Identification of inverse kinematic parameters in redundant systems: Towards quantification of inter-joint coordination in the human upper extremity.

Understanding and quantifying inter-joint coordination is valuable in several domains such as neurorehabilitation, robot-assisted therapy, robotic prosthetic arms, and control of supernumerary arms. Inter-joint coordination is often understood as a consistent spatiotemporal relation among kinematically redundant joints performing functional and goal-oriented movements. However, most approaches in the literature to investigate inter-joint coordination are limited to analysis of the end-point trajectory or correlation analysis of the joint rotations without considering the underlying task; e.g., creating a desirable hand movement toward a goal as in reaching motions. This work goes beyond this limitation by taking a model-based approach to quantifying inter-joint coordination. More specifically, we use the weighted pseudo-inverse of the Jacobian matrix and its associated null-space to explain the human kinematics in reaching tasks. We propose a novel algorithm to estimate such Inverse Kinematics weights from observed kinematic data. These estimated weights serve as a quantification for spatial inter-joint coordination; i.e., how costly a redundant joint is in its contribution to creating an end-effector velocity. We apply our estimation algorithm to datasets obtained from two different experiments. In the first experiment, the estimated Inverse Kinematics weights pinpoint how individuals change their Inverse Kinematics strategy when exposed to the viscous field wearing an exoskeleton. The second experiment shows how the resulting Inverse Kinematics weights can quantify a robotic prosthetic arm's contribution (or the level of assistance).