A parking system includes a plurality of trays having a parking platform for supporting a vehicle and legs for keeping the parking platform in an elevated position on a supporting surface of the parking facility. The parking system also has at least one automated guided vehicle for moving the tray with the vehicle thereon between an access location and a specified parking location. The automated guided vehicle has a frame and drive devices mounted on the frame. Each drive device has a turntable rotatable about a vertical axis and two independently driven wheels mounted on the turntable. The automated guided vehicle can fit beneath the parking platform of the tray and can lift the tray for moving the tray and the vehicle between the access location and the specified parking location.
