Minimum-Fuel Trajectories and Near-Optimal Explicit Guidance for Pinpoint Landing from Low Lunar Orbit

This research addresses minimum-fuel pinpoint lunar landing at the South Pole, focusing on trajectory design and near-optimal guidance aimed at driving a spacecraft from a circular low lunar orbit (LLO) to an instantaneous hovering state above the lunar surface. Orbit dynamics is propagated in a high-fidelity ephemeris-based framework, which employs spherical coordinates as the state variables and includes several harmonics of the selenopotential, as well as third-body gravitational perturbations due to the Earth and Sun. Minimum-fuel two-impulse descent transfers are identified using Lambert problem solutions as initial guesses, followed by refinement in the high-fidelity model, for a range of initial LLO inclinations. Then, a feedback Lambert-based impulsive guidance algorithm is designed and tested through a Monte Carlo campaign to assess the effectiveness under non-nominal conditions related to injection and actuation errors. Because the last braking maneuver is relatively large, a finite-thrust, locally flat, near-optimal guidance is introduced and applied. Simplified dynamics is assumed for the purpose of defining a minimum-time optimal control problem along the last thrust arc. This admits a closed-form solution, which is iteratively used until the desired instantaneous hovering condition is reached. The numerical results in non-nominal flight conditions testify to the effectiveness of the guidance approach at hand in terms of propellant consumption and precision at landing. © 2025 by the authors.