The unified lateral control algorithm for automatic valet parking for various types of vehicles is presented and its feasibility is shown experimentally via field tests for the given parking scenario. First, a trajectory generation algorithm for forward driving and backward multi-step parking maneuvers is developed. Then, with consideration of different types of vehicles and operating conditions, a kinematic vehicle model is used and validated using field test data. Using the nonlinear vehicle model, the lateral controller is designed based on dynamic surface control. Finally the proposed lateral control law is validated via hardware-in-the-loop simulations for different types of vehicles and experimentally using a test vehicle through field tests.