Legendre pseudospectral method for rapid lunar soft-landing trajectory optimization

The problem of rapid Lunar soft-landing trajectory optimization by using a Legendre pseudospectral method was studied in this paper. Firstly, according to the distinguished features of the lunar and soft-landing trajectory, the set of dynamics and kinematics equations of the Lunar soft-landing was simplified in order to reduce the computation load. Then, the soft-landing trajectory optimization problem was transformed into a constrained parameter optimization problem by using a Legendre pseudospectral method, and a combination of nonlinear programming methods (Methods of Multipliers and BFGS algorithm) was used to solve the transformed problem. Finally, some simulation works were carried out and the minimum principle of Pontryagin was used to verify the optimal condition of the optimal trajectory, Simulation results show the methodology and algorithms were able to generate a feasible soft-landing trajectory quickly on a desktop computer.