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.>

The authors study a certain class of stabilizing laws for a flexible arm either in torsion or in compression. They first choose a discrete-model of this arm, and then the arm is modeled by a classical partial differential equation. A sufficient condition for the stability of both closed-loop systems is given. This sufficient condition requires that the gain of the control law act positively on the eigenfunctions of the autonomous system.>