Journal of Jilin University(Engineering and Technology Edition) ›› 2025, Vol. 55 ›› Issue (10): 3108-3118.doi: 10.13229/j.cnki.jdxbgxb.20240020

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Evolution of gait dynamics of passive walking robot on rough terrain

Jian-she GAO(),Yu-meng BAO,Tian ZHAO,Shun-liang DING,Xiao-bo RAO()   

  1. School of Mechanical and Power Engineering，Zhengzhou University，Zhengzhou 450001，China
  • Received:2024-01-06 Online:2025-10-01 Published:2026-02-03
  • Contact: Xiao-bo RAO E-mail:gao_jianshe@zzu.edu.cn;rxbaizxp@163.com

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Abstract:

In order to study the excitation effect of gait displacement caused by rough terrain environment on passive walking robot， the sinusoidal function model is used to describe the concave and convex characteristics of the road surface， and the random variation of amplitude and frequency is introduced to simulate the unevenness in the real road environment. By using bifurcation diagram and Lyapunov exponent， the influence of road unevenness on the gait stability of robot is compared and analyzed， and the boundary crisis event in global bifurcation is deeply studied. In addition， a robot prototype is built and ADAMS walking simulation is performed to verify the walking capability of the model. It is shown that， on an uneven sinusoidal road surface， the robot's gait exhibits quasi-periodic motion and transitions into chaos with the change of system parameter， occurring via the torus multiplication bifurcation. The excitation effect of the robot gait caused by the rough terrain makes the robot deviate from the limit cycle trajectory， and this results in system degradation in terms of stability. In the walking environments above， the double boundary crisis event triggered by the unstable orbit generated by the saddle-node bifurcation is the main reason for the disappearance of the gait attractor.

Key words: robotics, passive walking, rough terrain, bifurcation, Lyapunov exponents, double boundary crisis

CLC Number: 

  • TP242

Fig.1

Schematic diagram of the compass model"

Table 1

Structural parameters of robot"

参数符号数值单位
a500mm
b500mm
m5kg
mH10kg

Fig.2

Sinusoidal wave-like terrain structure diagram"

Fig.3

Randomized terrain structure diagram"

Fig.4

Bifurcation and LEs diagrams of system on flat ramp（A=0.0）"

Fig.5

Bifurcation and LEs diagrams of the system on sinusoidal wave-like terrain（A=0.1）"

Fig.6

Poincaré section of system on sinusoidal wave-like terrain（A=0.1）"

Fig.7

Bifurcation and LEs diagrams of system on sinusoidal wave-like terrain（A=0.3）"

Fig.8

Bifurcation and LEs diagrams of system on andomized terrain（A'=0.1）"

Fig.9

Bifurcation and LEs diagrams of system on randomized terrain（A'=0.3）"

Fig.10

Poincaré section of system on randomized terrain（A'=0.3）"

Fig.11

Bifurcation diagram of system on flat ramp（A=0.0）"

Fig.12

Bifurcation diagram of system on sinusoidal wave-like terrain（A=0.1）"

Fig.13

Bifurcation diagram of system on randomized terrain（A'=0.1）"

Fig.14

Comparison of walking evolution of robots under different A"

Fig.15

Robot prototype and walking ramps in ADAMS simulation"

Fig.16

Walking process and time response diagrams of robot"

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