Geometric Path Planning for Automatic Parallel Parking in Tiny Spots

This paper deals with path planning for car-like vehicle in parallel parking problems. Our path planning method uses simple geometry of the vehicle kinematic model. The presented strategy consists in retrieving the vehicle from the parking spot and reversing the obtained path to park the vehicle. Two methods for parking in tiny spaces, where parking in one trial is not possible, are proposed. In these cases, the number of needed trials to park the vehicle can be calculated from a simple formula or from an iterative algorithm. The proposed planning methods are independent of the initial position and the orientation of the vehicle. Reference trajectories are generated so that the vehicle can park by following them. Simulations are provided for both methods.