  Planning trajectories for automated vehicles in urban environments requires
methods with high generality, long planning horizons, and fast update rates.
Using a path-velocity decomposition, we contribute a novel planning framework,
which generates foresighted trajectories and can handle a wide variety of state
and control constraints effectively. In contrast to related work, the proposed
optimal control problems are formulated over space rather than time. This
spatial formulation decouples environmental constraints from the optimization
variables, which allows the application of simple, yet efficient shooting
methods. To this end, we present a tailored solution strategy based on ILQR, in
the Augmented Lagrangian framework, to rapidly minimize the trajectory
objective costs, even under infeasible initial solutions. Evaluations in
simulation and on a full-sized automated vehicle in real-world urban traffic
show the real-time capability and versatility of the proposed approach.
