The article is devoted to the research, development and implementation of an artificial neural network with reinforcement for controlling a mobile robot with a differential drive to solve the task of following a target. The authors of the study present a detailed description of the architecture of the neural network, its training using a deep deterministic gradient policy algorithm, and integration with the robot control system. A distributed neural network structure was selected for specialized generation of controls, for which the authors chose the angular and linear speed of the robot. A system of rules has been synthesized that takes into account changes in the distance between the robot and the target object and tracking of the heading angle in real time. A mathematical model of a robot with a differential drive is considered, on the basis of which a simulation program is implemented for intermediate training of a neural network, as a result of which the initial weighting coefficients are formed. Using this program, you can get by with less energy and time costs at the initial stage of the study. Experiments to test the effectiveness of the developed neural network were carried out in the Gazebo simulation environment using the ROS2 communication interface. The article describes the process of integrating a neural network with a robot control system in a simulation environment, as well as test results and analysis of the obtained data. The results of experiments are presented for three scenarios in which the initial position of the robot is the same, the remaining parameters are generated according to the rules described by the authors. The effectiveness of using such a solution for trajectory planning has been confirmed. The research contributes to the field of autonomous systems and demonstrates the potential of artificial reinforcement neural networks in robotics.