The minimum expected energy cost model, which has been proposed as one of the optimization principles for movement planning, can reproduce many characteristics of the human upper-arm reaching movement when signal-dependent noise and the co-contraction of the antagonist’s muscles are considered. Regarding the optimization principles, discussion has been mainly based on feedforward control; however, there is debate as to whether the central nervous system uses a feedforward or feedback control process. Previous studies have shown that feedback control based on the modified linear-quadratic gaussian (LQG) control, including multiplicative noise, can reproduce many characteristics of the reaching movement. Although the cost of the LQG control consists of state and energy costs, the relationship between the energy cost and the characteristics of the reaching movement in the LQG control has not been studied. In this work, I investigated how the optimal movement based on the LQG control varied with the proportion of energy cost, assuming that the central nervous system used feedback control. When the cost contained specific proportions of energy cost, the optimal movement reproduced the characteristics of the reaching movement. This result shows that energy cost is essential in both feedforward and feedback control for reproducing the characteristics of the upper-arm reaching movement.

When we move our body to perform a movement task, our central nervous system selects a movement trajectory from an infinite number of possible trajectories under constraints that have been acquired through evolution and learning. Minimization of the energy cost has been suggested as a potential candidate for a constraint determining locomotor parameters, such as stride frequency and stride length; however, other constraints have been proposed for a human upper-arm reaching task. In this study, we examined whether the minimum metabolic energy cost model can also explain the characteristics of the upper-arm reaching trajectories. Our results show that the optimal trajectory that minimizes the expected value of energy cost under the effect of signal-dependent noise on motor commands expresses not only the characteristics of reaching movements of typical speed but also those of slower movements. These results suggest that minimization of the energy cost would be a basic constraint not only in locomotion but also in upper-arm reaching.