Optimality of Upper-Arm Reaching Trajectories Based on the Expected Value of the Metabolic Energy Cost

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.

Optimal reaching trajectories based on feedforward control

In human upper-arm reaching movements, the variance of the hand position increases until the middle of the movement and then decreases toward the endpoint. Such decrease in positional variance has been suggested as an evidence to support the hypothesis that our nervous system uses feedback control, rather than feedforward control, for arm reaching tasks. In this study, we computed the optimal trajectories based on feedforward control under several criteria for a one-link two-muscle arm model with considering the stochastic property of muscle activities in order to reexamine the hypothesis. The results showed that the feedforward control also represents the decrease in positional variance in the latter half of the movement when the control signal is planned under the minimum energy cost and minimum variance models. Furthermore, the optimal trajectory that minimizes energy cost represents not only the decrease in positional variance but also many other characteristics of the human reaching movements, e.g., the three-phasic activity of antagonistic muscle, bell-shaped speed curve, N-shaped equilibrium trajectory, and bimodal profile of joint stiffness. These results suggest that minimum energy cost model well expresses the characteristics of hand reaching movements, and our central nervous system would make use of not only a feedback control but also feedforward control.

Motor cost affects the decision of when to shift gaze for guiding movement

Frequent gait modifications are often required to navigate our world. These can involve long or wide steps or changes in direction. People generally prefer to minimize the motor cost (or effort) of a movement, although with changes in gait this is not always possible. The decision of when and where to shift gaze is critical for controlling motor actions, since vision informs the brain about the available choices for movement-in this case, where to step. Here we asked how motor cost influences the allocation of gaze. To address this, we had participants walk and step to the center of sequential targets on the ground. We manipulated the motor cost associated with controlling foot placement by varying the location of one target in the lateral direction on a trial-to-trial basis within environments with different numbers of targets. Costlier steps caused a switch from a gaze strategy of planning future steps to one favoring visual feedback of the current foot placement when participants had to negotiate another target immediately after. Specifically, costlier steps delayed gaze shifts away from the manipulated target. We show that this relates to the cost of moving the leg and redirecting the body's center of mass from target to target. Overall, our results suggest that temporal gaze decisions are affected by motor costs associated with step-to-step demands of the environment. Moreover, they provide insight into what affects the coordination between the eyes and feet for the control of stable and accurate foot placement while walking. NEW & NOTEWORTHY Changes in gait allow us to navigate our world. For instance, one may step long or wide to avoid a spilled drink. The brain can direct gaze to gather relevant information for making these types of motor decisions; however, the factors affecting gaze allocation in natural behaviors are poorly understood. We show how the motor cost associated with a step influences the decision of when to redirect gaze to ensure accurate foot placement while walking.

What makes a reach movement effortful? Physical effort discounting supports common minimization principles in decision making and motor control

When deciding between alternative options, a rational agent chooses on the basis of the desirability of each outcome, including associated costs. As different options typically result in different actions, the effort associated with each action is an essential cost parameter. How do humans discount physical effort when deciding between movements? We used an action-selection task to characterize how subjective effort depends on the parameters of arm transport movements and controlled for potential confounding factors such as delay discounting and performance. First, by repeatedly asking subjects to choose between 2 arm movements of different amplitudes or durations, performed against different levels of force, we identified parameter combinations that subjects experienced as identical in effort (isoeffort curves). Movements with a long duration were judged more effortful than short-duration movements against the same force, while movement amplitudes did not influence effort. Biomechanics of the movements also affected effort, as movements towards the body midline were preferred to movements away from it. Second, by introducing movement repetitions, we further determined that the cost function for choosing between effortful movements had a quadratic relationship with force, while choices were made on the basis of the logarithm of these costs. Our results show that effort-based action selection during reaching cannot easily be explained by metabolic costs. Instead, force-loaded reaches, a widely occurring natural behavior, imposed an effort cost for decision making similar to cost functions in motor control. Our results thereby support the idea that motor control and economic choice are governed by partly overlapping optimization principles.

Economic choice in humans and animals can be understood as a weighing of benefits (e.g., reward) against costs (e.g., effort, delay, risk), leading to a preference for the behavioral option with highest expected utility. The costs of the action associated with a choice can thereby affect its utility: for equivalent benefits, an action that requires less physical effort will be preferred to a more effortful one. Here, we characterized how human subjects assess physical effort when choosing between arm movements. We show that the effort cost of a movement increases with its duration and with the square of the force it is performed against but not with the distance covered. Therefore, the subjective cost that determines decisions does not reflect the objective energetic cost of the actions—i.e., the corresponding metabolic expenditure. Instead, the subjective cost has commonalities with the cost that our central nervous system is believed to minimize for controlling the motor execution of actions. Our findings thus argue in favor of action selection and action control sharing common underlying optimization principles.