Fuel near-optimal guidance law for the powered descending phase of a lunar module

This article proposes a fuel near-optimal robust guidance law for a lunar module during the powered descending phase in the lunar soft landing mission. At first, a three-dimensional kinetic model is introduced based on the defined target coordinate frame, where a single thruster misalignment and the moon rotation are considered. Next, with a computational method in conjunction with a time transform, a fuel optimal open-loop guidance law is derived for the nominal model without any disturbance. Then, to attenuate disturbances caused by thrust error and external disturbances, an additional robust H∞ feedback controller is designed to track the obtained reference trajectory and meet the constraints of control input, by solving a convex optimization problem with linear matrix inequality conditions. Finally, numerical simulation illustrates the effectiveness of the proposed approach.