Nonlinear Dynamics

, Volume 91, Issue 1, pp 459–473 | Cite as

Modeling, control and analysis of a curved feet compliant biped with HZD approach

  • S. D. Yazdi-Mirmokhalesouni
  • M. A. SharbafiEmail author
  • M. J. Yazdanpanah
  • M. Nili-Ahmadabadi
Original Paper


Bipedal walking with hybrid and nonlinear dynamics is a complex control problem. In this paper, a new model of bipedal walker with compliant legs and curved feet is developed and controlled using hybrid zero dynamics (HZD) controller. We analyze the effect of foot design in generating stable gaits characteristics regarding robustness and efficiency. For this, HZD is employed for the first time in a model in which the unactuated degrees of freedom are higher than actuated ones. Compliant legs and curved feet are two design features that can be employed to reduce energy consumption and to mimic human gait characteristics. In addition to these mechanical properties, optimizing the virtual constraints through coefficients of the Bezier polynomials supports increasing the stability margin and efficiency. With that, we benefit from both design and control to improve gait characteristics. The results conform with optimal foot curvature parameters, found in human experiments with and without prosthetic shoes. Finally, robustness of the presented controller against parameter uncertainties and external perturbations is investigated.


HZD control Hybrid invariance Poincare map Curved feet 


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • S. D. Yazdi-Mirmokhalesouni
    • 1
  • M. A. Sharbafi
    • 1
    Email author
  • M. J. Yazdanpanah
    • 1
  • M. Nili-Ahmadabadi
    • 1
  1. 1.Control and Intelligent Processing Center of ExcellenceUniversity of TehranTehranIran

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