Fu Chunjiang, Suzuki Yasuyuki, Morasso Pietro, Nomura Taishin
Graduate School of Engineering Science, Osaka University, Osaka, 5608531, Japan.
Honda R&D Innovative Research Excellence, Wako, Japan.
Biol Cybern. 2020 Feb;114(1):95-111. doi: 10.1007/s00422-020-00816-y. Epub 2020 Jan 20.
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.
类1/f步态周期变异性是一种有充分记录的步态特征，其特点是在人体稳态行走过程中步幅时间间隔的时间变化。这种步态分形性在健康的年轻人中很明显，但在老年人和神经疾病患者中往往会消失。然而，导致步态分形性的机制尚未完全阐明。我们旨在基于双足行走的数值模拟模型，为步态分形性的神经力学机制提供新的见解。我们实现并扩展了一个先前开发的矢状面具有类人体参数的足跟到足尖的七刚体双足模型。研究表明，对于线性反馈控制器，通过具有大比例（P）和微分（D）增益的阻抗控制来刚性稳定的步态模型，仅在低维特征空间中不稳定，因为P和D降至临界值以下甚至远低于临界值。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、相位相关作用来补偿，从而使模型中具有关节阻抗的灵活行走与人类的行走一样小。在这里，我们向模型中添加白噪声，以研究小D值下模型的P值相关随机动力学。模拟结果表明，只要模型在稳定性边缘附近运行，在模型中引入非线性控制器就能在很宽的P值范围内确定步态的分形特征。换句话说，即使在线性稳定性边缘仅通过纯阻抗控制稳定的模型，以及通过特定非线性控制器稳定但P值远在稳定区域内的模型，都不会诱导步态分形性。尽管只研究了有限类型的控制器，但我们认为脉冲式非线性控制器和临界性可能是步态分形性产生的主要机制。
