Ensuring autonomous navigation of mobile robots remains an important and relevant challenge in robotics. A variety of approaches have been proposed in the scientific community to address this problem. This paper provides an overview of existing robot navigation methods and focuses on the problem of optimal control of a mobile robot’s movement. It is assumed that during its motion, the robot periodically receives data about its current position in a given coordinate system from an onboard positioning system. However, these data may contain measurement errors – meaning that the actual coordinates are determined with a certain degree of approximation. The paper presents an algorithm for correcting the robot’s trajectory, which ensures reaching the final destination with a specified level of accuracy, even in the presence of measurement inaccuracies. A corresponding theorem is formulated and proven, justifying the correctness and effectiveness of the proposed approach. The foundation of the developed method is based on two well-known theoretical frameworks are the classical theory of optimal control synthesis for second-order systems and the graph-based method for finding the shortest path in a connected graph. Thus, the article offers an efficient solution to the problem of mobile robot navigation under conditions of uncertain localization – a crucial aspect for real-world applications.