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This paper presents identification and modeling of dynamic ankle mechanical impedance in relaxed muscles. A multi-variable estimation method using a wearable therapeutic robot enabled clear interpretation of dynamic ankle impedance both in the sagittal and frontal planes. Estimation results showed that dynamic ankle behavior apparently cannot be reconciled with a simple 2nd order model. Measurements in a seated and standing position verified that ankle impedance changes substantially depending on lower-limb posture. Identification results were fitted with a modified Hill model with a mass between the muscle and tendon elements. When coupled with foot inertia, either singly or antagonistically, this model successfully captured the dynamic behavior of the ankle impedance both in the seated and standing positions up to 20 Hz. At least a 4th order model having 2 complex zero and 1 complex pole pairs was required to describe relaxed ankle impedance either in the sagittal or frontal plane up to 20Hz. In the seated position, a 6th order model was slightly better than the 4th order model but with the expense of complexity, and a 8th order model might be used to describe dynamic ankle behavior up to 30∼40Hz.Copyright © 2011 by ASME

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.Copyright © 2010 by ASME

This article presents the results of two in-vivo studies providing measurements of human static ankle mechanical impedance. Accurate measurements of ankle impedance when muscles were voluntarily activated were obtained using a therapeutic robot, Anklebot, and an electromyographic recording system. Important features of ankle impedance, and their variation with muscle activity, are discussed, including magnitude, symmetry and directions of minimum and maximum impedance. Voluntary muscle activation has a significant impact on ankle impedance, increasing it by up to a factor of three in our experiments. Furthermore, significant asymmetries and deviations from a linear two-spring model are present in many subjects, indicating that ankle impedance has a complex and individually idiosyncratic structure. We propose the use of Fourier series as a general representation, providing both insight and a precise quantitative characterization of human static ankle impedance.Copyright © 2010 by ASME

Characterization of multi-variable ankle mechanical impedance is crucial to understanding how the ankle supports lower-extremity function during interaction with the environment. This paper reports quantification of steady-state ankle impedance when muscles were active. Vector field approximation of repetitive measurements of the torque-angle relation in two degrees of freedom (inversion/eversion and dorsiflexion/plantarflexion) enabled assessment of spring-like and non-spring-like components. Experimental results of eight human subjects showed direction-dependent ankle impedance with greater magnitude than when muscles were relaxed. In addition, vector field analysis demonstrated a non-spring-like behavior when muscles were active, although this phenomenon was subtle in the unimpaired young subjects we studied.

In this paper, we report measurements of the multi-variable torque-displacement relation at the ankle. The passive behavior of the ankle in two degrees of freedom (inversion-eversion and dorsiflexion-plantarflexion) was quantified using the Anklebot. The measured torque-displacement relationship was represented as a vector field using thin-plate spline smoothing with generalized cross validation. Analysis of the experimental results showed that, when maximally relaxed, the ankle behaved like a mechanical spring. However, if muscles were active, the torque-displacement relation was not spring-like. Implications for the contribution of neural feedback to ankle impedance are discussed.Copyright © 2009 by ASME

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 time-invariant 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.Copyright © 2009 by ASME

Though ankle mechanical impedance plays an important role in posture and locomotion, it has been inadequately characterized. Unlike previous studies, which confined themselves to measurements along the primary axes of the ankle in an isolated fashion, the study reported here characterized the static component of ankle impedance in two degrees of freedom. In addition, the effect of active muscle contraction on ankle static impedance was measured. We found that ankle static impedance varied significantly with direction under passive conditions. We further observed that, while muscle contraction increased the magnitude of ankle static impedance, its directional variation was essentially unchanged.Copyright © 2009 by ASME

Using Anklebot, a therapeutic robot module, we perturbed human gait by applying external torque to the human ankle at various frequencies. We observed that with a properly designed perturbation, 8 subjects out of 10 exhibited entrained gaits: their gait frequencies were adapted to the frequency of mechanical perturbation, and they synchronized their ankle actuation with the external torque supplied by the robot. This preliminary result suggests that a limit-cycle oscillator, a plausible element of the coupled system of central nervous system and musculo-skeletal periphery, plays a significant role in the neuro-motor execution of human locomotion. The entrainment of human gait by periodic torque from a robotic aid may provide a novel approach to walking therapy that is uniquely supportive of normal biological function.Copyright © 2008 by ASME

Growing interest in robotic treatment of patients with neurological injury motivates the development of therapeutic robots for basic research into recovery. Though humans are the ultimate beneficiaries, basic research frequently involves rodent models of neurological injury, which motivates robotic devices that can interact with rats or mice. This paper proposes an overground therapeutic robot suitable for rodent studies of recovery after for spinal cord injury. Advantages and challenges of an overground machine are compared with treadmill-type machines. Design and implementation issues, including its kinematic configuration, control scheme, biomechanical coupling and partial body weight support system, are presented and discussed. Current development progress is reported along with possible future applications of the device.Copyright © 2008 by ASME