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 σ, σ′, let ℓ(σ, σ′) be the length of a shortest bounded-curvature path from σ to σ′ without obstacles. For d ≥ 0, let ℓ(d) be the supremum of ℓ(σ, σ′), over all pairs (σ, σ′) 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) = 7π/3 to dub(d ∗ ) = 2π, and is constant for d ≥ d ∗ . Here d ∗ ≈ 1.5874. We describe pairs of configurations that exhibit the worst-case of dub(d) for every distance d.
This research is supported in part by Mid-career Researcher Program through NRF grant (No. R01-2008-000-11607-0) funded by the MEST and in part by SRC-GAIA through NRF grant (No. 2011-0030044) funded by the Government of Korea.
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References
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Kim, HS., Cheong, O. (2012). The Cost of Bounded Curvature. In: Gudmundsson, J., Mestre, J., Viglas, T. (eds) Computing and Combinatorics. COCOON 2012. Lecture Notes in Computer Science, vol 7434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32241-9_22
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DOI: https://doi.org/10.1007/978-3-642-32241-9_22
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