Abstract
We present an efficient algorithm for planning the motion of a convex polygonal bodyB in two-dimensional space bounded by a collection of polygonal obstacles. Our algorithm extends and combines the techniques of Leven and Sharir and of Sifrony and Sharir used for the case in whichB is a line segment (a “ladder”). It also makes use of the results of Kedem and Sharir on the planning of translational motion ofB amidst polygonal obstacles, and of a recent result of Leven and Sharir on the number of free critical contacts ofB with such polygonal obstacles. The algorithm runs in timeO(knλ 6(kn) logkn), wherek is the number of sides ofB, n is the number of obstacle edges, and λ,(q) is an almost linear function ofq yielding the maximal number of connected portions ofq continuous functions which compose the graph of their lower envelope, where it is assumed that each pair of these functions intersect in at mosts points.
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Work on this paper by the second author has been supported by Office of Naval Research Grant N00014-82-K-0381, National Science Foundation Grant No. NSF-DCR-83-20085, and by grants from the Digital Equipment Corporation, and the IBM Corporation.
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Kedem, K., Sharir, M. An efficient motion-planning algorithm for a convex polygonal object in two-dimensional polygonal space. Discrete Comput Geom 5, 43–75 (1990). https://doi.org/10.1007/BF02187779
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DOI: https://doi.org/10.1007/BF02187779