A novel model for estimating the endpoint stiffness of a limb

Abstract

In past years, the muscle activation, collected from a human operator, was used to drive not only the endpoint force and trajectory, but also the impedance of robotic devices. Therefore, different groups proposed algorithms for real-time estimation of endpoint stiffness from muscle activation, but these estimations were based on complex models of the human, which required the control of subject-specific anatomically accurate musculo-skeletal models, or oversimplified models, which reduced the high redundancy of the musculo-skeletal system by collecting the activity of few couples of antagonist muscles. This study describes and tests a novel algorithm which approximates the stiffness exerted by a multi-joint multi-muscle system, from the muscle activation. This algorithm approximates the stiffness of a limb as the component of the muscle activation that do not generates any endpoint force, which is calculated as the projection of the muscle activation vector onto the null space of the mapping between muscle activation and endpoint force. The proposed approximation was verified on an upper limb model made of two joints and six muscles, modeled as the Hill muscle model. This study identifies the null space component of the muscle activation as an acceptable estimation of the major axis of the stiffness ellipse, especially for low muscle activation. The presented model could be directly implemented in myoelectric controlled devices for the real-time estimation of the endpoint forces, or endpoint movement, from the mapping between muscle activation and force, without any more calibrations.