Motion planning for a steering-constrained robot through moderate obstacles
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
The complexity of the two dimensional curvature-constrained shortest-path problem
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Approximation Algorithms for Curvature-Constrained Shortest Paths
SIAM Journal on Computing
Curvature-Constrained Shortest Paths in a Convex Polygon
SIAM Journal on Computing
Approximation of Curvature-Constrained Shortest Paths through a Sequence of Points
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Curvature-bounded traversals of narrow corridors
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Planning Algorithms
A Complete Approximation Algorithm for Shortest Bounded-Curvature Paths
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
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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 @s,@s^', let @?(@s,@s^') be the shortest bounded-curvature path from @s to @s^'. For d=0, let @?(d) be the supremum of @?(@s,@s^'), over all pairs (@s,@s^') that are at Euclidean distance d. We study the function dub(d)=@?(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@p/3 to dub(d^@?)=2@p, 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.