Orbit design of lunar precise fixed-point soft landing and selection of initial point

A method of applying parametric control and enhancing technique in order to solve optimal control problem of lunar probe precise Fixed-point soft landing is studied. Firstly the inequality constraint is approximated by using constraint transformation technique. Secondly the piece-wise constant value is used to approach the optimal solution. Based on enhancing technique, each period of duration of parameters is transformed into a term of new parameters. So the optimal control problem is transformed into the parameter selection problem which can be solved by the classical parameter optimization method. By means of increasing the number of parameters and the iteration of optimization, the parametric solution which approaches the continuous optimal solution is derived. In the optimization process, the selection of the initial point is also studied. The result of the simulation demonstrates the proposed design scheme is simple and effective.