从地球到日-火系平动点轨道的转移

Low-Thrust Transfer to the Libration Point Orbits of Sun-Mars System from the Earth

平动点轨道特殊的空间位置及动力学特征,使其在深空探测中具有重要的应用。以日-火系平动点轨道(Lissajous与Halo轨道)任务为目标,结合平动点轨道的不变流形理论,研究了小推力转移问题。首先给出了圆型限制性三体动力学模型下平动点附近不变流形(稳定和不稳定流形)高阶分析解以及相应的计算实例。接着以流形分析解为基础,建立了初始小推力轨道优化模型,并利用改进的协作进化算法求解初始小推力轨道。最后将初始轨道离散,采用多点打靶法将最优控制问题转化为参数优化问题,并用序列二次规划方法(SQP)求解。仿真结果证明轨道设计方法的有效性。

Libration point orbits have played an important role in deep space exploration due to their special geometry configuration and dynamical characteristics in the solar system.In this paper,the problem of low-thrust transfer to libration point orbits of Sun-Mars system is investigated in combination with the invariant manifold theory of libration point orbits.Firstly,the high-order solutions of invariant manifolds（i.e.stable and unstable manifold）,of the restricted three-body problem are introduced,and some computational examples are given.On the basis of analytical solution of invariant manifold,the optimization problem of initial low-thrust transfer is established and solved by using an improved cooperative evolutionary algorithm（ICEA）.Then the initial trajectories are discretized,and the optimal control problem is directly converted into the parameter optimization problem by means of multiple shooting scheme.The parameter optimization problem is solved by using the Sequential Quadratic Programming（SQP） algorithm.Lissajous orbit and Halo orbit with suitable amplitude around the L1 point in the Sun-Mars system are selected as target orbits.The simulation results demonstrate the effectiveness of the proposed orbit design method.