The use of near-Earth space is currently complicated by the presence of space debris objects in Earth's orbit, which include spent stages of launch vehicles, inoperative spacecraft, and other large and small objects associated with human activity in space. One of the elements of solving the problem of space debris is the docking and capture of an uncontrolled non-cooperative space object or spacecraft by a so-called on-orbit servicing spacecraft to carry out further actions to repair it, refuel or change its orbit. The situation is complicated by the fact that, under the influence of various factors, uncontrolled space objects are in a state of rotation. The parameters of the orbital motion of such objects are known quite accurately from measurements from the Earth. To carry out safe approach and docking, knowledge of the parameters of rotational motion, as well as the parameters of relative motion, is also required. The most general case of motion of a non-cooperative tumbling spacecraft located in an elliptical orbit is considered. It is assumed that the three-dimensional graphic model of such spacecraft is known. The servicing spacecraft (SSC) is equipped with a mono camera that takes pictures of the non-cooperative spacecraft (NSC). Based on a comparison of the characteristic features of photographs and images obtained using the graphical model, the computer vision system (CVS) determines the distance vector to the so-called graphical coordinate system, rigidly fixed on the NSC and the quaternion of its relative attitude. The specific type of CVS is not considered. It is assumed that the SSC carries out some maneuvers near the satellite. All parameters of the SSC angular motion are assumed to be known. This work considers the most general case of the relative motion of SSC and NSC. Using quaternion calculus, all basic kinematic and dynamic equations are obtained. The measured parameters are not enough to ensure safe rendezvous and docking with the NSC. The stochastic characteristics of errors of the CVS measurement are not assumed to be known and, accordingly, are not used. Only their maximum values are specified for them. We consider the use of new dynamic set-membership filter using ellipsoids to solve the problem of determining the parameters of the relative motion of the NSC which is in free uncontrolled motion. The filter can be implemented under conditions of the limited computational capability available on onboard processors. The relative motion parameters include the distance vector between the centers of mass (c.m.) of the NSC and the SSC, the relative velocity vector, the quaternion of the orientation of the main axes of inertia of the satellite relative to the inertial coordinate system, the ratio of the moments of inertia of the satellite, the vector of the position of the NSC c.m. in the graphical coordinate system. The properties of the proposed algorithm are demonstrated using numerical simulation. The results obtained are expected to be used in the development, creation and testing of a navigation system for the rendezvous and docking of the SSC, developed by a group of Ukrainian space industry enterprises under the leadership of the LLC "Kurs-orbital" (https://kursorbital.com/).

• Мельничук Сергій Дмитрович (1970–) (біологічні науки)
• Мельничук Сергій Вікторович (фізико-математичні науки)
• Губарев Вячеслав Федорович (1939–) (фізико-математичні науки)

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