Iteration procedure of choosing a low-thrust rendezvous transfer control program in problems of space debris disposal in the geostationary orbit

The problem of controlling rendezvous between a “debris collector” spacecraft and fragments of space debris in the geostationary orbit is studied. Relative motion in the orbital cylindrical coordinate system is considered. A linearized model of motion is used; relative motion is divided into periodic and secular components on the basis of the model. Motion control is carried out by thrust acceleration reversal. The problem of control is divided into two parts. The first iteration implies analytical determination of a control program using a linearized motion model. The program is based on the control of secular components of relative motion. The second iteration consists in refining the control program obtained earlier using the original math model and the analytical solution obtained in the first iteration. Numerical simulation of motion is carried out. We established that it is rational to start the rendezvous transfer at the moment when the “debris collector” spacecraft is positioned below and to the right or above and to the left relative to the space debris fragment.