Abstract
In the problem ofparts feeding we are given a class of feasible operations for reorienting a part, and we are asked to find a fixed sequence of these operations which is guaranteed to bring the part into a known goal orientation from any possible initial orientation. Goldberg addressed this problem in [2], and showed that, for planar polygonal parts, there is always a sequence of simple operations which can be performed by a simple parallel-jaw gripper, which is guaranteed to orient the part (up to symmetry) without the use of any sensor information; he also conjectured thatO(n) steps are sufficient.
In this paper we prove Goldberg's conjecture by explicitly constructing plans of at most2n − 1 steps for orienting polygonal parts in this model. We also give a lower bound on the number of steps required for such plans to show that this upper bound is tight.
Finally, we extend these results to the problem ofdistinguishing among a finite set of parts using minimal sensing. Specifically, we assume that we are given a set
of known polygonal parts, and a parallel-jaw gripper able to sense the distance between its jaws upon closure. We construct a simple oblivious plan of linear complexity which, when presented with a polygonal part
, determines the index of this part.
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Communicated by C. H. Papadimitriou.
This research was supported in part by the NSF under Grant CCR-9207422, and by a Zumberge Fellowship. A preliminary version of this paper appeared in theProceedings of the Fourth Canadian Conference on Computational Geometry [1].
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Chen, YB., Ierardi, D.J. The complexity of oblivious plans for orienting and distinguishing polygonal parts. Algorithmica 14, 367–397 (1995). https://doi.org/10.1007/BF01192046
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DOI: https://doi.org/10.1007/BF01192046