Grasping Optimization Using a Required External Force Set

In this paper, we investigate optimal grasp points on an arbitrary-shaped grasped object using a required external force set. The required external force set is given based on a task, and consists of the external forces and moments, which must be balanced by virtue of contact forces applied by a robotic hand. When the origin is in the interior of the set, a force-closure grasp is required. When the dimension of the set is one, an equilibrium grasp is required. Therefore, we can investigate whatever the desired grasp is, such as when the desired grasp is a force closure and equilibrium grasps. Also, we only have to consider the forces contained in a given required external force set, not the whole set of possible resulting forces. Furthermore, we can avoid the frame-invariant problem (the criterion value changes with the change of the task (object) coordinate frame). We consider an optimization problem from the viewpoint of decreasing the magnitudes of the contact forces needed to balance any external force and moment contained in a given required external force set. In order to solve the problem, we present an algorithm based on a branch-and-bound method. We also present some numerical examples to show the validity of our approach. Note to Practitioners-This paper is concerned with grasping an object by a robotic hand. This article address how to grasp the object, namely, how to position every finger on the object. Recently, robots are desired to be used in housekeeping and in caring for elderly people. For this purpose, robot (multifingered) hands are equipped with the robots as general-purpose end effectors. The robot hands are required to automatically move to accomplish such tasks. In this case, the most fundamental issue for robot hands is to grasp the object. At home, there are many various-shaped objects. Consider the case where the robot (hand) is commanded to perform a certain task, such as putting the object into a box. In this case, the robot (hand) must grasp such an object (of any arbitrary shape) with appropriate grasp positions for completing the task. Therefore, the appropriate grasp positions must be calculated automatically. This article addresses a method to solve this problem. But to complete the grasping task, the following problems remain: calculation and control of the appropriate grasping forces