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Complete Algorithms for
Feeding Polyhedral Parts using Pivot Grasps

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Anil Rao, David Kriegman, Ken Goldberg

IEEE Transactions on Robotics and Automation, To appear April, 1996

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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 ``capture region'' 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.