A GEOMETRIC APPROACH TO SHORTEST BOUNDED CURVATURE PATHS

Consider two elements in the tangent bundle of the Euclidean plane (x;X); (y;Y ) 2 TR 2 . In this work we address the problem of charac- terizing the paths of bounded curvature and minimal length starting at x, nishing at y and having tangents at these points X and Y respectively. This problem was rst investigated in the late 50's by Lester Dubins. In this note we present a constructive proof of Dubins' result giving special emphasis on the geometric nature of this problem.