This paper presents a novel collision-free trajectory planner for mobile car-like robot navigation in an unknown extra-road environment subject to nonholonomic constraints. The environment is represented by a parking lot with real traffic conditions, this meaning that static and dynamic obstacles are to be taken into consideration. The final goal that must be fulfilled by the system is to find a free parking space for the vehicle and safely make the parking manoeuvre while simultaneously detect and avoid obstacles. The planner relies on the combination of the potential field method, the 3rd degree Bezier curves method and on the newly designed “look ahead trajectory predictions” method. The major advantages of this method are the very short calculation time and a continuous stable behaviour of the trajectory. The results presented demonstrate the capabilities of the proposed method for solving the collision-free path-planning problem.