Dynamic Models, Control Synthesis and Stability of Biped Robots Gait

  • M. Vukobratovic
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 375)


In this chapter modeling of artificial biped gait, control synthesis and stability analysis are presented. Beside that, in a separate section control of biped gait is considered, partly based on application of fuzzy logic theory.

Modeling of biped gait is based on introduction of the ZMP notion, representing point in which total reaction of the support surface onto the foot, belonging to the supporting leg, is acting. The leg trajectories are prescribed and the compensating movements of the trunk are calculated in such a way, that system stays in dynamic equilibrium.

In order to enable gait control of the biped system at the level of perturbed regimes, control was synthesized in two steps. First, in each joint of the system control with constrained accelerations is applied and then, on the global level, to some of the joints the stabilization task is assigned of the whole, where the basic task lies in ensuring the gait and preventing the overturning the system. For the system analysis the aggregation-decomposition method was applied, using vector functions in bounded regions of state space. In order to include in the stability analysis the unpowered degrees of freedom, too, models of the composite subsystems were formed, incorporating one powered and one unpowered degree of freedom. In that way it was enabled to apply the mentioned method for stability analysis, developed for the systems, in which all the degrees of freedom are powered.

In the last chapter, simulation experiments of biped control with a hybrid approach that combines the traditional model-based and fuzzy logic-based control techniques. The combined model is developed by. extending a model-based decentralized control scheme by fuzzy logic based tuners for modifying parameters of joint servo controllers. The simulation experiments performed on simplified two-legged mechanism demonstrate the suitability of fuzzy logoc-based methods for improving the performance of the robot control system.


Reaction Force Fuzzy Controller Ground Reaction Force Kinematic Chain Control Synthesis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    M. Vukobratovié and D. Jurieié, “Contribution to the synthesis of biped gait,” IEEE Trans. on Biomedical Engineering, vol. BME-16, pp. 1–6, January 1969.Google Scholar
  2. [2]
    M. Vukobratovié, “How to control artificial anthropomorphic systems,” IEEE Trans. on Systems, Man, and Cybernetics, vol. SMC-3, pp. 497–507, September 1973.Google Scholar
  3. [3]
    M. Vukobratovié, Legged locomotion robots and anthropomorphic mechanisms, research monograph. Belgrade: Mihailo Pupin Institute, 1975.Google Scholar
  4. [4]
    M. Vukobratovié and D. Stokié, Control of Manipulation Robots. Vol. 2 of Scientific fundamentals of robotics, Springer Verlag, 1982.Google Scholar
  5. [5]
    B. Borovac, M. Vukobratovié, and D. Stokié, “Stability analysis of mechanisms having unpowered degrees of freedom,” Robotica, vol. 7, pp. 349–357, 1989.CrossRefGoogle Scholar
  6. [6]
    M. Vukobratovié, B. Borovac, D. Surla, and D. Stokié, Biped locomotion. Vol. 7 of Scientific fundamentals of robotics, Springer-Verlag, 1990.Google Scholar
  7. [7]
    M. Vukobratovié and O. Timeenko, “Experiments with nontraditional hybrid control technique of biped locomotion robots,” Journal of intelligent and robotic systems, vol. 16, pp. 25–43, 1996.CrossRefGoogle Scholar
  8. [8]
    L. A. Zadeh, “Outline of a new approach to the analysis of complex systems and decision processes,” IEEE Transactions on systems, man, and cybernetics, vol. 3, pp. 28–44, January 1973.Google Scholar
  9. [9]
    H. Ying, W. Siler, and J. J. Buckley, “Fuzzy control theory: a nonlinear case,” Automatica, the journal of IFAC, vol. 26, pp. 513–520, May 1990.MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1997

Authors and Affiliations

  • M. Vukobratovic
    • 1
  1. 1.Mihajlo Pupin InstituteBelgradeYugoslavia

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