Optimality of Reaching Movements Based on Energetic Cost under the Influence of Signal-Dependent Noise

As candidates of a constraint which determines human arm reaching trajectories, criteria of the minimum torque change and of the minimum end-point variance have been proposed and it has been shown that these criteria well predict the characteristics of reaching trajectories. In our previous work, we have shown that these criteria would also suppress the energy cost for reaching movements, when motor command is affected by signal-dependent noise. In this study, we computed the trajectories which minimize the energy cost under the effect of the signal-dependent noise, and compared them with those of human subjects. The optimal trajectories were in good agreement with the measured trajectories at the points that when the movement duration is short, the speed profile of the hand movement takes a bell shape, and when the duration is long, the speed profiles take a collapsed shape. These results would suggest that human brain solves the redundancy problem of trajectory planning by the constraint of minimization of the expected value of energy cost.