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暴雨萌, 饶晓波, 丁顺良, 高建设. 圆弧足被动行走机器人步态多重稳定性研究. 力学学报, 2024, 56(6): 1-12. DOI: 10.6052/0459-1879-23-545
引用本文: 暴雨萌, 饶晓波, 丁顺良, 高建设. 圆弧足被动行走机器人步态多重稳定性研究. 力学学报, 2024, 56(6): 1-12. DOI: 10.6052/0459-1879-23-545
Bao Yumeng, Rao Xiaobo, Ding Shunliang, Gao Jianshe. Research on multistability of gaits in the passive walking robot with round feet. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(6): 1-12. DOI: 10.6052/0459-1879-23-545
Citation: Bao Yumeng, Rao Xiaobo, Ding Shunliang, Gao Jianshe. Research on multistability of gaits in the passive walking robot with round feet. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(6): 1-12. DOI: 10.6052/0459-1879-23-545

圆弧足被动行走机器人步态多重稳定性研究

RESEARCH ON MULTISTABILITY OF GAITS IN THE PASSIVE WALKING ROBOT WITH ROUND FEET

  • 摘要: 目前关于被动行走步态的研究主要是揭示参数变化对其稳定性的影响, 而对于步态多重稳定性的研究则较为少见. 步态的多重稳定性不仅是行走模式多样化产生的根源, 还是引发步态突变的关键因素. 尽管当前共存步态的存在性已受到关注, 但关于这些步态的产生、演化以及消失机制的系统性研究尚未开展. 为此, 文章以圆弧足被动行走机器人为研究对象, 应用胞映射及点映射算法探索到与周期一步态共存的几种高周期步态, 绘制了共存步态的三维吸引盆并对这些步态的行走特性进行了详细的对比分析. 此外, 基于跳跃矩阵法改进了Poincaré-Newton-Floquet (PNF)算法, 对被动行走系统的不稳定轨道及其对应的Floquet乘子进行了求解, 并结合吸引盆进一步揭示了步态演化过程中的分岔和激变现象. 研究结果表明, 共存步态的周期越高, 其平均步速越快, 但步态稳定性越差; 这些共存步态均由极限环的折叠分岔产生, 并由倍周期级联路径通向混沌, 最终与不稳定轨道在吸引盆边界上产生碰撞而消失. 文章的研究结果有助于理解被动行走步态的多重稳定性, 并为机器人的优化设计及稳定控制提供理论依据.

     

    Abstract: Current research on passive walking gaits mainly reveals the effects of parameter changes on their stability, while there are fewer studies on the multistability of gaits. The multistability of gaits is not only a source of walking pattern diversity but also a key factor in triggering sudden gait changes. Although the existence of coexisting gaits has received attention, systematic studies on the mechanisms of their generation, evolution, and disappearance have still not been carried out. To this end, this paper takes a round-footed passive walking robot as the research object, applies the cell mapping and point mapping algorithms to explore several high-periodic gaits coexisting with period-one gaits, plots the three-dimensional basin of attraction of the coexisting gaits, and carries out a detailed comparative analysis of the walking characteristics of these gaits. In addition, the Poincaré-Newton-Floquet (PNF) algorithm is improved based on the jump matrix method to solve the unstable orbits and their corresponding Floquet multipliers of the passive walking system and the bifurcation and crisis phenomena in the gait evolution are further revealed by combining with the basin of attraction. The results show that the higher the period of the coexisting gaits, the faster their average gait speeds, but the worse their gait stability; all these coexisting gaits are generated by the fold bifurcation of the limit cycle and lead to chaos by the period-doubling cascade path, eventually disappearing with the unstable orbitals by collisions on the boundary of the basins of attraction. This paper contributes to the understanding of the multistability of passive walking gaits and provides a basis for optimal robot design and stability control.

     

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