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This paper describes the development of an efficient automated parking support system for passenger cars. By using recent advances in the Artificial Neural Network technology and a classical combination of linear feedback and feedforward control, we propose a novel design of the parking motion controller. The paper presents the results of the controller design and analysis, including parking problem analysis, feedback controller stability analysis, formulation and optimal solution of the parking trajectory planning problem, and design of a novel parking motion planning architecture based on a Radial Basis Function network. Three general cases of backward parking considered in this work are emulated using the proposed controller. The emulation results reveal high efficiency of the presented approach and demonstrate that the proposed system can be implemented on a typical passenger car.