The 1/f-like gait cycle variability, characterized by temporal changes in stride-time intervals during steady-state human walking, is a well-documented gait characteristic. Such gait fractality is apparent in healthy young adults, but tends to disappear in the elderly and patients with neurological diseases. However, mechanisms that give rise to gait fractality have yet to be fully clarified. We aimed to provide novel insights into neuro-mechanical mechanisms of gait fractality, based on a numerical simulation model of biped walking. A previously developed heel-toe footed, seven-rigid-link biped model with human-like body parameters in the sagittal plane was implemented and expanded. It has been shown that the gait model, stabilized rigidly by means of impedance control with large values of proportional (P) and derivative (D) gains for a linear feedback controller, is destabilized only in a low-dimensional eigenspace, as P and D decrease below and even far below critical values. Such low-dimensional linear instability can be compensated by impulsive, phase-dependent actions of nonlinear controllers (phase resetting and intermittent controllers), leading to the flexible walking with joint impedance in the model being as small as that in humans. Here, we added white noise to the model to examine P-value-dependent stochastic dynamics of the model for small D-values. The simulation results demonstrated that introduction of the nonlinear controllers in the model determined the fractal features of gait for a wide range of the P-values, provided that the model operates near the edge of stability. In other words, neither the model stabilized only by pure impedance control even at the edge of linear stability, nor the model stabilized by specific nonlinear controllers, but with P-values far inside the stability region, could induce gait fractality. Although only limited types of controllers were examined, we suggest that the impulsive nonlinear controllers and criticality could be major mechanisms for the genesis of gait fractality.

中文翻译：

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在简单的两足动物模型中，在稳定性边缘的相位重置和间歇控制会产生类似1 / f的步态周期可变性。

1 / f式步态周期可变性的特征是步态稳定，是步态稳定的人类步行过程中步幅时间间隔随时间变化的特征。这种步态分形在健康的年轻人中很明显，但在老年人和神经系统疾病患者中则趋于消失。但是，引起步态不规则性的机制尚未完全阐明。我们的目的是基于两足动物步行的数值模拟模型，为步态分形的神经机械机制提供新颖的见解。实施并扩展了先前开发的脚后跟脚，七刚性链接的两足动物模型，其在矢状面中具有类人的身体参数。已经证明，步态模型 对于线性反馈控制器，通过具有较大比例（P）和微分（D）增益的阻抗控制，通过阻抗控制进行严格稳定，仅当P和D减小到临界值以下，甚至远低于临界值时，它才在低维特征空间中不稳定。这种低维线性不稳定性可以通过非线性控制器（相位重置和间歇控制器）的脉冲式，与相位有关的动作来补偿，从而导致模型中的关节阻抗与人类一样小，并且可以灵活行走。在这里，我们向模型中添加了白噪声，以检查D值较小时模型的P值依赖的随机动力学。仿真结果表明，在模型中引入非线性控制器可确定各种P值的步态的分形特征，前提是模型在稳定性边缘附近运行。换句话说，既不能通过纯阻抗控制来稳定模型，即使在线性稳定性的边缘，也不能通过特定的非线性控制器来稳定模型，而是P值位于稳定区域内，则不会诱发步态分形。尽管只检查了有限类型的控制器，但我们建议脉冲非线性控制器和临界度可能是步态分形发生的主要机制。