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

doi:10.3901/JME.260092

Abstract

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

CLC Number:

TP242

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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