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

This study presents time-domain and frequency-domain, multiple-input, multiple-output (MIMO) linear system identification techniques that can be used to estimate the dynamic endpoint stiffness of a multi-joint limb. The stiffness 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 movement. Estimates of endpoint stiffness can therefore be used to characterize its modulation during physiological tasks and may provide insight into how the nervous system normally controls motor behavior. Previous MIMO stiffness estimates have focused upon the static stiffness components only or assumed simple parametric models with elastic, viscous, and inertial components. The method presented here captures the full stiffness dynamics during a relatively short experimental trial while assuming only that the system is linear for small perturbations. Simulation studies were performed to investigate 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 force perturbations. Distortion of these linear estimates by nonlinear centripetal and Coriolis forces was virtually undetectable for these perturbations. The system identification techniques were also found to be robust in the presence of significant output measurement noise and input coupling. These results indicate that the approach described here will allow the estimation of endpoint stiffness dynamics in an experimentally efficient manner with minimal assumptions about the specific form of these properties.