Shortest paths of bounded curvature in the plane

Abstract

Given two oriented points in the plane, the authors determine and compute the shortest paths of bounded curvature joining them. This problem has been solved by L.E. Dubins (1957) in the no-cusp case, and by J.A. Reeds and L.A. Shepp (1990) with cusps. A solution based on the minimum principle of Pontryagin is proposed. The approach simplifies the proofs and makes clear the global or local nature of the results. The no-cusp case and the more difficult case with cusps are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>