A Fast Procedure for Optimizing Dynamic Force Distribution in Multifingered Grasping

This correspondence deals with the dynamic force distribution (DFD) problem, i.e., computing the contact forces to equilibrate a dynamic external wrench on the grasped object. The sum of the normal force components is minimized for enhancing safety and saving energy. By this optimality criterion, the DFD problem can be transformed into a linear programming (LP) problem. Its objective function is the inner product of the dynamic external wrench and a vector, and the constraints on the vector, given by a set of linear inequalities, define a polytope. The solution to the LP problem can always be attained at the vertex of the polytope called the solution vertex. We notice that the polytope is determined by the grasp configuration. Along with the direction change of the dynamic external wrench, only the solution vertex moves to an adjacent vertex sequentially, whereas the polytope with all its vertices remains unchanged. Therefore, the polytope and the adjacencies of each vertex can be computed in the offline phase. Then, in the online phase, simply search the adjacencies of the old solution vertex for the new one. Without lost of optimality, such a DFD algorithm runs a thousandfold faster than solving the LP problem by the simplex method in real time