  The paper addresses the problem of providing suitable reference trajectories
in motion planning problems for autonomous vehicles. Among the various
approaches to compute a reference trajectory, our aim is to find those
trajectories which optimize a given performance criterion, for instance fuel
consumption, comfort, safety, time, and obey constraints, e.g. collision
avoidance, safety regions, control bounds. This task can be approached by
geometric shortest path problems or by optimal control problems, which need to
be solved efficiently. To this end we use direct discretization schemes and
model-predictive control in combination with sensitivity updates to predict
optimal solutions in the presence of perturbations. Applications arising in
autonomous driving are presented. In particular, a distributed control
algorithm for traffic scenarios with several autonomous vehicles that use
car-to-car communication is introduced.
