In the era of rapid technological invitation, artificial intelligence techniques have become a driving force in the evolution of various fields, and the robotics domain is no exception. One of the areas where AI has proven to be especially influential is in robotics vision, where machine learning algorithms, particularly artificial neural networks, are revolutionizing how robots perceive and interact with their environment. Therefore, in this paper, we examine the use of artificial neural networks in the context of mobile robot visual servoing. Differential drive mobile robot RAICO equipped with a fish-eye lens camera is utilized. The fish-eye lenses have a significant advantage regarding their wide-angle field of view; however, they also introduce significant optical distortions that can affect the accuracy of the robot's perception and, therefore, 3D pose estimation, which is paramount for visual servoing. Position-based visual servoing based on the ArUco marker is employed within the 3-step switching mobile robot controller. Given the pose estimation errors inherited by distortions in the fish-eye lens, the accuracy of pose estimation is enhanced by utilizing neural networks. The experimental results show a high level of final pose accuracy achieved by RAICO with the proposed control algorithm.