In many fields of knowledge there are tasks, which require filming of the behavior of a dynamic object with the use of high-speed cameras. Usually, the existing industrial systems do not combine a large work area and a high speed of filming of the equipment's field of view. In this regard, the quality parameters of the resulting footage, such as motion blur, illuminance, depth of field, angular resolution, suffer on complex trajectories. The goal of our work was to design a new robotic system structure, based on a study of the classical approaches of the automated high-speed flight follower systems. An original structure with two mirrors, leveling several disadvantages of the known structures, was proposed. The paper describes the mathematical dependencies of the size parameters, inverse kinematics and an algorithm for minimizing the velocity of the elements of the system. It also offers a method for estimation of the parameters of the work area. A robotic system based on the proposed optical layout will allow filming objects moving not only along the linear, but also more complex trajectories, in a wide range of speeds, combining the advantages of both the optical system with a moving camera and the panning mirror systems. The proposed optical layout allows us to reduce the angular velocities of the primary mirror during tracking, and it can be used not only for filming, but also for projecting images on dynamic objects.