Bayesian geodesic path for human motor control

Despite a near-infinite number of possible movement trajectories, our body movements exhibit certain invariant features across individuals; for example, when grasping a cup, individuals choose an approximately linear path from the hand to the cup. Based on these experimental findings, many researchers have proposed optimization frameworks to determine desired movement trajectories. Successful conventional frameworks include the geodesic path, which considers the geometry of our complicated body dynamics, and stochastic frameworks, which consider movement variability. The former succeed in explaining the kinematics in human reaching movements, and the latter succeed in explaining the variability in those movements. However, the conventional geodesic path framework does not consider variability, and the conventional stochastic frameworks do not consider the geometrical properties of our bodies. Thus, how to reconcile these two successful frameworks remains unclear. Here, I show that the conventional geodesic path can be interpreted as a Bayesian framework in which no uncertainty is considered. Hence, by introducing uncertainty into the framework, I propose a Bayesian geodesic path framework that can simultaneously consider the geometric properties of our bodies and movement variability. I demonstrate that the Bayesian geodesic path generates a mean movement trajectory that corresponds to the conventional geodesic path and a variability of movement trajectory, thus explaining the characteristic variability in human reaching movements.