Control of the Process of Rapprochement of a Tether System with a Passive Space Object in a Near-Circular Orbit

Abstract: The article deals with the control of the process of rapprochement of a tether system with a passive space object (cargo, space debris, etc.) in an almost circular near-Earth orbit. It is assumed that the active spacecraft, which includes a tether system with a capture device (not deployed), is located in a close (relative to the orbit of the cargo) orbit, which was formed using some known long-range guidance algorithm. It is assumed that the active spacecraft, which includes a tether system with a capture device (not deployed), is located in a close (relative to the orbit of the cargo) orbit, which was formed using some known long-range guidance algorithm. The position of the dummy point is chosen based on the fact that, after the deployment of the tether system, the capture device appears in the vicinity of the cargo immediately or after some small portion of passive movement in orbit. The control of the process of approaching the spacecraft with a fictitious point in the spatial case is constructed using the Bellman dynamic programming principle using a linearized system. Continuous control is used with the help of jet engines with finite thrust. The components of the reactive forces for which the control is being constructed are directed along the transversal and binormal in the orbital coordinate system. It is assumed that the unavoidable guidance errors can be corrected by changing the length of the tether or in some other way. A numerical example of modeling the processes under consideration using nonlinear equations of motion is given illustrating the proposed control scheme.