The Planar Motion with Bounded Derivative of the Curvature and Its Suboptimal Paths
Vladimir Petrov Kostov, Elena V. Degtiariova-Kostova, 06 - Valbonne (France). Unite de Recherche de Sophia-Antipolis Institut National de Recherche en Informatique et en Automatique (INRIA) · 1994
. We describe the construction of suboptimal trajectories of the problem of a planar motion with bounded derivative of the curvature and we prove their suboptimality. `Suboptimal' means longer than the optimal by no more than a constant depending only on the bound B for the curvature's derivative. The initial and final coordinates, curvatures and tangent angles are given. The tangent angle and the curvature of the path are assumed to be continuous. The bound B and the distance d between the initial and final points satisfy an inequality of the kind d AE 1= p B. 1. Introduction We consider the problem of finding the shortest path connecting two given points of the Euclidian plane which has given initial and final tangent angles and initial and final curvatures, whose tangent angle and curvature vary continuously, the speed of changing the curvature being bounded by some constant B. We consider paths which contain no cusps. The problem has a real background --- this is the problem to...