Optimization of grasping by using a required external force set

In this paper, we consider an optimization of grasping by using a required external force set. Using the set, we cannot only deal with whatever a desired grasp is, such as force closure or equilibrium grasp, but also evaluate the magnitudes of the resistible external forces and moments. Then, we define an optimization problem from the viewpoint of decreasing the magnitudes of the contact forces required to resist the required external force, and show that we can solve the problem by using a branch-and-bound method. Lastly we present some numerical simulations to show the validity of our approach.