一种新的共线平动点拟周期轨道稳定保持策略

限制性三体问题下共线平动点附近的拟周期轨道在深空探测中具有重要的实际应用价值,得到了各航天大国的广泛重视。通过将动力学中心流形结构引入轨道控制方法的设计之中,得到了基于投影到中心流形的共线平动点拟周期轨道稳定保持策略。首先推导了会合坐标到中心流形坐标的正则变换方法,在此基础上设法通过引入轨道机动,将偏差状态点投影到中心流形上,从而达到消除不稳定分量的目的。该方法充分整合了平动点的动力学特性,并且也适用于周期轨道的稳定保持。通过对Lissajous轨道和晕轨道的数值仿真表明,该方法较以往方法具有更强的稳定性,能在显著降低轨控燃料消耗的基础上达到较好的稳定保持效果。     

Spacecraft formation flying control around L2 sun-earth libration point using on–off SDRE approach

In this paper, on–off SDRE control approach is presented for spacecraft formation flying control around sun-earth L2 libration point. Orbits around libration points are significant targets for many space missions mainly because of efficient fuel consumption. Furthermore, less propellant usage can be achieved by considering optimal control approaches in spacecraft formation flying control design. Among various nonlinear and optimal control methods, SDRE has shown to be a popular controller in various missions due to the privileges including efficiency, accuracy and robustness. The spacecraft are assumed to have on–off thrusters as actuators. It requires them to be fed with a sequence of on–off pulses which is regarded as a challenge for spacecraft designers. Hence, the main contribution of this paper is designing an on–off SDRE approach for the formation flight around sun-earth L2 point with uncertainty with energy and accuracy considerations. Including on–off input as a constraint is not feasible for SDRE implementation because it makes the system non-affine. An alternative is utilizing an integral action technique and an auxiliary control to make the system affine which leads to on–off SDRE approach. It has also been shown that the proposed method is robust against parametric uncertainties of the states. Present study aims to design an energy-beneficial, simple and attractive controller for a complex nonlinear system with on–off inputs and uncertainty in CRTBP. Simulation results show that the on–off SDRE control could provide the formation flight around L2 point with high accuracy using less energy consumption.     

解析计算在月球中继卫星Halo轨道设计中的应用

面向月球中继卫星工程轨道设计需求,研究解析计算方法在地月系L2点halo轨道设计中的应用问题。在讨论圆型限制性三体问题三阶解析近似计算方法的基础上,分析了解析计算与数值计算的差异,给出了解析近似计算在工程约束下的适用范围,进而提出了基于解析计算的轨道设计和特征筛选方法。分别采用解析初值和数值初值进行halo轨道外推,比对验证采用解析计算设计轨道的可行性。研究结果表明,解析计算方法适用于月球中继卫星轨道的初步设计、特征分析和构型筛选。     

小推力航天器的地月低能转移轨道

 在限制性四体模型下研究基于小推力方式的地月低能转移问题,通过借助于平动点轨道的相空间结构来揭示小推力转移的机理。重点研究了小推力转移自由飞行段的构造：经由LL₁点穿越获得最小能量的低能转移;而经由LL₁点Halo轨道穿越,得到(M,N)圈穿越轨道;由于Halo轨道相对于平动点增加了一维度的选择,根据(2,2)圈穿越轨道构造该转移的自由飞行段。在地球势阱逃逸和月球势阱捕获段,分别设计了合适的小推力的控制律及发动机开/关机时间,成功实施近地球段的小推力加速和近月球段的减速。尽管未对所得到的结果进行优化,所得转移轨道的燃料消耗也与类似边界条件的SMART-1轨道基本一致。     

环月轨道器运动中的月球物理天平动问题

采用类似对地球岁差章动的处理方法,讨论月球物理天平动对月心赤道坐标系 以及月球卫星轨道的影响。在对月球物理天平动的分析表达式与高精度数值历表进行比较的 基础上,给出了相应的月球引力位的变化及相应的坐标系附加摄动解,清楚地表明了对月球 卫星轨道影响的规律。所获结果与数值解进行了比对,证实了从定性和定量两个方面来看本 文的讨论都是有意义的,从而表明月球物理天平动分析解的简单表达式在某些问题中（特别 是定轨和预报）是有实用价值的,而且在建立轨道摄动分析解时,无需像地球卫星那样,去 引进混合形式的轨道坐标系,采用历元月心平赤道坐标系即可。最终表明：无论是采用数值 法定轨和预报还是分析法定轨和预报,均可采用统一的月心平赤道坐标系,这可避免一些不 必要的坐标转换。     

