Orienting polygonal parts without sensors

In manufacturing it is often necessary to orient parts prior to packing or assembly. We say that a planar part ispolygonal if its convex hull is a polygon. We consider the following problem: given a list ofn vertices describing a polygonal part whose initial orientation is unknown, find the shortest sequence of mechanical gripper actions that is guaranteed to orient the part up to symmetry in its convex hull. We show that such a sequence exists for any polygonal part by giving anO[n2 logn) algorithm for finding the sequence. Since the gripper actions do not require feedback, this result implies that any polygonal part can be orientedwithout sensors.

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