A NARMAX method for the identification of time-varying joint stiffness

Dynamic joint stiffness defines the dynamic relationship between the position of a joint and the torque acting about it and can be separated into intrinsic and reflex components. Under stationary conditions, these can be identified using a nonlinear parallel-cascade algorithm that models intrinsic stiffness and reflex stiffness as parallel pathways. Experimental results demonstrate that both intrinsic and reflex stiffness depend strongly on the operating point defined by mean joint position and the activation level. Consequently, both intrinsic and reflex stiffness will appear to be time-varying (TV) whenever the operating point changes, as during movement. This paper describes and validates a new method for identification of TV ankle stiffness. The method is based on the TV nonlinear autorregresive, moving average exogenous (NARMAX) model class. Simulation results demonstrated that the algorithm can accurately estimate the TV parameters of the ankle stiffness. We conclude that the algorithm is potentially a powerful new tool for the study of joint stiffness during TV conditions.