IEEE Trans Neural Syst Rehabil Eng. 2013 Sep;21(5):840-8. doi: 10.1109/TNSRE.2013.2264920. Epub 2013 Jun 4.
Robust motor behaviors emerge from neuromechanical interactions that are nonlinear, have delays, and contain redundant neural and biomechanical components. For example, in standing balance a subject's muscle activity (neural control) decreases as stance width (biomechanics) increases when responding to a lateral perturbation, yet the center-of-mass motion (behavior) is nearly identical regardless of stance width. We present stability radius, a technique from robust control theory, to overcome the limitations of classical stability analysis tools, such as gain margin, which are insufficient for predicting how concurrent changes in both biomechanics (plant) and neural control (controller) affect system behavior. We first present the theory and then an application to a neuromechanical model of frontal-plane standing balance with delayed feedback. We show that stability radius can quantify differences in the sensitivity of system behavior to parameter changes, and predict that narrowing stance width increases system robustness. We further demonstrate that selecting combinations of stance width (biomechanics) and feedback gains (neural control) that have the same stability radius produce similar center-of-mass behavior in simulation. Therefore, stability radius may provide a useful tool for understanding neuromechanical interactions in movement and could aid in the design of devices and therapies for improving motor function.
稳健的运动行为源于神经机械相互作用，这些相互作用是非线性的、具有延迟的，并且包含冗余的神经和生物力学组件。例如，在站立平衡中，当对侧向扰动做出反应时，受试者的肌肉活动（神经控制）随着站立宽度（生物力学）的增加而减少，但质心运动（行为）几乎相同，无论站立宽度如何。我们提出了稳定性半径，这是稳健控制理论中的一种技术，用于克服经典稳定性分析工具的局限性，例如增益裕度，增益裕度不足以预测生物力学（植物）和神经控制（控制器）的同时变化如何影响系统行为。我们首先介绍了理论，然后介绍了在具有延迟反馈的额状面站立平衡神经机械模型中的应用。我们表明，稳定性半径可以量化系统行为对参数变化的敏感性差异，并预测缩小站立宽度会增加系统的稳健性。我们进一步证明，选择具有相同稳定性半径的站立宽度（生物力学）和反馈增益（神经控制）组合可以在模拟中产生相似的质心行为。因此，稳定性半径可能是理解运动中神经机械相互作用的有用工具，并有助于设计改善运动功能的设备和治疗方法。
