Optimization of grasping an object by using required acceleration and equilibrium-force sets

In this paper, we search optimal grasp points and configurations of fingers for not only resisting an external force applied to a grasped object but also generating a desirable acceleration of the object. Based on the concept of required external force set, we define required acceleration and equilibrium-force sets. By using the sets, we formulate an optimization problem from the viewpoint of decreasing the magnitudes of the joint torques required to generate the required acceleration and equilibrium-force. We also show that we can solve the problem by using a branch-and-bound method. The validity of our approach is shown by numerical examples.