Reachability by paths of bounded curvature in a convex polygon

Heekap Ahn; Otfried Cheong; Jiřǐ Matoušek; Antoine E. Vigneron

doi:10.1016/j.comgeo.2011.07.003

Reachability by paths of bounded curvature in a convex polygon

Heekap Ahn, Otfried Cheong, Jiřǐ Matoušek, Antoine E. Vigneron

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most 1, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P, we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n2) time algorithm to compute this region. We show that a point is reachable only if it can be reached by a path of type CCSCS, where C denotes a unit circle arc and S denotes a line segment. © 2011 Elsevier B.V.

Original language	English (US)
Pages (from-to)	21-32
Number of pages	12
Journal	Computational Geometry
Volume	45
Issue number	1-2
DOIs	https://doi.org/10.1016/j.comgeo.2011.07.003
State	Published - Jan 2012

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Work by Cheong was supported by Mid-career Researcher Program through NRF grant funded by the MEST (No. R01-2008-000-11607-0). Work by Ahn was supported by the National IT Industry Promotion Agency (NIPA) under the program of Software Engineering Technologies Development.

ASJC Scopus subject areas

Control and Optimization
Computational Theory and Mathematics
Computational Mathematics
Geometry and Topology
Computer Science Applications

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10.1016/j.comgeo.2011.07.003

Cite this

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title = "Reachability by paths of bounded curvature in a convex polygon",

abstract = "Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most 1, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P, we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n2) time algorithm to compute this region. We show that a point is reachable only if it can be reached by a path of type CCSCS, where C denotes a unit circle arc and S denotes a line segment. {\textcopyright} 2011 Elsevier B.V.",

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AU - Matoušek, Jiřǐ

AU - Vigneron, Antoine E.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: Work by Cheong was supported by Mid-career Researcher Program through NRF grant funded by the MEST (No. R01-2008-000-11607-0). Work by Ahn was supported by the National IT Industry Promotion Agency (NIPA) under the program of Software Engineering Technologies Development.

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AB - Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most 1, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P, we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n2) time algorithm to compute this region. We show that a point is reachable only if it can be reached by a path of type CCSCS, where C denotes a unit circle arc and S denotes a line segment. © 2011 Elsevier B.V.

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Reachability by paths of bounded curvature in a convex polygon

Abstract

Bibliographical note

ASJC Scopus subject areas

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