This paper presents the architecture of a highdensity parking solution based on car-like robots specifically designed to move cars. The main difficulty is to park the vehicles close to one another which implies hard constraints on the robot motion and localization. In particular, this paper focuses on navigation in narrow lanes. We propose a Lyapunovbased control strategy that has been derived after expressing the problem in a Configuration Space formulation. The current solution has been implemented and tested on Stanley Robotics' robots and has been running in production for several months. Thanks to the Configuration Space formulation, we are able to guarantee the obstacles' integrity. Moreover, a method for calibrating the GPS orientation with a high-precision is derived from the present control strategy.