Motion Planning for a Convex Polygon in a Polygonal Environment

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Motion Planning for a Convex Polygon in a Polygonal Environment (1997)

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by Pankaj K. Agarwal , Boris Aronov , Micha Sharir

Venue:	Geom
Citations:	17 - 8 self

BibTeX

@ARTICLE{Agarwal97motionplanning,
    author = {Pankaj K. Agarwal and Boris Aronov and Micha Sharir},
    title = {Motion Planning for a Convex Polygon in a Polygonal Environment},
    journal = {Geom},
    year = {1997},
    volume = {22},
    pages = {201--221}
}

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Abstract

We study the motion-planning problem for a convex m-gon P in a planar polygonal environment Q bounded by n edges. We give the first algorithm that constructs the entire free configuration space (the 3-dimensional space of all free placements of P in Q) in time that is near-quadratic in mn, which is nearly optimal in the worst case. The algorithm is also conceptually relatively simple. Previous solutions were incomplete, more expensive, or produced only part of the free configuration space. Combining our solution with parametric searching, we obtain an algorithm that finds the largest placement of P in Q in time that is also near-quadratic in mn. In addition, we describe an algorithm that preprocesses the computed free configuration space so that `reachability' queries can be answered in polylogarithmic time. All three authors have been supported by a grant from the U.S.-Israeli Binational Science Foundation. Pankaj Agarwal has also been supported by a National Science Foundation Gr...

Keyphrases

motion planning polygonal environment convex polygon computed free configuration space u.s. israeli binational science foundation motion-planning problem entire free configuration space previous solution parametric searching free configuration space first algorithm free placement 3-dimensional space planar polygonal environment national science foundation gr polylogarithmic time convex m-gon pankaj agarwal

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