Identification of time-varying intrinsic and reflex 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-a linear dynamic response to position-and reflex stiffness-a nonlinear dynamic response to velocity-as parallel pathways. Experiments using this method show that both intrinsic and reflex stiffness depend strongly on the operating point, defined by position and torque, likely because of some underlying nonlinear behavior not modeled by the parallel-cascade structure. Consequently, both intrinsic and reflex stiffness will appear to be time-varying whenever the operating point changes rapidly, as during movement. This paper describes and validates an extension of the parallel-cascade algorithm to time-varying conditions. It describes the ensemble method used to estimate time-varying intrinsic and reflex stiffness. Simulation results demonstrate that the algorithm can track rapid changes in joint stiffness accurately. Finally, the performance of the algorithm in the presence of noise is tested. We conclude that the new algorithm is a powerful new tool for the study of joint stiffness during functional tasks.