Optimal distribution of fingertip force functions in dynamic grasping

The dynamics and forces associated with grasping by robot hands are discussed. Based on features of a grasping state, the geometrical and frictional constraints for a multi-fingered hand are characterized. To optimize the power consumed by the hand, a quality measure is defined by the squared sum of the fingertip force functions during task execution and used in an interior penalty function involving the closed region functional extreme value. A computational algorithm is proposed for determining an optimal distribution of fingertip force functions. The solution is based on a formulation as a nonlinear programming problem subject to the dynamic equations of motion, geometrical constraints, and frictional conditions. The authors give an example of a three-fingered hand grasping a pen and drawing a planar sine curve to demonstrate the approach