The Cost of Bounded Curvature
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.
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- 2.Goaoc, X., Kim, H.-S., Lazard, S.: Bounded-curvature shortest paths through a sequence of points. Technical Report inria-00539957, INRIA (2010), http://hal.inria.fr/inria-00539957/en
- 3.Kim, H.-S., Cheong, O.: The cost of bounded curvature (2011), http://arxiv.org/abs/1106.6214
- 4.Kim, J.-H.: The upper bound of bounded curvature path. Master’s thesis, KAIST (2008)Google Scholar
- 5.LaValle, S.M.: Planning Algorithms. Cambridge University Press (2006)Google Scholar
- 7.Ma, X., Castañón, D.A.: Receding horizon planning for Dubins traveling salesman problems. In: 45th IEEE Conference on Decision and Control, pp. 5453–5458 (December 2006)Google Scholar
- 8.Le Ny, J., Feron, E., Frazzoli, E.: The curvature-constrained traveling salesman problem for high point densities. In: Proceedings of the 46th IEEE Conference on Decision and Control, pp. 5985–5990 (2007)Google Scholar