Legendre pseudospectral method for rapid lunar soft-landing trajectory optimization

Determining the best soft-landing trajectory of the lunar probe from the lunar satellite orbit involves the solution of an optimal control problem. This problem, which was considered to be difficult, was traditionally solved on the ground prior to flight. First, a new hypothesis was introduced according to the distinguished features of the lunar and soft-landing trajectory. Then, a set of dynamics and kinematics equations of motion was simplified, and this simplification reduced the computation load greatly. Next, the optimal control problem of soft-landing trajectory was transformed into a constrained parameter problem by using Legendre pseudospectral method, and nonlinearprogramming method (methods of multipliers and BFGS) was applied to solve the transformed problem. The simulation results show that the algorithm can generate a feasible soft-landing trajectory of about 300 seconds flight time in 30 seconds on the desktop computer.