Estimation of Ankle Joint Stiffness During Quiet Standing Using Only a Force Plate Without Perturbation

Abstract

We investigated a system identification method for modeling the standing posture without external perturbation. Assuming that postural sway during quiet standing is caused by internal white noise, the method adopts an autocorrelation matrix consisting of body position and velocity parameters. We showed that the method can be applied to center-of-mass fluctuation measurement data. Since we used only a force plate to minimize the burden on the subjects, the velocity could not be measured directly. Therefore, we first demonstrated through simulation that ankle joint stiffness can be estimated by numerically deriving the velocity from the displacement. The velocity was calculated using the central difference approximation, and the ankle stiffness estimation error was obtained. The system identification method was then applied to the center-of-mass measurement data, and the ankle stiffness was estimated. Simulations showed that even when the velocity was calculated through numerical differentiation, the ankle joint stiffness could still be estimated with an accuracy of less than 1% error. The ankle stiffness estimated from the measured center of mass was slightly higher than the gravitational torque coefficient, but lower than that obtained in our previous electrical stimulation study (Uchiyama T: Adv Biomed Eng. 13, 223‒229, 2024). This suggests that the control method for ankle stiffness may depend on the presence or absence of external disturbances.