Whole-Body Reaching Movements Formulated by Minimum Muscle-Tension Change Criterion

It is well known that planar reaching movements of the human shoulder and elbow joints have invariant features: roughly straight hand paths and bell-shaped velocity profiles. The optimal control models with the criteria of smoothness or precision, which determine a unique movement pattern, predict such features of hand trajectories. In this letter on expanding the research on simple arm reaching movements, we examine whether the smoothness criteria can be applied to whole-body reaching movements with many degrees of freedom. Determining a suitable joint trajectory in the whole-body reaching movement corresponds to the optimization problem with constraints, since body balance must be maintained during a motion task. First, we measured human joint trajectories and ground reaction forces during whole-body reaching movements, and confirmed that subjects formed similar movements with common characteristics in the trajectories of the hand position and body center of mass. Second, we calculated the optimal trajectories according to the criteria of torque and muscle-tension smoothness. While the minimum torque change trajectories were not consistent with the experimental data, the minimum muscle-tension change model was able to predict the stereotyped features of the measured trajectories. To explore the dominant effects of the extension from the torque change to the muscle-tension change, we introduced a weighted torque change cost function. Considering the maximum voluntary contraction (MVC) force of the muscle as the weighting factor of each joint torque, we formulated the weighted torque change cost as a simplified version of the minimum muscle-tension change cost. The trajectories owing to the minimum weighted torque change criterion also showed qualitative agreement with the common features of the measured data. Proper estimation of the MVC forces in the body joints is essential to reproduce human whole-body movements according to the minimum muscle-tension change criterion.