The Cost of Bounded Curvature

  • Hyo-Sil Kim
  • Otfried Cheong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7434)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hyo-Sil Kim
    • 1
  • Otfried Cheong
    • 2
  1. 1.Department of Computer Science & EngineeringPOSTECHPohangKorea
  2. 2.Department of Computer ScienceKAISTDaejeonKorea

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