Lunar descent and landing via two-phase explicit guidance and pulse-modulated reduced-attitude control

Abstract

This work considers the three-dimensional descent path of a space vehicle, from periselenium of its operational orbit to the lunar surface. The trajectory is split in two arcs: (1) descent path, up to an altitude of 50 m, and (2) terminal approach and soft touchdown. For phase 1, a new, three-dimensional locally-flat near-optimal guidance is introduced that is based on the local projection of the position and velocity variables. A minimum-time problem is defined using the locally flat coordinates of position and velocity. This leads to identifying closed-form functions of time for the two thrust angles, which identify the commanded thrust direction. During terminal approach (phase 2), correct vertical alignment, modest velocity, and negligible angular rate at touchdown are pursued. With this intent, a predictive bang-off-bang guidance algorithm is proposed that is capable of guaranteeing the desired final conditions. In both phases, the attitude control system has the objective of aligning the actual thrust direction with the commanded one, provided by the guidance algorithm. The resulting reduced-attitude control problem is addressed through the use of a new quaternion-based nonlinear control algorithm, which is proven to enjoy asymptotic stability properties. The attitude actuation system is composed of 12 monopropellant thrusters, ignited using pulse width modulation. Monte Carlo simulations are run, assuming significant displacements from the nominal initial conditions and including several harmonics of the selenopotential. The numerical results unequivocally prove that the guidance and control architecture proposed in this study is effective to achieve lunar descent and safe touchdown in nonnominal flight conditions.