Constrained trajectory optimization of a soft lunar landing from a parking orbit

Abstract

A trajectory optimization study for a soft landing on the Moon, which analyzed the effects of adding operationally based constraints on the behavior of the minimum fuel trajectory, has been completed. Metrics of trajectory evaluation included fuel expenditure, terminal attitude, thrust histories, etc.. The vehicle was initialized in a circular parking orbit and the trajectory divided into three distinct phases: de-orbit, descent, and braking. Analysis was initially performed with two-dimensional translational motion, and the minimally constrained optimal trajectory was found to be operationally infeasible. Operational constraints, such as a positive descent orbit perilune height and a vertical terminal velocity, were imposed to obtain a viable trajectory, but the final vehicle attitude and landing approach angle remained largely horizontal. This motivated inclusion of attitude kinematics and constraints to the system. With rotational motion included, the optimal solution was feasible, but the trajectory still had undesirable characteristics. Constraining the throttle to maximum during braking produced a steeper approach, but used the most fuel. The results suggested a terminal vertical descent was a desirable fourth segment of the trajectory. which was imposed by first flying to an offset point and then enforcing a vertical descent, and provided extra safely margin prior to landing. In this research, the relative effects of adding operational constraints were documented and can be used as a baseline study for further detailed trajectory optimization.