4 research outputs found
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 ,
let be the shortest bounded-curvature path from
to . For , let be the supremum of
, over all pairs that are at
Euclidean distance . 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
An algorithm for computing a convex and simple path of bounded curvature in a simple polygon
Article dans revue scientifique avec comité de lecture.International audienceIn this paper, we study the collision-free path planning problem for a point robot, whose path is of {\em bounded curvature} (i.e., constrained to have curvature at most 1), moving in the plane inside an -sided simple polygon . Given two points and inside and two directions of travel, one at and one at , the problem is to compute a convex and simple path of bounded curvature inside from to consisting of straight-line segments and circular arcs such that (i) the radius of each circular arc is at least 1, (ii) each segment on the path is the tangent between the two consecutive circular arcs on the path, (iii) the given initial direction at is tangent to the path at and (iv) the given final direction at is tangent to the path at . We propose an time algorithm for this problem. Using the notion of complete visibility, is pruned to another polygon such that any convex and simple path from to inside also remains inside . Then our algorithm constructs the locus of center of a circle of unit radius translating along the boundary of and using this locus, the algorithm constructs a convex and simple path of bounded curvature. Our algorithm is based on the relationship between the Euclidean shortest path, link paths and paths of bounded curvature, and uses several properties derived here on convex and simple paths of bounded curvature. We also show that the path computed by our algorithm can be transformed in time to a {\it minimal} convex and simple path of bounded curvature. Using this transformation and two necessary conditions proposed here for the shortest convex and simple path of bounded curvature, a {\it minimal} bounded curvature path is located in time whose length, except in special situations involving arcs of length greater than , is at most twice the length of a shortest convex and simple path of bounded curvature