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- W4302436285 abstract "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 $ell(sigma, sigma')$ be the shortest bounded-curvature path from $sigma$ to $sigma'$. For $d geq 0$, let $ell(d)$ be the supremum of $ell(sigma, sigma')$, over all pairs $(sigma, sigma')$ that are at Euclidean distance $d$. We study the function $dub(d) = ell(d) - d$, 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 $dub(0) = 7pi/3$ to $dub(ds) = 2pi$, and is constant for $d geq ds$. Here $ds approx 1.5874$. We describe pairs of configurations that exhibit the worst-case of $dub(d)$ for every distance $d$." @default.
- W4302436285 created "2022-10-06" @default.
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- W4302436285 date "2011-06-30" @default.
- W4302436285 modified "2023-09-26" @default.
- W4302436285 title "The Cost of Bounded Curvature" @default.
- W4302436285 doi "https://doi.org/10.48550/arxiv.1106.6214" @default.
- W4302436285 hasPublicationYear "2011" @default.
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