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. 

Lossless Convex Guidance for Lunar Powered Descent

With regards to a typical lunar soft landing guidance formulation, it is required to reach the desired position with terminal velocity and orientation constraints. For the terminal phase of lunar powered descent, an existing proportional navigation law developed for missile guidance is modified. Presently in the algorithm, at the beginning of each guidance cycle, a normal acceleration perpendicular to the instantaneous missile-target line-of-sight is computed. The design augmentation proposed in this paper for lunar landing, introduces a polynomial acceleration term along the line-of-sight direction in addition to the existing normal acceleration which would then ensure terminal velocity requirements. It also has the capability to meet zero line-of-sight angles at the end of trajectory maneuver. Simulation results indicate that the developed methodology can be successfully utilized in lunar landing scenarios, especially in the terminal phases where the Lander orientation has to be vertical at the end.

M P Rijesh

Papers

Terminal State Constrained Proportional Navigation Law for Lunar Soft Landing Mission