| Satellite formation is defined as that some small satellites in the orbit around the earthaccomplish a space task while maintaining the distance and configuration with respect to the centralsatellite. Compared with the traditional large satellite, small satellite formation has the advantages oflow cost, outstanding safety and reliability, high flexibility and the capability of reconstruction andredundancy, which makes it more qualified for space tasks. Therefore, small satellite formation hasbeen employed in more and more applications during last few years. Orbital elements method andCartesian coordinate method are two prevailing methods for the research in relative motions ofsatellites. The former method is mainly utilized in track design and investigation on the influence tothe track caused by perturbation, while the latter one mostly in control law design.HCW equation is the most commonly used equation in Cartesian coordinate method, since it is asecond order differential equation with constant coefficients and of analytical solutions, making thecontrol law design easier. Its prerequisites include small spacing between the master satellite and aslave one, circle reference orbit and neglect of perturbation. In this paper improvements are achievedbased on simplified conditions of the HCW equation. First, the basic methods of satellite formationare introduced. Second, the contribution of linearity to the initialization error of the formation isinvestigated, and long-term drift is calibrated. What’s more, the conclusion that the long-term driftcaused by linearity can be neglected within a short time range is drawn. Third, the optimal controlproblem of the elliptical reference orbit is studied, and comparison between the objective functions ofoptimal control in true-anomaly domain and time domain is performed. The optimal control lawdesign for fuel consumption in time domain is given the priority when analytical solutions are notrequired. Finally, some perturbations are taken into account for the configuration of satellite formationin low earth orbit, including the J2perturbation causing relative perturbation to the configuration, andthe air resistance perturbation which decreases the orbit height of a single satellite but doesn’t lead torelative perturbation to the configuration. The optimal control law for fuel consumption in circle orbitunder perturbations is further designed and implemented by employing thrust-generating equipmentsin two directions, and its effectiveness is validated through numerical simulations. |
