Nonlinear Orbit Acquisition and Maintenance of a Lunar Navigation Constellation Using Low-Thrust Propulsion

In this research, a feedback nonlinear control law was designed and tested to perform acquisition and station-keeping maneuvers for a lunar navigation constellation. Each satellite flies an Elliptical Lunar Frozen Orbit (ELFO) and is equipped with a steerable and throttleable low-thrust propulsion system. Lyapunov stability theory was employed to design a real-time feedback control law, capable of tracking all orbital elements (including the true anomaly), expressed in terms of modified equinoctial elements (MEEs). Unlike previous research, control synthesis was developed in the complete nonlinear dynamical model, and allows for driving the spacecraft toward a time-varying desired state, which includes correct phasing. Orbit propagation was performed in a high-fidelity framework, which incorporated several relevant harmonics of the selenopotential, as well as third-body effects due to the gravitational pull of the Earth and Sun. The control strategy at hand was successfully tested through two Monte Carlo campaigns in the presence of nonnominal flight conditions related to estimation errors of orbit perturbations, accompanied by the temporary unavailability and misalignment of the propulsive thrust.