Optimal control of reaching includes kinematic constraints.

We investigate adaptation under a reaching task with an acceleration-based force field perturbation designed to alter the nominal straight hand trajectory in a potentially benign manner: pushing the hand off course in one direction before subsequently restoring towards the target. In this particular task, an explicit strategy to reduce motor effort requires a distinct deviation from the nominal rectilinear hand trajectory. Rather, our results display a clear directional preference during learning, as subjects adapted perturbed curved trajectories towards their initial baselines. We model this behavior using the framework of stochastic optimal control theory and an objective function that trades off the discordant requirements of 1) target accuracy, 2) motor effort, and 3) kinematic invariance. Our work addresses the underlying objective of a reaching movement, and we suggest that robustness, particularly against internal model uncertainly, is as essential to the reaching task as terminal accuracy and energy efficiency.