Minimum fuel guidance law for the powered descending phase of a lunar module

This paper deals with the fuel optimal control for the powered descending phase of a lunar module. Firstly, in the target coordinate frame, a 3-dimensional precise kinetic model is formulated. Secondly, the fuel optimal control problem for the powered descending phase is transformed into a standard constrained optimal control problem. By using a computational method and a time scaling transform technique, an open-loop parametric optimal guidance law is obtained. Then, to accurately track the minimum fuel orbit designed in the second step, based on parametric eigenstructure assignment method, a state feedback control law is derived. At last, the approach proves effective by numerical simulation.