In this paper, we consider the problem of computing a shortest path of bounded curvature amidst obstacles in the plane. More precisely, given prescribed initial and final configurations (i.e. positions and orientations) and a set of obstacles in the plane, we want to compute a shortest $C¨$ path joining those two configurations, avoiding the obstacles, and with the further constraint that, on each $C©$ piece, the radius of curvature is at least 1. In this paper, we consider the case of moderate obstacles (as introduced by Agarwal et al.) and present a polynomial-time exact algorithm to solve this problem.