Relaxed-Constraint Pinpoint Lunar Landing Using Geometric Mechanics and Model Predictive Control

This paper addresses the pinpoint landing of a spacecraft on the moon during the touchdown phase via geometric mechanics and nonlinear model predictive control (NMPC). The six-degree-of-freedom continuous dynamics of the rigid spacecraft are formulated on the special Euclidean group SE(3) and then discretized using a Lie group variation integrator arising from discrete geometric mechanics. The state and control constraints are handled by a novel relaxation mechanism by introducing relaxation factors, and then a landing guidance and control algorithm is developed by combining NMPC on manifolds. Relaxed constraints are convex and contain the target landing site as an interior point, which significantly improves the practicality and performance of the developed landing algorithm. Numerical simulations demonstrate the effectiveness of the proposed method for autonomous precision lunar landing with multiple constraints.