When the desired motion of the grasped object is given or planned, the coordination of motion of the manipulator and manipulation with its gripper is needed in order to achieve the desired motion of the object. In this paper, we have defined "graspability", "manipulability", and "virtual gripper". These concepts are necessary to deal with the geometric relation between a dexterous hand and its grasped object in the planning process and designing process. Since the coordination of motion of the manipulator and manipulation of its gripper is needed in order to achieve the desired motion of the grasped object, we have developed an algorithm that generates these coordinated motions: the path of the manipulator and the manipulation path of the object with respect to the coordinate frame of the gripper. This paper describes "graspability", "manipulability", "virtual gripper", an algorithm that generates the coordinated motions, and estimation of a "manipulable region" of a dexterous gripper which is needed in a specific task.
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