Trajectory and Correction Maneuver During the Transfer from Earth to Halo Orbit

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,

Halo Orbits around Sun-Earth L1 in Photogravitational Restricted Three-Body Problem with Oblateness of Smaller Primary

This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. Both the terms due to oblateness of the smaller primary are considered. Numerical as well as analytical solutions are obtained around the Lagrangian point L1, which lies between the primaries, of the Sun-Earth system. A comparison with the real time flight data of SOHO mission is made. Inclusion of oblateness of the smaller primary can improve the accuracy. Due to the effect of radiation pressure and oblateness, the size and the orbital period of the halo orbit around L1 are found to increase.

Oblateness Effect of Saturn on Halo Orbits of L1 and L2 in Saturn-Satellites Restricted Three-Body Problem

The Circular Restricted Three-Body Problem (CRTBP) with more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries is considered to generate the halo orbits around L1 and L2 for the seven satellites (Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Iapetus) of Saturn in the frame work of CRTBP. It is found that the oblateness effect of Saturn on the halo orbits of the satellites closer to Saturn has significant effect compared to the satellites away from it. The halo orbits L1 and L2 are found to move towards Saturn with oblateness.

Halo Orbits in the Photo-Gravitational Restricted Three-Body Problem

We study of halo orbits in the circular restricted three-body problem (CRTBP) with both the primaries as sources of radiation. The positioning of the triangular equilibrium points is discussed in a rotating coordinate system.

地月周期轨道对地月L1与L2附近Halo轨道的可见性分析

随着去往月球航天器的增多,现有的近地空间光学卫星与地基光学望远镜的探测能力已无法满足要求,急需增强地月空间观测能力,通过使用地月周期轨道来填补地月空间观测能力的不足被认为是一种有效手段。针对地月周期轨道的特性,文章基于微分校正原理对三体轨道建模,并完成了算法的设计,提出了地月周期轨道的选择原则,并优选了3条轨道。在地月周期轨道对地月拉格朗日点L1、L2附近Halo轨道的可见性分析中,为方便评估,采用类球体的物体星等评估模型来定义可见性的评估标准;基于卫星工具包提供模型计算中涉及的自然天体、物体和观测卫星三者的时空关系,给出了可见性分析过程及结果,研究表明地月周期轨道对地月拉格朗日点L1、L2附近Halo轨道均有不错的观测效果,其中轨道1对地月周期轨道的可见性综合最高,均大于95%。

微流星体碰撞对日地L_(2)点Halo轨道的影响

空间中存在大量高速运动的微流星体,与在轨运行的航天器发生碰撞后将导致轨道偏离、性能下降、结构破坏甚至航天器失效.由于Halo轨道具有不稳定的特性,本文主要探究微流星体碰撞对日地L_(2)点Halo轨道动力学演化规律的影响.首先,建立日地L_(2)点附近轨道的动力学模型,通过微分修正法构造Halo轨道的初始条件,基于Grün微流星体通量模型计算微流星体与航天器碰撞的数量和碰撞引起的速度改变量.然后,采用Runge-Kutta算法求解Halo轨道的动力学方程,研究碰撞速度改变量引起的轨道偏差随时间的演化规律.此外,采用状态转移矩阵方法分析初始状态偏差的演化规律,并与数值积分方法对比.最后基于状态转移矩阵方法分析了不同碰撞速度改变量的大小和方向引起的动力学响应.研究发现,状态转移矩阵在短时间内得到的结果与数值积分方法基本一致,而且只需一次矩阵乘法即可通过初始状态偏差计算得到末时刻状态偏差,具有非常高的效率.研究结果表明,由于Halo轨道固有的不稳定特性,所以初始时刻微流星体碰撞引起的微小状态偏差会快速增长,导致消耗更多控制燃料,最终将影响航天器的寿命.此外,微流星体碰撞的速度改变量的方向对偏差传递的规律有重要的影响.

Nonlinear dynamics and station-keeping control of a rotating tethered satellite system in halo orbits

The dynamics of a rotating tethered satellite system （TSS） in the vicinity of libration points are highly nonlinear and inherently unstable. In order to fulfill the station-keep control of the rotating TSS along halo orbits, a nonlinear output tracking control scheme based on the θ- D technique is proposed. Compared with the popular time-variant linear quadratic regulator （LQR） controller, this approach overcomes some limitations such as on-line computations of the algebraic Riccati equation. Besides, the obtained nonlinear suboptimal controller is in a closed form and easy to implement. Numerical simulations show that the TTS trajectories track the periodic reference orbit with low energy consumption in the presence of both tether and initial injection errors. The axis of rotation can keep pointing to an inertial specific object to fulfill an observation mission. In addition, the thrusts required by the controller are in an acceptable range and can be implemented through some low-thrust propulsion devices.

