The Cost of Bounded Curvature
Abstract
We study the motionplanning problem for a carlike 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 boundedcurvature 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 boundedcurvature path length and the Euclidean distance of its endpoints. We show that $\dub(d)$ decreases monotonically from $\dub(0) = 7\pi/3$ to $\dub(\ds) = 2\pi$, and is constant for $d \geq \ds$. Here $\ds \approx 1.5874$. We describe pairs of configurations that exhibit the worstcase of $\dub(d)$ for every distance $d$.
 Publication:

arXiv eprints
 Pub Date:
 June 2011
 arXiv:
 arXiv:1106.6214
 Bibcode:
 2011arXiv1106.6214K
 Keywords:

 Computer Science  Computational Geometry