A Computationally Efficient Inverse Dynamics Solution Based on Virtual Work Principle for Biped Robots

  • Majid KhadivEmail author
  • Mahdokht Ezati
  • S. Ali A. Moosavian
Research Paper


This paper deals with proposing a computationally efficient solution for the inverse dynamics problem of biped robots. To this end, the procedure of developing a closed-form dynamic model using D’Alembert’s-based virtual work principle (VWP) for a biped robot is described. Then, a closed-form inverse dynamics solution is developed during different phases of walking. For a given motion, the closed-form solution is evaluated at each control cycle to yield the joint torques and interaction forces. This procedure is time-consuming for robots with a large number of degrees of freedom such as 3D biped robots. Alternatively, to improve the computational efficiency of the procedure, a method is proposed to solve inverse dynamics efficiently without the need to develop a closed-form solution. In order to show the computational efficiency of the proposed method, its calculation time is compared to the closed-form solutions obtained from the VWP and Lagrange approaches, while this comparison reveals the merit of the proposed method in terms of computational efficiency. For an example application of the proposed solution for inverse dynamics, a dynamic-based optimization procedure is carried out to show the significance of employing toe-off and heel-contact gait phases during biped walking.


Biped robots Dynamic modeling D’Alembert’s principle Virtual work principle Gait planning 


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Copyright information

© Shiraz University 2017

Authors and Affiliations

  • Majid Khadiv
    • 1
    Email author
  • Mahdokht Ezati
    • 1
  • S. Ali A. Moosavian
    • 1
  1. 1.Center of Excellence in Robotics and Control, Advanced Robotics and Automated Systems (ARAS) Lab, Department of Mechanical EngineeringK. N. Toosi University of TechnologyTehranIran

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