Implicit learning of object geometry by reducing contact forces and   increasing smoothness
  Moving our hands smoothly is essential to execute ordinary tasks, such as carrying a glass of water without spilling. Past studies have revealed a natural tendency to generate smooth trajectories when moving the hand from one point to another in free space. Here we provide a new perspective on movement smoothness by showing that smoothness is also enforced when the hand maintains contact with a curved surface. Maximally smooth motions over curved surfaces occur along geodesic lines that depend on fundamental features of the surface, such as its radius and center of curvature. Subjects were requested to execute movements of the hand while in contact with a virtual sphere that they could not see. We found that with practice, subjects tended to move their hand along smooth trajectories, near geodesic pathways joining start to end positions, to reduce contact forces with constrained boundary, variance of contact force, tangential velocity profile error and sum of square jerk along the time span of movement. Furthermore, after practicing movements in a region of the sphere, subjects executed near-geodesic movements, less contact forces, less contact force variance, less tangential velocity profile error and less sum of square jerk in a different region. These findings suggest that the execution of smooth movements while the hand is in contact with a surface is a means for extracting information about the surface's geometrical features. 
Daohang Sha, James L. Patton, Ferdinando A. Mussa-Ivaldi
cs.SY math.OC