Stochastic Estimation of the Multi-variable Mechanical Impedance of the Human Ankle with Active Muscles

This article compares stochastic estimates of multi-variable human ankle mechanical impedance when ankle muscles were fully relaxed, actively generating ankle torque or co-contracting antagonistically. We employed Anklebot, a rehabilitation robot for the ankle, to provide torque perturbations. Muscle activation levels were monitored electromyographically and these EMG signals were displayed to subjects who attempted to maintain them constant. Time histories of ankle torques and angles in the Dorsi-Plantar flexion (DP) and Inversion-Eversion (IE) directions were recorded. Linear time-invariant transfer functions between the measured torques and angles were estimated for the Anklebot alone and when it was worn by a human subject, the difference between these functions providing an estimate of ankle mechanical impedance. High coherence was observed over a frequency range up to 30 Hz. The main effect of muscle activation was to increase the magnitude of ankle mechanical impedance in both DP and IE directions. INTRODUCTION The mechanical impedance of the human ankle plays a major role in lower extremity functions that involve mechanical interaction of the foot with the contacted surface. Examples include maintaining upright posture and shock-absorption, lowerlimb joint coordination, steering, and propulsion during walking on level ground, slopes or stairs. One method for measuring ankle mechanical impedance uses stochastic perturbations. It provides a quantitative estimate of ankle impedance without requiring apriori assumptions about its dynamic structure. In particular, this method avoids the common assumption that impedance is composed of inertia, damping and stiffness, but is applicable to more complex, higher-order dynamics. A stochastic perturbation method was used by Kirsch et. al. [1] to estimate ankle mechanical impedance in one degree of freedom. Small stochastic motion perturbations were applied during a large dorsiflexion motion of the foot. Motion perturbations were used by Van der Helm et. al. [2] utilizing a linear hydraulic actuator to identify intrinsic and reflexive components of the human arm dynamics [2]. Applying motion perturbations requires care to avoid exerting excessive forces on subjects’ joints. 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]. We recently applied the same methodology to estimate the mechanical impedance of the relaxed human ankle in two degrees of freedom using Anklebot [4]. In this paper, we report application of the method to estimate the mechanical impedance of the human ankle with active muscles.