Research on the transfers to Halo orbits from the view of invariant manifolds

This paper discusses the evolutions of invariant manifolds of Halo orbits by low-thrust and lunar gravity. The possibility of applying all these manifolds in designing low-thrust transfer, and the presence of single-impulse trajectories under lunar gravity are also explained. The relationship between invafiant manifolds and the altitude of the perigee is investigated using a Poincare map. Six types of single-impulse transfer trajectories are then attained from the geometry of the invariant manifolds. The evolutions of controlled manifolds are surveyed by the gradient law of Jacobi energy, and the following conclusions are drawn. First, the low thrust （acceleration or deceleration） near the libration point is very inefficient that the spacecraft free-flies along the invariant manifolds. The purpose is to increase its velocity and avoid stagnation near the libration point. Second, all con- trolled manifolds are captured because they lie inside the boundary of Eatlh＇s gravity trap in the configuration space. The evo- lutions of invariant manifolds under lunar gravity are indicated from the relationship between the lunar phasic angle and the altitude of the perigee. Third and last, most of the manifolds have preserved their topologies in the circular restricted three-body problem. However, the altitudes of the perigee of few manifolds are quite non-continuous, which can be used to generate single-impulse flyby trajectories.

Opportunities search of transfer between interplanetary halo orbits in ephemeris model

In this paper,a two-level search method for searching transfer opportunities between interplanetary halo orbits,exploiting the invariant manifolds of the restricted three-body problem,is proposed.In the method,the first-level search procedure is performed under the conditions of the initial time of escape manifold trajectory of the Sun-Earth halo orbit and the terminal time of capture manifold of the target planet fixed,by solving the optimal two-impulsive heliocentric trajectory to connect the two manifold trajectories.The contour map,helpful to the understanding of the global characteristics of the transfer opportunities,taking the initial time of escape manifold and the terminal time of capture manifold as variables,the optimal velocity increment of the first-level search as objective function,is used for the second-level search.Finally,taking the Earth-Mars and Earth-Venus halo to halo transfers for example,the transfer opportunities in 2015-2017 are searched.The results show the effectiveness of the proposed method and reveal the property of quasi-period of transfer opportunities between interplanetary halo orbits.

利用halo导航星的地月空间联合自主轨道确定

面向未来地月空间的自主导航定位需求,研究了利用halo导航星的地月空间联合自主轨道确定(LAOD)。首先,建立了基于星间测距的地月空间联合自主定轨模型;其次,讨论了利用halo导航星联合自主定轨的可观性;最后,数值分析了不同误差条件下导航星与用户星的联合自主定轨精度,其中用户星轨道涵盖了典型的地月空间任务轨道,包括低地球轨道(LEO)、地月转移飞行轨道(CTT)和环月低轨道(LLO)。针对CTT自主定轨精度问题,特别分析了利用2颗halo导航星的定轨情况。结果表明,单颗halo导航星条件下LEO和LLO的定轨精度最高,导航星次之,CTT最差,增加1颗halo导航星可将CTT的定轨精度提高至少2倍,可为星间联合自主轨道确定技术在后续月球和深空探测任务中的应用提供参考借鉴。

约束条件下的Halo轨道转移轨道设计

平动点任务的转移轨道往往存在约束条件,以往的研究集中于无约束条件下的Halo轨道转移轨道设计,研究约束条件下的Halo轨道的转移轨道设计问题。首先分析了平动点任务转移轨道的约束条件,然后给出了一种约束条件下Halo轨道转移轨道设计的一般方法,重点推导了考虑轨道高度、航迹角、轨道倾角、升交点约束的微分修正公式。然后以日地L1点附近的Halo轨道为目标轨道,在约束条件下设计了其转移轨道,仿真结果验证了本文方法的有效性。

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。

不同月球借力约束下的地月Halo轨道转移轨道设计

针对地月系L2点不同任务需求下的低耗能转移轨道设计问题,基于不变流形理论与混合优化技术,深入研究了不同月球借力约束与不同幅值Halo轨道的入轨点(简称HOI点)对转移轨道飞行时间与燃料消耗的影响,给出了HOI点选择策略。首先结合任务要求并考虑月球引力影响,在月球借力点施加不同约束条件,通过微分修正算法调整Halo轨道的稳定流形,设计月球到Halo轨道的转移轨道。采用遗传算法与微分修正算法相结合的混合优化策略,在同时考虑地球停泊轨道高度、倾角、升交点赤经与航迹角等多约束条件下,对燃料最优的地月转移轨道进行研究。最后,分析月球借力高度、借力方位角和不同HOI点对平动点转移轨道飞行时间与燃耗变化量的影响,对于考虑月球借力的地月平动点转移轨道设计与应用具有重要的参考价值。

