Complete algorithms for feeding polyhedral parts using pivot grasps

To rapidly feed industrial parts on an assembly line, Carlisle et. al. [7] proposed a flexible part feeding system that drops parts on a flat conveyor belt, determines position and orientation of each part with a vision system, and then moves them into a desired orientation. A robot arm with 4 degrees of freedom (DoF) is capable of moving parts through 6 DoF when equipped with a passive pivoting axis between the parallel jaws of its gripper. The idea is to grasp a part with 2 hard finger contacts such that it pivots, under gravity, into a desired orientation when lifted and replaced on the table. 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 faces and stable configurations, we give an algorithm to generate the matrix of pivot grasps. When the part is star shaped, this reduces to . 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.