COMPLETE ALGORITHMS FOR FEEDING POLYHEDRAL PARTS USING PIVOT GRASPS

To rapidly feed industrial parts on an assembly line, Carlisle et al, proposed a flexible part feeding system that drops parts on a flat con veyor belt, determines position and orientation of each part with a vi sion system, and then moves them into a desired orientation [1], When a part is grasped with two hard finger contacts and lifted, it pivots under gravity into a stable configuration, We refer to the sequence of picking up the part, allowing it to pivot, and replacing it on the ta ble as a pivot grasp, We show that under idealized conditions, a robot arm with four degrees of freedom (DOF) can move (feed) parts arbitrar ily in 6 DOF using pivot grasps. This paper considers the following pl anning problem: Given a polyhedral part shape, coefficient of friction , and a pair of stable configurations as input, find pairs of grasp po ints that will cause the part to pivot from one stable configuration t o the other, For a part with n faces and m stable configurations, we g ive an O(m(2)n log n) algorithm to generate the m x m matrix of pivot grasps, When the part is star-shaped, this reduces to O(m(2)n), Since pivot grasps may not exist for some transitions, multiple steps may be needed, Alternatively, we consider the set of grasps where the part p ivots to a configuration within a ''capture region'' around the stable configuration; when the part is released, it will tumble to the desir ed configuration, Both algorithms are complete in that they are guaran teed to find pivot grasps when they exist.