The natural impedance, or dynamic relationship between force and motion, of a human operator can determine the stability of exoskeletons that use interaction-torque feedback to amplify human strength. While human impedance is typically modelled as a linear system, our experiments on a single-joint exoskeleton testbed involving 10 human subjects show evidence of nonlinear behavior: a low-frequency asymptotic phase for the dynamic stiffness of the human that is different than the expected zero, and an unexpectedly consistent damping ratio as the stiffness and inertia vary. To explain these observations, this article considers a new frequency-domain model of the human joint dynamics featuring complex value stiffness comprising a real stiffness term and a hysteretic damping term. Using a statistical F-test we show that the hysteretic damping term is not only significant but is even more significant than the linear damping term. Further analysis reveals a linear trend linking hysteretic damping and the real part of the stiffness, which allows us to simplify the complex stiffness model down to a 1-parameter system. Then, we introduce and demonstrate a customizable fractional-order controller that exploits this hysteretic damping behavior to improve strength amplification bandwidth while maintaining stability, and explore a tuning approach which ensures that this stability property is robust to muscle co-contraction for each individual.

中文翻译：

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具有可定制外骨骼控制的复杂刚度人体阻抗模型


人类操作员的自然阻抗或力与运动之间的动态关系可以确定使用交互扭矩反馈来放大人类力量的外骨骼的稳定性。虽然人体阻抗通常被建模为线性系统，但我们在涉及 10 名受试者的单关节外骨骼测试台上进行的实验显示了非线性行为的证据：人体动态刚度的低频渐近阶段不同于预期的零，以及随着刚度和惯量变化而出乎意料地一致的阻尼比。为了解释这些观察结果，本文考虑了一种新的人体关节动力学频域模型，该模型具有复值刚度，包括真实刚度项和迟滞阻尼项。使用统计 F 检验，我们表明迟滞阻尼项不仅显着，而且比线性阻尼项更显着。进一步的分析揭示了滞后阻尼和刚度实部之间的线性趋势，这使我们能够将复杂的刚度模型简化为一参数系统。然后，我们介绍并演示了一种可定制的分数阶控制器，该控制器利用这种迟滞阻尼行为来提高强度放大带宽，同时保持稳定性，并探索一种调整方法，以确保这种稳定性特性对每个个体的肌肉共同收缩具有鲁棒性。