Identification of Time-Varying Stiffness, Damping, and Equilibrium Position in Human Forearm Movements

Knowledge of how stiffness, damping, and the equilibrium position of specific limbs change during voluntary motion is important for understanding basic strategies of neuromotor control. Presented here is an algorithm for identifying time-dependent changes in joint stiffness, damping, and equilibrium position of the human forearm. The procedure requires data from only a single trial. The method relies neither on an analysis of the resonant frequency of the arm nor on the presence of an external bias force. Its validity was tested with a simulated forward model of the human forearm. Using the parameter estimations as forward model input, the angular kinematics (model output) were reconstructed and compared to the empirically measured data. Identification of mechanical impedance is based on a least-squares solution of the model equation. As a regularization technique and to improve the temporal resolution of the identification process, a moving temporal window with a variable width was imposed. The method's performance was tested by (a) identifying a priori known hypothetical time-series of stiffness, damping, and equilibrium position, and (b) determining impedance parameters from recorded single-joint forearm movements during a hold and a goal-directed movement task. The method reliably reconstructed the original angular kinematics of the artificial and human data with an average positional error of less than 0.05 rad for movement amplitudes of up to 0.9 rad, and did not yield hypermetric trajectories like previous procedures not accounting for damping.