Multiple-input, multiple-output system identification for characterizationof limb stiffness dynamics

This study presents time-domain and frequency-domain, multiple-input, multi ple-output (MIMO) linear system identification techniques that can be used to estimate the dynamic endpoint stiffness of a multijoint limb. The stiffn ess of a joint or limb arises from a number of physiological mechanisms and is thought to play a fundamental role in the control of posture and moveme nt. Estimates of endpoint stiffness can therefore be used to characterize i ts modulation during physiological tasks and may provide insight into how t he nervous system normally controls motor behavior. Previous MIMO stiffness estimates have focused upon the static stiffness components only or assume d simple parametric models with elastic, viscous, and inertial components. The method presented here captures the full stiffness dynamics during a rel atively short experimental trial while assuming only that the system is lin ear for small perturbations. Simulation studies were performed to investiga te the performance of this approach under typical experimental conditions. It was found that a linear MIMO description of endpoint stiffness dynamics was sufficient to describe the displacement responses to small stochastic f orce perturbations. Distortion of these linear estimates by nonlinear centr ipetal and Coriolis forces was virtually undetectable for these perturbatio ns. The system identification techniques were also found to be robust in th e presence of significant output measurement noise and input coupling. Thes e results indicate that the approach described here will allow the estimati on of endpoint stiffness dynamics in an experimentally efficient manner wit h minimal assumptions about the specific form of these properties.