Abstract
A part feeder is a mechanism that receives a stream of identical parts in arbitrary orientations and outputs them oriented the same way. Various sensorless part feeders have been proposed in the literature. The feeder we consider consists of a sequence of fences that extend partway across a conveyor belt; a polygonal part P carried by the belt is reoriented by each fence it encounters. We present ail O(m + n 2 log3 n)-time algorithm to compute a sequence of fences that uniquely orients P, if one exists, where m is the total number of vertices and n is the number of stable edges of P. As in [3], we reduce the problem to searching for a path in a state graph that has O(n 3) edges. By exploiting various geometric properties of the state graph, we show that it can be represented implicitly and a desired path can be found in O(m + n 2 log3 n) time. Our technique is quite general and is applicable to other part manipulation problems.
Research by P.A. is supported by the NSF under grants CCR-00-86013 EIA-98-70724, EIA-01-31905, ITR-333-1050, and CCR-97-32787, and by a grant from the U.S.-Israel Binational Science Foundation. Research by R.B. was supported by the Dutch Organization for Scientific Research (N.W.O.). Research by A.C. was supported by the NSF under grants ITR-333-1050, CCR-97-32787, DMS-0107621, DMS-9983320, and DMS-0101364. Part of this work was done while R.B. was visiting Department of Computer Science, University of North Carolina, Chapel Hill.
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Agarwal, P.K., Berretty, RP., Collins, A.D. (2004). A Near-Quadratic Algorithm for Fence Design. In: Boissonnat, JD., Burdick, J., Goldberg, K., Hutchinson, S. (eds) Algorithmic Foundations of Robotics V. Springer Tracts in Advanced Robotics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45058-0_21
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DOI: https://doi.org/10.1007/978-3-540-45058-0_21
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