基于凸优化理论的含约束月球定点着陆轨道优化

摘要

Abstract:Taking account of the navigation and hazard detecting sensor FOV (Filed of View) constraint and the thrust constraint,the trajectory optimization algorithm for lunar pin-point landing is studied in this paper.Firstly,a three dimensional trajectory optimization model is established,the optimal thrust switch function is given out according to the Pontryagin maximum principle.Also,the singular interval of thrust is proved to be nonexistent.Then the nonlinear constrained optimal control problem is transformed into a second-order-cone parameter optimization problem through convex transformation and discretization.In the meanwhile,the parameter optimization problem is solved by using interior-point method.The feasibility and validity of the algorithm are verified by simulation results of different scenarios.%针对月球精确定点软着陆问题,考虑导航及障碍检测敏感器视场约束及制动发动机推力大小约束,对月球动力下降段轨道优化方法进行了研究.首先建立了含约束条件的三维定点软着陆轨道优化问题模型,根据庞德亚金极小值原理推导了最优推力开关方程,并给出了推力奇异区间不存在的证明.针对优化模型中的复杂非线性约束,引入凸优化理论将问题转化为二阶锥优化问题,并采用内点法求解了最优标称轨迹.最后给出了月球软着陆制动段、接近段的仿真结果,验证了该着陆轨道优化方法的有效性.