Optimal control for soft landing of lunar probe

In order to decrease the fuel consumption under a finite thrust, a method applying nonlinear programming is presented to solve the optimal control problem on the soft landing of a lunar probe. Based on Pontryagin maximum principle, the lunar soft landing problem is transformed into a two-point boundary value problem in mathematics. In consideration of the bound condition and transversality condition, the resulted two-point boundary value problem is converted into a parameter optimization problem aiming at the initial values of conjugate variables and the terminal time, then it is solved by the nonlinear programming. To reduce the sensitivity of conjugate initial values, the initial values of control variables are used to replace the initial values of conjugate variables based on the transformation between conjugation variables and control variables. The simulated result demonstrates that the proposed method leads to a successful implementation of the lunar soft landing and reduces by 2.1% fuel consumption as compared with that of the traditional method, which shows that the proposed design scheme is simple and effective.