In the near future parking assistance systems will perform parking maneuvers without human help. Planning a suitable trajectory online which guides the car collision-free to the required destination into the parking space represents a major task for such systems. At the Chair of Automatic Control of the University Erlangen-Nuremberg a two-step approach based on concepts from robotics was developed, which can be applied to systematically plan collision-free trajectories with suitable properties. The method can be used for all relevant types of parking situations, i.e. the parking space may be positioned parallel, vertical or declined with respect to the driving direction.