In this paper, we present the strategy for trajectory planning that was used on-board the vehicle that completed the 103 km of the Bertha-Benz-Memorial-Route fully autonomously. We suggest a local, continuous method that is derived from a variational formulation. The solution trajectory is the constrained extremum of an objective function that is designed to express dynamic feasibility and comfort. Static and dynamic obstacle constraints are incorporated in the form of polygons. The constraints are carefully designed to ensure that the solution converges to a single, global optimum.