Abstract: To meet the on-orbit autonomous and robust operation requirements for satellite strictly-regressive orbit initialization, a low-thrust autonomous guidance and control method is adopted. This method aims to achieve fuel-optimal, large-scale autonomous trajectory capture with high precision under given mission time and tube constraints. Using non-singular relative orbital elements as state variables, an optimized dynamics model for the strictly-regressive orbit is established by mapping the relationship between tube deviations and relative orbital elements. The state transition matrix incorporates various perturbation effects, including atmospheric drag and third-body gravitational perturbations from the Sun and Moon. By expressing the geometric tube constraints in the form of second-order cones, a convex optimization framework is constructed, enabling real-time on-orbit optimization with stable convergence. The thrust commands from the convex optimization are regularized to generate thrust sequences that conform to the practical on-off characteristics of thrusters. Through a receding horizon architecture embedded with model predictive control, the closed-loop control is transformed into a sequential iterative convex optimization problem, ensuring high precision in spatial trajectory capture.

Key words: strictly-regressive orbit, trajectory capture, convex optimization, thrust regularization, model predictive control, orbital transfer