Stabilization of kinematic variables in the control of bimanual pointing movements

Human voluntary movements face a problem of kinematic redundancy. We study a planar bimanual task, when one hand moves a target and the other hand moves a pointer that must reach the target. We hypothesized that the stabilized task variable was the vectorial difference of the pointer tip and the target. The 6D state space was defined by “joint configuration vectors” whose elements were intersegmental joint angles. The subjects repeated the movements 15 times, and the movements were recorded by a movement analysis system. Then, the subjects practised the movements (300 trials). After practice 15 trials were recorded again. We computed the variance of the joint configurations before and after practice. Six joint rotations affected the 2D task variable. The uncontrolled manifold (UCM) corresponding to this variable is 4D, while the subspace of the state space that is orthogonal (ORT) to the UCM is 2D. The variance within the UCM was larger than in the ORT conforming to the UCM hypothesis. After practice the joint variance decreased and the drop in the component of variance that did not affect the task variable was larger than the drop of the other component. Thus, practice lead to more stable time courses of the task variable and of the corresponding joint configuration