Identification of Stretch Reflex Dynamics from Closed-Loop Data

The torque and angle data used to identify models of limb impedance are usually generated under closed-loop conditions. In many cases, the joint position is controlled using a powerful position servo, so that the joint interacts with a very stiff environment. Under these conditions, the data may be treated as if they had been obtained in open-loop conditions. When experiments are performed under compliant conditions, the effects of feedback can no longer be ignored. A closed-loop identification algorithm which identifies a finite impulse response model of joint admittance has previously been developed, and used to estimate the admittance of the elbow joint under a variety of experimental conditions. The approach was based on prediction error minimization, and identified the FIR system model with an ARMA noise model. The experimental input was chosen to minimize the effects of reexes, so that the system would be very nearly linear. Standard correlation based tests were used to validate the resulting models. In this paper, we use two simulation models of the human ankle joint together with a typical experimental apparatus. The actuator was configured so that it could create both stiff and compliant environments, which allowed for the simulation of a broad range of joint dynamics experiments. In one case, a linear model was used, while the other included a nonlinear model of the stretch reex. Data from both simulations was processed using the closed-loop linear identification methods described above. Significant differences were noted between the models obtained from the linear and nonlinear simulations. Thus, the presence of the reex pathway biased the linear identification. However, the standard correlation based model tests suggested that the linear model structures were appropriate in both cases. The residuals appeared to be white noise, and not causally correlated with the input torque. High-order correlation based tests, normally used in the validation of parametric nonlinear models, revealed the presence of unmodeled nonlinearities in the system. This analysis is then applied to experimental data from a study on elbow compliance.