Оптимізація перельотів між низькими орбітами з суттєвою різницею довгот висхідних вузлів

Abstract

At present, satellite systems, each comprising hundreds of satellites, are, and are to be, deployed in low orbits. In addition, existing satellite systems are replenished. There has appeared a trend towards the development of modular satellites, which will lead to the development of easy-to-maintain spacecraft consisting of many small structural modules with standardized interface mechanisms. To extend the life of all these systems and reduce their maintenance cost, it is advisable to develop a system for their maintenance. Despite the relatively large number of works on the rendezvous problem, this problem is considered in a somewhat simplified formulation, which is not sufficient for spacecraft servicing in low orbits. As a rule, the consideration is limited to coplanar rendezvous problems in an impulse formulation. In real conditions, rendezvous maneuvers in low orbits are nontrivial. As is known, the orbital parameters of low-orbit spacecraft may differ significantly: the difference in the longitude of ascending nodes (LAN) may reach tens and even hundreds of degrees. Because of this, the energy consumption for an orbital plane change becomes unacceptably high for modern service spacecraft. This energy consumption can be reduced by using the precession of the line of nodes due to the non-centrality of the Earth's gravitational field. A waiting maneuver of a service spacecraft in a well-chosen orbit makes it possible to eliminate the mismatch between the LANs of the service spacecraft’s parking and destination orbits, thus significantly reducing the orbital transfer energy consumption. However, the long wait time of the service spacecraft in its parking orbit significantly increases the total orbital transfer time. The aim of this article is to develop a mathematical model of bicriteria optimization of a transfer of a service spacecraft with a low constant thrust engine between low near-circular orbits with significantly different LANs. This problem is solved by averaging the service spacecraft’s dynamics equations over a fast parameter and using a genetic algorithm of global Pareto optimization. The novelty of the results obtained lies in a formulation of a bicriteria optimization problem and the development of a mathematical model for choosing an optimal service spacecraft parking orbit. The mathematical model developed may be used in planning service spacecraft transfers between low near-circular orbits with significantly different LANs.