Lossless Convex Guidance for Lunar Powered Descent

This paper builds upon a convex programming approach to propellant-optimal planetary landing guidance originally developed for Mars landings and adapts it to lunar soft landings. These novel adaptations include the addition of state and control constraints that were previously not part of the lossless convexification framework: maximum tilt rate, maximum tilt acceleration, maximum thrust ramp rate, and a terminal vertical descent phase. Additionally, we have included an inverse square central gravity model and a minimum altitude constraint in the Moon-centered, Moon-fixed (MCMF) frame. These constraints are convexified and the resulting second-order cone program is solved for an Apollo-like sample case.