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Two-stage optimization for energy-efficient bipedal walking

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Abstract

This paper proposes a two-stage optimization strategy for energy-efficient gait generation. At the first stage, by tracking the reference zero moment point (ZMP) trajectory, the optimal center of mass (CoM) trajectory, which contributes to the minimal unit energetic cost (UEC) of one step, is solved analytically by using an unconstrained optimization method. At the second stage, to minimize the multi-joint mechanical work, the ZMP reference during the single support phase is optimized by a constrained optimization method. As a result, by considering the feasibility constraints such as the limitation on ZMP movement, the energy-efficient walking patterns can be generated in real-time. Furthermore, the energetic performances under different step parameter configurations, which consist of step length, step duration, and time ratio of double support, are discussed. Simulations and hardware experiments have demonstrated the energetic benefits of the proposed strategy when compared with other state-of-the-art works.

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Acknowledgments

This work is supported by National Natural Science Foundation of China (Grant 51175383, 51675385). Besides, the first author is sponsored by the Chinese Scholarship Council.

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Authors and Affiliations

  1. School of Power and Mechanical Engineering, Wuhan University, Wuhan, 430072, China

    Jiatao Ding & Xiaohui Xiao

Authors
  1. Jiatao Ding
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  2. Xiaohui Xiao
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Corresponding author

Correspondence to Xiaohui Xiao.

Additional information

Jiatao Ding received his B.S. in Mechanical Engineering from Wuhan University, China, in 2014. Currently, he is pursuing a Ph.D. degree in Mechatronics from Wuhan University. At the present, he is also a visiting Ph.D. student in Italian Institute of Technology (IIT), Italy. His research interests include gait planning and walking control of biped robot, mathematical foundations of robotics and predictive control.

Xiaohui Xiao is currently a Full Professor with the Mechanical Engineering Department, Wuhan University. She received the B.S. and M.S. degrees in Mechanical Engineering from Wuhan University, Wuhan, China, in 1991 and 1998, respectively, and the Ph.D. degree in Mechanical Engineering from Huazhong University of Science and Technology, Wuhan, China, in 2005. Her research interests are in the fields of humanoid bipedal robot, force control for cooperative robot, high-precision positioning control. She has authored/co-authored more than 40 research papers, published in international journals or presented at international conferences.

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Cite this article

Ding, J., Xiao, X. Two-stage optimization for energy-efficient bipedal walking. J Mech Sci Technol 34, 3833–3844 (2020). https://doi.org/10.1007/s12206-020-0834-8

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  • DOI: https://doi.org/10.1007/s12206-020-0834-8

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