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Journal of Intelligent and Robotic Systems

, Volume 15, Issue 1, pp 67–133 | Cite as

Robust sliding-mode control applied to a 5-link biped robot

  • Spyros Tzafestas
  • Mark Raibert
  • Costas Tzafestas
Article

Abstract

In this paper the application of robust control to a 5-link biped robotic model is investigated through the sliding mode approach, and compared to pure computed torque control. The biped consists of five links, namely the torso and two links in each leg. These links are connected via four (two hip and two knee) rotating joints which are considered to be friction-free and driven by independent d.c. motors. The locomotion of the biped is assumed to be constrained on the sagittal plane. The paper provides a full derivation of the biped dynamic model (single-leg support phase, biped-in-the-air phase) and an outline of the computed torque and sliding mode control algorithms. The simulation results were derived with two sets of parameters (one of which corresponds to a human-sized biped) and several degrees of parametric uncertainty (from 10% to 200%). In all cases the results obtained through the sliding mode control were much better than those obtained with the computed torque control. This superiority was shown to become stronger as the degree of uncertainty and the size of the biped increases.

Key words

Biped robots robust control sliding mode control single leg-support phase computer torque control 

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References

  1. 1.
    Raibert, M.: Legged Robots that Balance, MIT Press, Cambridge, MA, 1986.Google Scholar
  2. 2.
    Chow, C. K. and Jacobson: Further studies of human locomotion: Postural stability and control, Math. Biosci. 15 (1972), 93–108.Google Scholar
  3. 3.
    Hemami, H., Wil, C. and Goliday, G. L.: The inverted pendulum and biped stability, Math. Biosci. 34 (1977), 95–110.Google Scholar
  4. 4.
    Hemami, H. and Katbab, A.: Constrained inverted pendulum model for evaluating upright postural stability, ASME J. Dyn. Syst. Meas. Contr. 104 (1982), 343–349.Google Scholar
  5. 5.
    Mochon, S.: A mathematical model of human walking, Lectures on Mathematics in Life Sciences, Vol. 14, Amer. Math. Soc., 1981.Google Scholar
  6. 6.
    Hemami, H., Zheng, Y. F. and Hines, M. J.: Initiation of walk and tiptoe of a planar nine-link biped, Math. Biosci. 61 (1982), 163–189.Google Scholar
  7. 7.
    Miura, H. and Shinoyama, I.: Dynamic walk of a biped, Intl. J. Robotics Res. 3(2) (1984).Google Scholar
  8. 8.
    Furusho, J. and Masubuchi, M.: Control of a dynamic biped locomotion system for steady walking, ASME J. Dyn. Syst. Meas. Contr. 108 (1986), 111–118.Google Scholar
  9. 9.
    Furusho, J. and Masubuchi, M.: A theoretically motivated reduced-order model for the control of dynamic biped locomotion, ASME J. Dyn. Syst. Meas. Contr. 109 (1987), 155–163.Google Scholar
  10. 10.
    Yamada, M., Furusho, J. and Sano, A.: Dynamic control of walking robot with kickaction, Proc. 1985 Intl. Conf. on Advanced Robotics (ICAR'85), pp. 405–412, Tokyo (1985).Google Scholar
  11. 11.
    Sano, A. and Furusho, J.: 3D steady walking robot with kick-action, Proc. 1988 USA-Japan Symp. on Flexible Automation, Vol. II, Minneapolis, July 1988.Google Scholar
  12. 12.
    Mita, T., Yamguchi, T., Kashiwase, T. and Kawase, T.: Realization of a high speed biped using modern control theory, Int. J. Control 40 (1984), 107–119.Google Scholar
  13. 13.
    Takanishi, A., Egusa, Y., Tochizawa, M., Takeya, T. and Kato, I.: Realization of dynamic biped walking stabilized with trunk motion, Proc. Rob. Manuf. Syst. '88, September 1988.Google Scholar
  14. 14.
    Slotine, J. J.: The robust control of robot manipulators, Int. J. Robotics Res. 4(2) (1985).Google Scholar
  15. 15.
    Slotine, J. J. and Spong, M. W.: Robust robot control with bounded input torques, Int. J. Robotics Res. 2(4) (1985).Google Scholar
  16. 16.
    Slotine, J. J. and Li, W.: Applied Nonlinear Control, Prentice Hall (1991).Google Scholar
  17. 17.
    Zheng, Y. F. and Hemami, H.: Mathematical modeling of a robot collision with its environment, Int. J. Robotics Res. 2(3) (1985), 289–307.Google Scholar
  18. 18.
    Hemami, H. and Zheng, Y. F.: Dynamics and control of motion on the ground and in the air with application to biped robots, J. Robotic Systems 1(1) (1984), 101–116.Google Scholar
  19. 19.
    Walker, M. W. and Orin, D.: Efficient dynamic computer simulation of robot mechanisms, ASME J. Dyn. Syst. Meas. Control 104 (1982), 205–211.Google Scholar
  20. 20.
    Luh, J. Y. S., Walker, M. W. and Paul, R. P. C.: On-line computational scheme for mechanical manipulators, ASME J. Dyn. Syst. Meas. Control 102 (1980), 69–76.Google Scholar
  21. 21.
    Zheng, Y.-F.: The study of a nine link biped model with two feet, M.Sc. Thesis, The Ohio State University (1980).Google Scholar
  22. 22.
    Sias, F. R. Jr. and Zheng, Y.-F.: How many degrees-of-freedom does a biped need? Proc. IEEE Intl. Workshop on Intelligent Robots and Systems (IROS'90), pp. 297–302 (1990).Google Scholar
  23. 23.
    Tzafestas, S. G., Dritsas, L. and Kanellakopoulos, J.: Robust robot control: A comparison of three techniques through simulation, in P. Breedverld et al. (eds), Modeling and Simulation of Systems, J. C. Baltzer Co., 1989, pp. 255–260.Google Scholar
  24. 24.
    Tzafestas, S. G.: Adaptive, robust and rule-based control of robotic manipulators, in S. G. Tzafestas (ed), Intelligent Robotics Systems, Marcel Dekker, 1991, pp. 313–419.Google Scholar
  25. 25.
    Jaworska, I. and Tzafestas, S.: Robust stability analysis of robot control systems, Robotics and Autonomous Systems 17 (1991), 285–290.Google Scholar
  26. 26.
    Tzafestas, S. G.: Task grouping and scheduling for parallel processing, in T. Ono and F. Kozin (eds), Systems and Control-Topics in Theory and Applications, MITA Press, 1991, pp. 401–419.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Spyros Tzafestas
    • 1
  • Mark Raibert
    • 2
  • Costas Tzafestas
    • 1
  1. 1.Intelligent Robotics and Control UnitNational Technical University of AthensAthensGreece
  2. 2.Artificial Intelligence LaboratoryMITCambridgeU.S.A.

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