A Complex Stiffness Human Impedance Model with Customizable Exoskeleton Control

TL;DR

This paper presents a new complex stiffness model for human impedance in exoskeletons, revealing nonlinear behaviors and hysteretic damping, and introduces a fractional-order controller for improved stability and strength amplification.

Contribution

It introduces a complex-valued frequency-domain model of human joint impedance with hysteretic damping and develops a customizable fractional-order control approach for exoskeletons.

Findings

Hysteretic damping is more significant than linear damping.

A linear relationship links hysteretic damping and real stiffness.

The proposed controller enhances bandwidth and stability robustness.

Abstract

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 paper 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.