–535 (08, 1979).Google Scholar
4.Hemami, H. and Cheng, B., “Stability Analysis and Input Design of a Two-Link Planar Biped” Int. J. Robotics Research 3, No. 2, 93–100 (1984).Google Scholar
5.Katoh, R. and -Mori, M.. “Control Method of Biped Locomotion Giving Asymptotic Stability of Trajectory” Automatica 20, No. 4, 405–414 (1984).CrossRefGoogle Scholar
6.Furusho, J. and Masubuchi, M., “Control of a Dynamical Biped Locomotion System for Steady Walking” ASME, J. of Dynamic Systems, Measurement, and Control 108, 111–118 (06.1986).Google Scholar
7.Furusho, J. and Masubuchi, M., “A Theoretically Motivated Reduced Order Model for the Control of Dynamic Biped Locomotion” ASME. J. of Dynamic Systems, Measurement, and Control 109, 155–163(06, 1987).Google Scholar
8.Furusho, J. and Sano, A., “Sensor-Based Control of a Nine-Link Biped” Int. J. Robotics Research 9, No. 2. 83–98 (04 1990).CrossRefGoogle Scholar
9.Guckenheimer, J. and Holmes, P., Nonlinear Oscillations. Dvnatnical Svstems and Bifurcations of Vector Field (Springer-Verlag, Berlin, 1983).CrossRefGoogle Scholar
10.Wiggins, S.. Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer-Verlag, Berlin, 1990).Google Scholar
11.Vakakis, A. F.. Burdick, J. W. and Caughey, T. K., “An Interesting Strange Attractor in the Dynamics of a Hopping Robot” Int. J. Robotic Research 10, No. 6, 606–618 (12, 1991).CrossRefGoogle Scholar
12.M'Closkey, R. T. and Burdick, J. W., “Periodic Motions of a Hopping Robot with Vertical and Forward Motion” Int. J. Robotics Research 12, No. 3, 197–218 (06, 1993).Google Scholar
13.Hmam, H. M. and Lawrence, D. A., “Robustness Analysis of Nonlinear Biped Control Laws via Singular Perturbation Theory” Proceedings of the 31st Conference on Decision and Control.Tucson. Arizona(Dec, 1992) pp. 2656–2661.Google Scholar
14.Huzmuzlu, Y.. “Dynamics of Bipedal Gait: Part II-Stability Analysis of a Planar Fine-Link Biped” J. Applied Mechanics, ASME 60, 337–343 (06, 1993).CrossRefGoogle Scholar
15.Huzmuzlu, Y. and Basdogan, C., “On the Measurement of Dynamic Stability of Human Locomotion” J. Biomechanical Engineering, ASME 116, 31–36 (02, 1994).Google Scholar
16.Pars, L. A., A Treatise on Analytical Dynamics. London (Heinemann Educational Books, 1965) Ch. 14.Google Scholar
17.Seydel, R., From Equilibrium to Chaos-Practical Bifurcation and Stability Analysis, Elsevier, Amsterdam, 1988).Google Scholar
18.Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning. (Addison-Wesley, New York. 1989).Google Scholar