Fuel Optimal Guidance Law For Powered Descent Mars Landing

With the deepening researched about external space exploration activities, the exploration tasks have not limited in the earth and the moon, which have extended to planets and comets. The types of exploration tasks have been developed from flying-by, surrounded detection and hard landing to the soft landing and sampling return in recent years. The process of powered descending aims at completing the finial landing task, which is an important phase for studying planets closely. In order to meet the needs of reliability and fuel consumption, fuel-optimal trajectory optimization and the optimal tracking guidance strategy are researched deeply, which contains certain aspects as follows:Firstly, the motion equation is obtained by simplifying, and the trajectory optimization problem is transformed into the convex optimization problem, which can be solved. By the trajectory optimization, plenty of fuel-optimal trajectories are obtained with different initial states, which will be used in the following researches.Secondly, a tracking guidance law based on the second-order sliding mode is proposed. The classical variable structure control has certain shortcomings, such as the chattering phenomenon, the slow dynamic response rate and low robustness under atmospheric disturbances, therefore, a finite-time convergence second-order sliding mode with robustness is designed. Theories prove the existence, accessibility and robustness. The proposed sliding mode based tracking guidance law is deduced, which is shown effective in the numerical simulation.Thirdly, in order to save the storage space, a new method of the fuel-optimal trajectory is put forward, which is defined as way-points in this paper. New way-points are defined according to the thrust change rule, which combined with Linear Guidance Law(LGL) to constitute a new guidance strategy. The new guidance strategy can not only have the optimality of fuel, but also save the storage space compared with the classical nominal trajectory guidance. Then, the way-points with atypical initial positions are obtained by linear interpolation and cubic spline interpolation respectively, which are proved effective in the numerical simulation.