Research On Guidance Problem Of Lunar Probe For Soft Landing

Soft landing on the lunar surface is an indispensable part in lunar probing plan. And moreover, navigation, guidance and control are the key techniques for lunar soft landing. With the support of National Natural Science Foundation of key projects"research on basic theories and key technologies of modeling, sensing, navigation and control of lunar exploration systems", this dissertation systematically studies guidance problems in the lunar landing procedure employing optimal control, optimization, nonlinear control methods based on precursors'results.Main contribution of the dissertation include several guidance laws of soft landing, which can be divided into two parts, i.e. the guidance of two-dimensional unfixed point soft landing and that of three-dimensional pinpoint soft landing. To solve the guidance problem of unfixed point soft landing, two types of optimal open-loop guidance law are designed by using optimal control and optimization methods. To solve guidance problems of pinpoint soft landing, firstly an optimal open-loop guidance law is designed to obtain the optimal trajectory of main braking phase of soft landing by using optimal control and optimal parameter selection, and then a nominal trajectory guidance method is developed to track the optimal trajectory. The main contents of this dissertation are as follows.At first, an optimal switching guidance law is developed by Pontryagin maximum principle of the classic optimal control theory to solve the guidance problem of unfixed point soft landing. Then, it is proved that the singularity condition that causes control function uncertain can not hold along an optimal trajectory on any closed time interval. A two-point boundary value problem is to be solved by using nonlinear programming in order to obtain the numerical solution for the optimal trajectory. Moreover, a piece-wise constant parametric guidance law is designed by the method of parametric control to solve the guidance problem of unfixed point soft landing. The essence of this method is to use the piece-wise constant function to approximate the optimal solution of the optimal control problem. Then, the optimal control problem can be transformed into a parameter optimization problem by this method. Hence, the optimal parameters can be solved by the common mathematic programming. The approximating precision can be enhanced by increasing the number of parameters until an acceptable solution is derived.The process of three-dimensional pinpoint soft landing is divided into two phases, specificly, the main braking phase and final landing phase. To solve the guidance problem of the main braking phase, a method combined optimal control and optimal parameter selection is developed. The main idea of this method is to use the function of system parameters which is unrelated to time to indicate the undetermined initial state. The parametric controller is designed by using the piece-wise constant function. Then, the optimal control problem can be transformed into an optimization problem of two sets of parameters. With regard to the final landing phase, a which can improve safety and reduce deviation is designed, where two switching curve is obtained. The feasibility and advantages of the braking scheme of pinpoint soft landing are confirmed by the STK simulating results.At last, since the actual flight of the lunar lander is influenced by interference of the main braking phase, the tracking problem of the lander's control system to optimal trajectory is investigated based on the model reference tracking theory. The optimal trajectory is represented as reference models with frozen coefficients and the dynamic model of the lander is linearized. Consequently, the problem comes down to a standard model reference control problem. Then, base on the model reference control theory for linear switching systems,a parametric approach for the design of the controller is proposed. Following this method, a robust tracking to the optimal trajectory is realized by selecting optimal parameters.