The cost of bounded curvature

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We study the motion-planning problem for a car-like robot whose turning radius is bounded from below by one and which is allowed to move in the forward direction only (Dubins car). For two robot configurations sigma, sigma', let l (sigma, sigma') be the shortest bounded-curvature path from sigma to sigma'. For d >= 0, let l (d) be the supremum of l(sigma, sigma'), over all pairs (sigma, sigma') that are at Euclidean distance d. We study the function dub(d) = l(d) - d, which expresses the difference between the bounded-curvature path length and the Euclidean distance of its endpoints. We show that dub(d) decreases monotonically from dub(0) = 7 pi/3 to dub(d*) = 2 pi, and is constant for d >= d*. Here d* approximate to 1.5874. We describe pairs of configurations that exhibit the worst-case of dub(d) for every distance d. (C) 2012 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2013-08
Language
English
Article Type
Article
Keywords

CONSTRAINED SHORTEST PATHS; ALGORITHM; POLYGON; CONVEX

Citation

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, v.46, no.6, pp.648 - 672

ISSN
0925-7721
DOI
10.1016/j.comgeo.2012.10.008
URI
http://hdl.handle.net/10203/174094
Appears in Collection
CS-Journal Papers(저널논문)
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