Complete algorithms for reorienting polyhedral parts using a pivoting gripper

To rapidly feed industrial parts on an assembly line, Carlisle et. al. (1994) proposed a flexible part feeding system that drops parts on a flat conveyor belt, determines the pose of parts with a vision system and manipulates them into a desired pose. A robot arm with 4-DOF is capable of moving parts through 6-DOF when equipped with a passive pivoting axis between the parallel jaws of its gripper. We refer to these actions as pivot grasps. This paper considers the planning problem. Given a polyhedral part shape, coefficient of friction and a pair of stable configurations as input, find pairs of grasp points that will cause the part to pivot from one stable configuration to the other. For some transitions, pivot grasps may not exist. For a part with n faces and m stable configurations, we give an O(m/sup 2/n log n) algorithm to generate the m/spl times/m matrix of pivot grasps. When the part is star shaped, this reduces to O(m/sup 2/n). We also study a generalization that considers "capture regions" around stable configurations. Both algorithms are complete in that they are guaranteed to find pivot grasps when they exist.