Low-Thrust Nonlinear Orbit Control for Very Low Lunar Orbits

In the next decades, both space agencies and private competitors are targeting the lunar environment as a scientific and technological resource for future space missions. In particular, the confirmed existence of water-ice deposits in the vicinity of the poles (predominantly the south pole) makes polar or near-polar low lunar orbits attractive for the purpose of designing space missions that could search for suitable Lunar base sites. However, traveling very-low-altitude orbits is very challenging, as they are strongly perturbed by the Moon's gravity field as well as third- and fourth-body effects due to the Earth and the Sun. Several studies demonstrate that these orbits are expected to impact the lunar surface in a few months. Therefore, the definition and implementation of an effective station-keeping strategy represents a crucial issue in order to extend satellites' lifetime. In this paper, a feedback nonlinear control law is employed in order to perform corrective maneuvers aimed at keeping the state of the satellite within acceptable margins. The satellite is assumed to be equipped with a steerable and throttleable low-thrust propulsion system. The control law is based on the Lyapunov stability theory and does not require any reference path to track, with a considerable decrease in the computational cost. The proposed real-time control law includes control saturation, related to the maximum available thrust magnitude, and is developed employing modified equinoctial elements, in order to avoid singularities and extend its range of application. Finally, the strategy at hand is tested in the presence of all the relevant perturbations (i.e., harmonics of the selenopotential, third- and fourth-body effects) in order to show its effectiveness and efficiency.