Hierarchical and synergistic organization of control variables during the multi-digit grasp of a free and an externally fixed object

Abstract

In the referent control theory, grip force emerges by designating the referent aperture (Ra) as a threshold position inside the object. This study quantified Ra and investigated whether the syn-ergistic control of digit referent coordinate (RC) and apparent stiffness (k) depend on the external mechanical constraints on the hand-held object. Subjects held a motorized handle capable of adjusting the grip width and performed static multi-digit prehension tasks in which the handle was free and externally fixed in different conditions. The RC and k of individual digits were reconstructed from the changes in digit normal forces and the positions as the grip width was modulated. RCs of the thumb and virtual finger were used to calculate the width and midpoint of Ra, and synergy indices quantifying the task-specific covariation in the space of the digit normal forces and {RC, k} variables were computed. We found that the k and width of the Ra were larger when holding a free handle than the fixed handle. The higher stiffness in the free condition could be a strategy to ensure grip stability. The midpoint of Ra was skewed toward the virtual finger, reflecting different magnitudes of k for the two digits. Further, the normal forces and control variables {RC, k} displayed synergistic covariation for stabilization of the total grasping force. Finally, the synergies were weaker when the handle was externally fixed, demonstrating the dependence of synergies on external constraints. These results add to the current literature by demonstrating that grasp control involves modulation of digit apparent stiffness in addition to the referent coordinate and by identifying the synergistic organization of the control variables during static grasp.