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The Passivity Paradigm in the Control of Bipedal Robots

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Climbing and Walking Robots

Summary

The concepts of Passivity and Passivity-Based Control are well established in control theory and provide powerful design tools for control. In this paper we give an overview of a remarkable relation between Passivity-Based Control and the notion of Passive Walking in bipedal locomotion. We show how passivity-based control theory can be used to design nonlinear control laws for bipedal robots that reproduce passive limit cycles independent of the ground slope while overcoming some of the limitations of passive gaits, such as extreme sensitivity to ground slope, small basins of attraction, and poor disturbance rejection.

The results in this paper are based on earlier joint work with Francesco Bullo and Gagandeep Bhatia. This research was partially supported by NSF Grants ECS-0128656, CCR-0209202, and CSM-0100162

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References

  1. Bhatia, G., Passivity Based Control of Biped Robots, Thesis, M.S. Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois, December, 2002.

    Google Scholar 

  2. Branicky, M.S., “Stability of Hybrid Systems: State of the Art,” Proc. IEEE Conf. on Decision and Control, San Diego, CA, December, 1997.

    Google Scholar 

  3. Collins, S.H., Wisse, M. and Ruina, A. “A 3-d Passive-Dynamic Walking Robot with Two Legs and Knees,” Int. J. Robotics Research, Vol. 20, No. 7, July, 2001.

    Google Scholar 

  4. Garcia, M., et al., “The Simplest Walking Model: Stability, Complexity, and Scaling,” ASME Journal of Biomechanical Engineering, April, 1998.

    Google Scholar 

  5. Goswami, A., Espiau, B., and Keramane, A. (1997), Limit cycles in a passive compass gait biped and passivity-mimicking control laws. Journal of Autonomous Robots, Vol. 4, No. 3.

    Google Scholar 

  6. Goswami, A., Thuilot, B., and B. Espiau, B. (1998), A Study of the Passive Gait of a Compass-like Biped Robot: Symmetry and Chaos, International Journal of Robotics Research, Vol. 17, No. 15.

    Google Scholar 

  7. Hiskens, I.A. “Stability of hybrid system limit cycles: application to the compass gait biped robot,” Proceedings of the 40th IEEE Conference on Decision and Control, pp. 774–779, Orlando, Fl., Dec. 2001.

    Google Scholar 

  8. Khalil, H.K., Nonlinear Systems, Second Edition, Prentice Hall, Englewood Cliffs, NJ, 1995.

    Google Scholar 

  9. Kuo, A.D., “Stabilization of Lateral Motion in Passive Dynamic Walking,” International Journal of Robotics Research, Vol. 18, No. 9, pp. 917–30, 1999.

    Google Scholar 

  10. Marsden, J.E. and T.S. Ratiu, Introduction to Mechanics and Symmetry. second ed. Springer Verlag. New York, NY, 1999.

    Google Scholar 

  11. McGeer, T., “Passive Dynamic Walking,” International Journal of Robotics Research, 1990.

    Google Scholar 

  12. Webster’s New World Dictionary, Warner Books, New York, NY, 1990.

    Google Scholar 

  13. McGeer, T. Dynamics and control of bipedal locomotion. Journal of Theoretical Biology, 163(3):277, August 1993.

    Article  Google Scholar 

  14. McMahon, T.A. Muscles, Reflexes, and Locomotion. Princeton University Press, Princeton, New Jersey, 1984.

    Google Scholar 

  15. Olver, P.J., “Application of Lie Groups to Differential Equations,” Graduate Texts in Mathematics, Vol. 107, Springer-Verlag, New York, 1993.

    Google Scholar 

  16. Parker T.S. and Chua, L.O. Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, New York, NY, 1989.

    Google Scholar 

  17. Spong M.W. and Praly, L. Energy based control of underactuated mechanical systems. In A.S. Morse, editor, Control Using Logic-Based Switching, pp. 162–172. Springer-Verlag, Berlin, 1996.

    Google Scholar 

  18. Spong, M.W. “Passivity Based Control of the Compass Gait Biped,” In: IFAC World Congress, Vol. B., pp. 19–24, Beijing, China, July, 5–9, 1999.

    Google Scholar 

  19. Spong, M.W. and Bullo, F. “Controlled Symmetries and Passive Walking,” IFAC World Congress, Barcelona, Spain, July, 2002.

    Google Scholar 

  20. Spong, M.W. and Vidyasagar, M. Robot Dynamics and Control, John Wiley & Sons, Inc., New York, 1989.

    Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Spong, M.W. (2005). The Passivity Paradigm in the Control of Bipedal Robots. In: Climbing and Walking Robots. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29461-9_76

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  • DOI: https://doi.org/10.1007/3-540-29461-9_76

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22992-6

  • Online ISBN: 978-3-540-29461-0

  • eBook Packages: EngineeringEngineering (R0)

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