Neighboring optimal guidance for soft lunar landing

This paper presents a general-purpose neighboring optimal guidance algorithm that is capable of driving a space vehicle along a specified nominal, optimal path. This goal is achieved by minimizing the second differential of the objec-tive function along the perturbed trajectory. This minimization principle leads to deriving all the corrective maneuvers, in the context of a closed-loop guidance scheme. Original analytical developments, based on optimal control theory, constitute the theoretical foundation for two relevant features: (i) a new, effi-cient law for the real-time update of the time of flight (the so called time-to-go), and (ii) a new formulation of the sweep method. Some challenging but never-theless promising projects have the purpose of building a stable lunar base for future interplanetary missions. For soft lunar landing, the nominal trajectory is represented by the minimum-time path departing from the periselenium of a given elliptic orbit and arriving at the Moon surface. Perturbations arising from the imperfect knowledge of the propulsive parameters and from errors in the ini-tial conditions are considered. Extensive Monte Carlo tests are performed and definitely prove the effectiveness, robustness, and accuracy of the neighboring optimal guidance, also in comparison with the well-established linear tangent steering law.