Identification of a Time-Varying, Box-Jenkins Model of Intrinsic Joint Compliance

The mechanical properties of a joint are determined by the combination of intrinsic and reflex mechanisms. However, in some situations the reflex contributions are small so that intrinsic mechanisms play the dominant role in the control of posture and movement. The intrinsic mechanisms, characterized by the joint compliance, can be described well by a second order, linear model for small perturbations around an operating point defined by mean position and torque. However, the compliance parameters depend strongly on the operating point. Thus, for functional activities, such as walking, where position and torque undergo large, rapid changes, the joint compliance will also present large, fast changes and so will appear to be Time-Varying (TV). Therefore, a TV system identification algorithm must be used to characterize these changes. This paper introduces a novel TV system identification algorithm that achieves this. The method extends an instrumental-variable based algorithm for the identification of linear, TV, parametric, Box-Jenkins models to use periodic data. Simulation studies demonstrate that the new algorithm accurately tracks the changes in intrinsic joint compliance expected during walking. Moreover, the method performs well with the complex noise encountered in practice. Consequently the new method should be a valuable tool for the study of joint mechanics during functional activities.