Length minimising bounded curvature paths in homotopy classes

摘要

Choose two points in the tangent bundle of the Euclidean plane (x, X), (y, Y) is an element of TR2. In this work we characterise the immersed length minimising paths with a prescribed bound on the curvature starting at x, tangent to X; finishing at y, tangent to Y, in each connected component of the space of paths with a prescribed bound on the curvature from (x, X) to (y, Y). (C) 2015 Elsevier B.V. All rights reserved.