Complex walking behaviours, chaos and bifurcations of a simple passive compass-gait biped model suffering from leg length asymmetry

H. Gritli, N. K. Haddad, S. Belghith
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引用次数: 8

Abstract

This paper is concerned with the analysis of the displayed nonlinear phenomena, chaos and bifurcations, in the planar passive dynamic walking of the planar compass-gait biped model under a leg length asymmetry as it goes down an inclined surface. The passive dynamic walking of the compass-gait model is modelled with an impulsive hybrid nonlinear dynamics. In this work, we present a normalised dynamics expressed in terms of dimensionless ratios. Our analysis and simulation of the passive bipedal gaits is realised mainly through bifurcation diagrams where a normalised leg length discrepancy is adopted as the bifurcation parameter. We report the exhibition of complex behaviours, namely the period-doubling bifurcation (PDB), the cyclic-fold bifurcation (CFB), the period-doubling route to chaos, the period-remerging scheme, the boundary crisis (BC), etc. We demonstrate also the exhibition of the Neimark-Sacker-2 bifurcation by investigating the tendency of the characteristic multipliers of the Jacobian matrix of the Poincare map.
腿长不对称的简单被动罗盘双足模型的复杂行走行为、混沌和分叉
分析了在腿长不对称的情况下,平面罗经-步态双足模型在斜面下行被动动态行走时所表现出的非线性混沌和分岔现象。采用脉冲混合非线性动力学方法对罗盘-步态模型的被动动态行走进行建模。在这项工作中,我们提出了一个用无因次比率表示的归一化动力学。我们对被动双足步态的分析和仿真主要是通过分岔图实现的,其中采用归一化腿长差异作为分岔参数。我们报道了复杂行为的表现,即倍周期分岔(PDB)、循环-褶皱分岔(CFB)、倍周期混沌路径、周期重合并方案、边界危机(BC)等。通过研究庞加莱映射的雅可比矩阵的特征乘子的趋向,我们也证明了neimmark - sacker -2分岔的存在。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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