被动双足机器人的吸引盆内部拓扑结构

doi:10.3901/JME.260092

机械工程学报 ›› 2026, Vol. 62 ›› Issue (3): 384-395.doi: 10.3901/JME.260092

• 机器人及机构学 • 上一篇

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被动双足机器人的吸引盆内部拓扑结构

高建设¹, 暴雨萌¹, 宛磊², 刘强³, 丁顺良¹, 饶晓波¹

1. 郑州大学机械与动力工程学院郑州 450001;
2. 漯河医学高等专科学校第二附属医院漯河 462000;
3. 河南省直第三人民医院郑州 450018

修回日期:2025-02-19 接受日期:2025-06-13 发布日期:2026-03-25
作者简介:高建设,男,1977年出生,博士,教授,博士研究生导师。主要研究方向为机械系统动力学及控制。E-mail:gao_jianshe@zzu.edu.cn
饶晓波(通信作者),男,1987年出生,博士,助理研究员。主要研究方向为非线性动力学、机器人学。E-mail:rxbaizxp@163.com

Internal Topology of the Basin of Attraction in a Passive Bipedal Robot

GAO Jianshe¹, BAO Yumeng¹, WAN Lei², LIU Qiang³, DING Shunliang¹, RAO Xiaobo¹

1. School of Mechanical and Power Engineering, Zhengzhou University, Zhengzhou 450001;
2. The Second Affiliated Hospital of Luohe Medical College, Luohe 462000;
3. The Third People's Hospital of Henan Province, Zhengzhou 450018

Revised:2025-02-19 Accepted:2025-06-13 Published:2026-03-25
Supported by:
国家自然科学基金(51906225)和河南省博士后研究(1902007)资助项目。

摘要/Abstract

摘要： 被动行走机器人全局动力学特性研究集中于探索吸引盆的形态变化，而对于盆内状态点的动态演化分析则较为薄弱。为此，以圆弧足被动行走机器人为研究对象，采用胞映射和点映射算法系统分析了吸引盆内各点的收敛步数，揭示了盆内部复杂的拓扑层级结构，并明确区分了引发机器人前倒和后倒的状态区域。此外，在ADAMS中对机器人样机的稳定行走和跌倒行为进行动力学仿真，验证了数值计算的正确性。随后，利用分岔图、Floquet乘子图及Lyapunov指数图等非线性数值工具，深入分析了机器人在不同参数条件下盆内部拓扑结构的演化过程。研究结果表明，机器人的吸引盆被引发前倒的状态区域包围，被动行走步态按照环绕的方式不断收敛到稳定状态；具有过高支撑腿角度以及过小支撑腿角速度的机器人极易后倒，反之前倒；随着斜面角度的增大，吸引盆的内部拓扑结构更加复杂，盆内各状态点的平均收敛步数与该点Floquet乘子的最大模量变化一致。上述分析结果有助于了解机器人吸引盆的内部演化机理，可为机器人行走初值选择及动态控制提供参考。

关键词: 被动行走, 吸引盆, ADAMS仿真, 内部拓扑, 跌倒, 平均收敛步数

Abstract: The global dynamics of the passive walking robot are primarily focused on the exploration of the shape change of the basin of attraction, while the dynamic evolution of the state points inside the basin is relatively scant. To this end, the round-footed passive walking robot is taken as the research object, and the cell mapping and point mapping algorithms are adopted to systematically analyze the number of convergence steps for each point in the basin of attraction. The complex topological structure within the basin is revealed, and the state regions that trigger the robot to fall forward or backward are clearly distinguished. In addition, dynamics simulations of the stable walking and falling behaviors of the robot prototype are conducted in ADAMS to verify the accuracy of the numerical calculations. Subsequently, nonlinear numerical tools such as bifurcation diagrams, Floquet multiplier diagrams and Lyapunov exponential diagrams are utilized to deeply analyze the evolution of the topology inside the basin of the robot under different parameter conditions. The results show that the robot's basin of attraction is surrounded by the state region that triggers the forward fall, and the passive walking gait is continuously converged to a stable state in a surrounding manner. The robot with an excessively high support leg angle and an overly low angular velocity of the support leg is highly susceptible to backward falls, while forward falls are more likely under the opposite conditions. The internal topology of the basin of attraction becomes more complicated with the increase of the angle of the ramp, and the average number of convergence steps of the state points inside the basin is related to the maximum modulus of the point. The above analysis results help to understand the internal evolution mechanism of the robot’s basin of attraction, which can provide a reference for the selection of the initial value of the robot’s walking and dynamic control.

Key words: passive walking, basin of attraction, ADAMS simulation, internal topology, fall, average convergence step

中图分类号:

TP242

高建设, 暴雨萌, 宛磊, 刘强, 丁顺良, 饶晓波. 被动双足机器人的吸引盆内部拓扑结构[J]. 机械工程学报, 2026, 62(3): 384-395.

GAO Jianshe, BAO Yumeng, WAN Lei, LIU Qiang, DING Shunliang, RAO Xiaobo. Internal Topology of the Basin of Attraction in a Passive Bipedal Robot[J]. Journal of Mechanical Engineering, 2026, 62(3): 384-395.

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被动双足机器人的吸引盆内部拓扑结构

Internal Topology of the Basin of Attraction in a Passive Bipedal Robot

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