In the context of this thesis, a special autonomous maneuvering task is realized for a car-like mobile robots, namely the automatic parking. While performing such a task, we expect the vehicle to map its environment, identify an appropriate parking lot, and the performing of the parking maneuver is required as well. I studied the methods recommended by the literature, which provide a solution to design a feasible path geometry without changing the direction during the motion. My task was to implement an algorithm on a mobile robot based on the Lego Mindstorms NXT kit taking into consideration the specificities of the hardware. This algorithm should be able to design the path geometry allowing motion direction changes. The development was carried out using the Matlab-Simulink environment, which allows to upload programs to the NXT controller with the ECRobot toolbox. The first step during my work was to create a position estimator function, using the differential drive vehicle model. Using the data about the motion of the car, and the measurement data of the ultrasonic sensor included in the Lego kit, one can solve the problem of mapping the environment of the robot. If the objects around the mobile robot are represented with a matrix, the parking lot identification can be solved according to that matrix. In case of known geometric parameters of the parking space, the reference paths geometry can be calculated. After that the identification of the whole system is necessary, so that the low-level controllers can be designed to track the reference path. Finally, the designed algorithms were tested during parking maneuvers with and without motion direction switch.