Two-stage optimization for energy-efficient bipedal walking
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DOI 10.1007/s12206-020-07 -y
Journal of Mechanical Science and Technology 34 (9) 2020 Original Article DOI 10.1007/s12206-020-0834-8 Keywords: · Energy efficiency · CoM optimization · ZMP movement · Bipedal walking
Correspondence to: Xiaohui Xiao [email protected]
Citation: Ding, J., Xiao, X. (2020). Two-stage optimization for energy-efficient bipedal walking. Journal of Mechanical Science and Technology 34 (9) (2020) 3833~3844. http://doi.org/10.1007/s12206-020-0834-8
Received October 27th, 2019 Revised
Two-stage optimization for energyefficient bipedal walking Jiatao Ding and Xiaohui Xiao School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China
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.
July 3rd, 2020
Accepted July 3rd, 2020 † Recommended by Editor Ja Choon Koo
© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2020
1. Introduction Humanoid robots have attracted considerable attention for their potential capabilities in accomplishing challenging tasks in real environments. Due to the limited battery capacity, high energy efficiency is one of the chief requirements in making humanoids practical [1]. For energy saving, passive walking and under-actuated walking have been demonstrated to be effective [2-4]. However, passive walkers can only walk on flat ground or down-slope while the under-actuated walkers rely on specific mechanism design. On the contrary, full-actuated walkers have made great process in stable walking as well as energy cost reduction. For these full-actuated humanoids, parameters optimization is useful for energy-saving [5-7]. Overall, the procedure of the optimization-based approaches can be divided into two steps: unit energetic consumption (UEC) evaluation and step parameters optimization, as demonstrated in Fig. 1. Firstly, given the reference step parameters, the center of mass (CoM) trajectory and swing foot trajectory are synthesized by satisfying a specific stability criterion. At this stage, the UEC of one walking cycle is calcula
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