Optimal Feedback Control for the Proportion of Energy Cost in the Upper-Arm Reaching Movement

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.