Modeling Dynamic Ankle Mechanical Impedance in Relaxed Muscle

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 2^nd 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 4^th 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 6^th order model was slightly better than the 4^th order model but with the expense of complexity, and a 8^th order model might be used to describe dynamic ankle behavior up to 30∼40Hz.