日地Halo轨道的多约束转移轨道分层微分修正设计

针对日-地系统L1点（简称SEL1点）Halo轨道转移轨道设计中存在的多约束与初值敏感性问题，提出一种基于分层微分修正与初值多项式的设计方法。首先定义平动点转移轨道设计过程中存在的约束条件，然后根据不同的终端约束条件，重点给出了同时考虑轨道高度、轨道倾角、升交点赤经与航迹角等多约束条件下的分层微分修正方法。通过分析约束变量与控制变量之间的关系，得到能够解决微分修正初值问题的初值表达式。最后在多约束条件下设计了从轨道高度为200km的地球停泊轨道到SEL1点Halo轨道的转移轨道。仿真结果表明，分层微分修正方法能够处理多约束问题，且初值表达式可以为微分修正提供良好的初始条件，从而保证算法收敛，方法具有较好的实用性。

Hierarchical Differential Correction Based Transfer Trajectory Design for Halo Orbit with Multiple Constraints

To cope with the orbit transfer problem with multiple constraints and sensitive initial values around the libration point L1 of the Sun-Earth system (SEL1 point), a transfer trajectory design method based on hierarchical differential corrections and initial value polynomial is proposed. At first, constraints are analyzed in the process of designing the transfer trajectory around the libration point. According to different terminal constraints, the hierarchical differential correction method is proposed by considering orbit altitude, orbit inclination, right ascension of ascending node and track angle simultaneously. Then, by analyzing relation between constraint variables and control variables,the initial value expression is got to solve the initial value problem of differential corrections. Finally, transfer trajectory from the earth parking orbit whose altitude is 200km to Halo orbit around SEL1 point is designed under the condition of multi-constraints. The simulation results indicate the hierarchical differential correction method can deal with the problem with multiple constraints and initial value polynomial can provide appropriate initial conditions for differential corrections so as to guarantee convergence of the algorithm. In conclusion, this method has good practicality.