Continuous-Thrust Station-Keeping of Cis-Lunar Orbits Using Optimal Sliding Mode Control with Practical Constraints

The cis-lunar space has been more and more attractive for human beings, and different kinds of missions have been proposed. For cis-lunar missions with long durations, the stationing-keeping is a pivotal problem. In this paper, the station-keeping problem with continuous thrust for different cis-lunar orbits, including distant retrograde orbits (DROs), near rectilinear halo orbits (NRHOs), and halo orbits, are investigated in the ephemeris model. The optimal sliding mode control (OSMC) based on the linear quadrant regulator (LQR) control is designed for the station-keeping problem. Simulations only considering the initial insertion error are conducted first to show performances of the OSMC controller, and the Jupiter gravity and solar radiation pressure (SRP) are then included as unknown perturbations to test the controller's robustness. Then, with considerations of more practical constraints caused by the navigation and propulsion systems, Monte-Carlo simulations are carried out to provide more realistic results, and station-keeping performances are compared and analyzed for different nominal orbits. The results can provide useful references for the selection of station-keeping strategy in future long-term lunar missions.