多引力场小推力引力借力轨道设计与优化

Design and optimization of low-thrust gravity-assist trajectory in multi gravitational fields

采用序贯法设计优化小推力引力借力轨道(low-thrust gravity-assist,LTGA)时,设计步骤复杂且优化结果最优性条件难以保证.本文提出一种多引力场LTGA问题联立求解框架.首先对多引力场环境和探测器动力学模型进行统一描述和处理.设计初始化策略,利用Radau伪谱法将发射窗口、借力顺序、初始轨道搜索以及轨道优化联立求解,简化设计步骤.利用hp自适应网格精细化策略保证优化结果最优性条件.该联立框架用于求解地木转移任务,得到地球–火星–地球–木星的转移方案.本文提出的联立求解框架,简化了设计步骤,保证了优化结果的最优性条件,得到比序贯求解更优的转移方案.

When low-thrust gravity-assist（LTGA） problems are designed and optimized with the sequential method,the design and optimization procedure is complex and the optimality conditions of the optimization results are difficult to be satisfied. This paper proposes a simultaneous framework of LTGA problems solving strategy in the multi gravitational fields. First, dynamic model of the probe as well as the multi gravitational fields are handled together in this method.An initialization strategy is designed and the launch window, gravity-assist scheme, initial orbit search, and trajectory optimization are solved in the simultaneous framework with the Radau pseudospectral method, which simplifies the design procedure of LTGA problems. An hp-adaptive mesh refinement strategy is utilized to satisfy the optimality conditions by adjusting the number of mesh and the order of the Lagrange Polynomial. The simultaneous framework is applied to solve the transfer mission from Earth to Jupiter and the transfer scheme of Earth-Mars-Earth-Jupiter is obtained. Simulation results show that the simultaneous framework of LTGA problems simplifies the LTGA design and optimization procedure,and guarantees the optimality conditions of the optimization results. Also a better transfer scheme is obtained comparing with the traditional sequential method.