The Cost of Bounded Curvature

Details The Cost of Bounded Curvature The Cost of Bounded Curvature

2011-06-30

arxiv.org/abs/1106.6214v2

Computer Science

Computational Geometry

Scientific paper

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 $\dub(0) = 7\pi/3$ 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 worst-case of $\dub(d)$ for every distance $d$.

Affiliated with

Also associated with

No associations

Rating

The Cost of Bounded Curvature does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Cost of Bounded Curvature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Cost of Bounded Curvature will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-35141