Variable-Time-Domain Neighboring Optimal Guidance, Part 2: Application to Lunar Descent and Soft Landing

In recent years, several countries have shown an increasing interest toward both manned and automatic lunar missions. The development of a safe and reliable guidance algorithm for lunar landing and soft touchdown represents a very relevant issue for establishing a real connection between the Earth and the Moon surface. This paper applies a new, general-purpose neighboring optimal guidance algorithm, proposed in a companion paper and capable of driving a dynamical system along a specified nominal, optimal path, to lunar descent and soft landing. This new closed-loop guidance, termed variable-time-domain neighboring optimal guidance, avoids the usual numerical difficulties related to the occurrence of singularities for the gain matrices, and is exempt from the main drawbacks of similar algorithms proposed in the past. For lunar descent, the nominal trajectory is represented by the minimum-time path departing from the periselenium of a given elliptic orbit and arriving at the Moon with no residual velocity. Perturbations arising from the imperfect knowledge of the propulsive parameters and from errors in the initial conditions are considered. At specified, equally spaced times the state displacements from the nominal flight conditions are evaluated, and the guidance algorithm yields the necessary control corrections. Extensive robustness and Monte Carlo tests are performed, and definitely prove the effectiveness, robustness, and accuracy of the new guidance scheme at hand, also in comparison with the well-established linear tangent steering law.