Some qualitative manifestations of the physical libration of the Moon by observing stars from the lunar surface

Targets and problems of the future Japanese project ILOM (In situ Lunar Orientation Measurement), which is planned to be realized as one kind of observations of lunar rotation at the second stage of SELENE-2 mission, are briefly described in the article. Inverse problem of lunar physical libration is formulated and solved. Accuracy of libration angles depending on accuracy of measuring selenographic coordinates is estimated. It is shown that selenographic coordinates of polar stars are insensitive to longitudinal librations τ(t). Comparing coordinates calculated for two models of a rigid and deformable Moon is carried out and components sensitive to Love number k₂ and to anelastic time delay are revealed.     

Halo轨道转移及中途修正问题研究(英文)

This article addresses the design of the trajectory transferring from Earth to Halo orbit, and proposes a timing closed-loop strategy of correction maneuver during the transfer in the frame of circular restricted three body problem （CR3BP）. The relation between the Floquet multipliers and the magnitudes of Halo orbit is established, so that the suitable magnitude for the aerospace mission is chosen in terms of the stability of Halo orbit. The stable manifold is investigated from the Poincar6 mapping defined which is different from the previous researches, and six types of single-impulse transfer trajectories are attained from the geometry of the invariant manifolds. Based on one of the trajectories of indirect transfer which are ignored in the most of literatures, the stochastic control theory for imperfect information of the discrete linear stochastic system is applied to design the trajectory correction maneuver. The statistical dispersion analysis is performed by Monte-Carlo simulation,     

On two kinds of intermediate orbits for asteroid explorations

In the paper, two kinds of intermediate orbits for asteroid explorations are proposed. One is around the collinear libration points of the Sun-asteroid restricted three-body problem. The other is around the asteroid itself. The first kind of intermediate orbit is applicable to asteroids with known masses, while the second is suitable for asteroids with unknown or negligible masses. Analytical solutions of these two intermediate orbits in the simplified models are introduced first, and then numerical algorithms are used to refine them to obtain the true orbits in the real force model. At last, the problem of station-keeping is addressed. The linear optimal feedback control law is used, and numerical simulations are made to both kinds of intermediate orbits. The results show that both kinds of orbits are feasible. The cost is reasonable and mainly depends on the initial insertion error.     

双站跟踪模式下“嫦娥4号”中继星定轨仿真分析

位于地月平动点的探测器因为较差的观测几何,需要地基USB/UXB与天文VLBI长时间的联合跟踪数据获取稳定精确的轨道。提出了利用中国深空网双站共视跟踪平动点探测器,获取双程、三程测距及VLBI测量数据,解算探测器精确轨道的模式。以"鹊桥"卫星为分析对象,首先评估中国深空网对"鹊桥"的跟踪能力。然后分析不同观测组合模式下的定轨计算精度。结果表明:双站共视约束下,深空站每天对"鹊桥"跟踪弧长大于5 h;使用长于6 h的双站跟踪数据进行定轨,系统差的解算更有利于轨道精度提升;跟踪时长超过2天时,必须在轨道解算的同时估计光压系数,并有望实现优于百米的轨道精度。     

地月L2点周期轨道的月球背面覆盖分析

地月L2点附近轨道具备独特的动力学和运动学特性,是月球背面探测任务的中继卫星首选布设位置。面向未来月球背面探测任务的中继通信需求,分析并研究了地月L2点周期轨道(halo轨道)对月球背面的覆盖。在圆型限制性三体问题模型下,研究并给出了halo轨道族延拓计算方法,基于延拓法设计了地月系大范围南北halo轨道族;给出了中继卫星的月球背面覆盖计算模型,定义了相应的时间覆盖因子;数值仿真了地月系南北halo轨道族的月球背面覆盖情况。研究结果表明:地月L2点周期轨道幅值和类型决定其对月面的覆盖性,幅值较小的轨道的月面整体覆盖性较好,幅值较大的轨道对月球南北极覆盖较好,南北族轨道分别有利于月球南北半球的覆盖。文章研究可为我国"嫦娥4号"月球背面探测任务的中继星轨道设计提供有益参考和借鉴。