Rapid lunar soft landing trajectory optimization based on time-approach method

A time-approach method was proposed for rapid lunar soft landing trajectory optimization. Firstly the landing time was analytically approximated, and the original lunar soft landing problem was transformed into a fixed final time optimal control problem. Then, the obtained new problem was optimized to satisfy soft landing constraints. According to the final energy state of the optimized trajectory, the landing time was modified and again a fixed final time optimal control problem was obtained. Iterations of optimization and modification were conducted to sequentially approach the optimal soft landing time. The fixed final time optimal control problem was converted into Nonlinear Programming (NLP) and was resolved by Quasi-Newton's method with 4th Admas predict-modification scheme as integration procedure. Simulation results show good accuracy, rapid convergence (