Complete Algorithms for Reorienting Polyhedral Parts using a Pivotting Gripper

@inproceedings { 248,
title = {Complete Algorithms for Reorienting Polyhedral Parts using a Pivotting Gripper},
booktitle = {IEEE Conference on Robotics and Automation},
year = {1995},
pages = {2242 - 2248},
abstract = {To rapidly feed industrial parts on an assembly line, Carlisle {\em et.~al.\ } 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~\cite{pivotI93}. 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 table as a {\em pivot grasp}. We show that under idealized conditions, a robot arm with 4 degrees of freedom (DoF) can move (feed) parts arbitrarily in 6 DoF using 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 a part with $n$ faces and $m$ stable configurations, we give an $O(m^2 n\log n)$ algorithm to generate the $m \times m$ 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 pivots to a configuration within a {\textquoteleft}{\textquoteleft}capture region{\textquoteright}{\textquoteright} around the stable configuration; when the part is released, it will tumble to the desired configuration. Both algorithms are complete in that they are guaranteed to find pivot grasps when they exist.},
author = {Anil Rao and David Kriegman and Ken Goldberg}
}