Stochastic Estimation of Multi-variable Human Ankle Mechanical Impedance

This article presents preliminary stochastic estimates of the multi-variable human ankle mechanical impedance. We employed Anklebot, a rehabilitation robot for the ankle, to provide torque perturbations. Time histories of the torques in Dorsi-Plantar flexion (DP) and Inversion-Eversion (IE) directions and the associated angles of the ankle were recorded. Linear timeinvariant transfer functions between the measured torques and angles were estimated for the Anklebot and when the Anklebot was worn by a human subject. The difference between these impedance functions provided an estimate of the mechanical impedance of the ankle. High coherence was observed over a frequency range up to 30 Hz, indicating that this procedure yielded an accurate measure of ankle mechanical impedance in DP and IE directions. INTRODUCTION The mechanical impedance of the human ankle plays a major role in lower extremity function during locomotion such as maintaining the upright posture, shock absorption, lower-limb joint coordination during walking, steering, and propulsion on level ground and slopes – all functions which involve mechanical interaction of the foot with the contacting surface. One method for measuring ankle impedance is stochastic perturbation. The advantage of stochastic methods over steady-state procedures is that they provide a quantitative estimate without requiring any apriori assumption about the order or dynamic structure of mechanical impedance. In particular, they do not require the common assumption that impedance is composed of inertia, damping and stiffness, but are applicable to more complex, higherorder dynamics. In prior work, Kirsch et. al. [1] estimated the ankle impedance in dorsiflexion direction by superimposing small stochastic motion perturbations during a large dorsiflexion motion of the foot. Application of position perturbations requires care to avoid applying excessive force to the subjects’ joints. Van der Helm et. al. [2] used a linear hydraulic actuator to impose force perturbations for identification of intrinsic and reflexive components of the human arm [2]. In earlier work, we employed MIT-MANUS to apply pseudo-random force perturbations to estimate the mechanical impedance of the arm in two degrees of freedom simultaneously [3]. In this paper, we employed Anklebot, a rehabilitation robot for the ankle, and a similar methodology for stochastic identification of human ankle mechanical impedance. The mechanical impedance of the ankle in DP and IE were determined from nonparametric estimation of the best-fit linear transfer functions relating torques to angles in DP and IE directions. Anklebot is backdrivable with low friction and allows human subjects to move their foot freely in three degrees of freedom (DOF) relative to the shank; a detailed description can be found in [4]. Of those, two DOFs are actuated. Two nearly parallel actuators generate a dorsi-plantarflexion torque if both apply identical forces in the same direction, and inversion-eversion torque if they apply identical forces in opposite directions. As a result, the robot can apply simultaneous perturbations in two degrees of freedom of the ankle. Displacements of the linear actuators are measured by linear encoders. The ankle torques and angles were described in detail in [4] and are estimated from: , ( ) dp right left tr len F F x    (1) 2 2 2 , , 1 , , sin ( ) 2 shank tr len link disp dp dp offset shank tr len L x x L x        (2) 1 Copyright © 2009 by ASME DSCC2009-2643 Proceedings of the ASME 2009 Dynamic Systems and Control Conference DSCC2009 October 12-14, 2009, Hollywood, California, USA