采用Gauss伪谱法的小推力日-火Halo轨道转移优化设计

针对日-地Halo轨道到日-火Halo轨道的小推力轨道转移问题,给出一种基于不变流形理论和Gauss伪谱法的优化设计方法。首先,在日心惯性坐标系中建立小推力轨道优化模型,并基于不变流形理论给出轨道转移中流形出口和入口的选择原则,应用该原则在日-地系统中选择流形出口,在日-火系统中选择流形入口,并将其作为轨道转移的初末状态;然后基于Gauss伪谱法将最优控制问题离散化为非线性规划(NLP)问题,并采用基于逆多项式的形状算法给出了NLP初值的计算方法;最后对该轨道转移问题进行了数学仿真。仿真结果表明:Gauss伪谱法可有效用于小推力日-火Halo轨道转移的优化,且采用逆多项式形状算法得到的初值具有初始误差小,使得NLP收敛速度快的特点。

地-月系平动点及Halo轨道的应用研究

地-月系统的平动点L1点及L2点的Halo轨道在探月工程中有重要的应用价值,可分别用于地月连续通信覆盖和月球背面的探测。由于在地-月系统中太阳的引力不可忽略,特别是在长时间作用以后,其动力学行为与摄动力较小的日-地系统有明显的不同。本文分析了如何利用太阳引力进入地-月系统的L1点及L2点的Halo轨道、以及由Halo轨道进入近月轨道的问题,两者综合起来构成了一条完整的地月低能转移轨道。研究结果对探月轨道设计有一定的参考价值。

Halo轨道族延拓方法及特性研究

对Halo轨道周期和运动范围等特性的研究是平动点任务设计的首要前提。针对大幅值Halo轨道和完整Halo轨道族的应用需求及其数值计算问题,面向当前应用广泛的地月系和日-地月系共线平动点,基于延拓法研究了圆型限制性三体问题下的Halo轨道族数值计算和运动学特性,给出了Halo轨道族延拓计算方法。数值仿真了族参数选择对轨道族计算的影响,得到了地月系和日-地月系共线平动点的大范围南北Halo轨道族,同时给出了轨道族的轨道周期变化和空间位置变化特性。研究结果表明,固定延拓步长下,L1点Halo轨道族应选择会合坐标系x坐标作为族参数,L2点Halo轨道族应选择y方向速度或者周期T作为族参数。方法适用于任意三体系统平动点的周期轨道族计算,特别是对其中的状态转移矩阵简单修改后可用于完整力模型下的Halo轨道(族)的数值设计。

航天器Halo轨道间转移的滚动时域控制

针对航天器在日/地系统共线平动点附近Halo轨道族之间的轨道转移问题,提出了一种在线实时求解滚动时域控制的新方法。首先采用高效的辛自适应非线性最优控制数值算法,离线规划出航天器在不同Halo轨道之间转移的最优轨迹和最优控制输入。然后提出一种在线实时求解滚动时域控制的新方法,基于已规划好的最优转移轨迹,应用滚动时域控制方法完成航天器在初始入轨偏差下的在线实时制导控制任务。最后的非线性动力学系统数值仿真结果表明:所提出的求解滚动时域控制的方法具有高效率特点,能够在线实时求解航天器在Halo轨道之间转移的制导控制问题,并很快消除初始入轨误差的影响。

基于脉冲星和太阳敏感器的日地系Halo轨道组合导航研究

为提高平动点轨道探测器的自主导航能力,提出一种利用X射线脉冲星和太阳敏感器的导航算法.利用X射线脉冲星导航理论,用X射线探测器测量X射线脉冲到达时间,同时利用太阳敏感器测量太阳视线方向矢量,建立导航系统观测方程.在高精度星历模型下,对日地系Halo轨道建立数学模型,利用二级微分修正方法获取地球质心惯性系下的标称轨道,利用基于UD分解的联邦Unscented卡尔曼滤波方法进行状态估计,并研究了摄动因素对导航结果的影响.仿真结果表明,该方法能够完成日地系平动点轨道的自主导航,并且比X射线脉冲星单独导航具有更高的导航精度.

Halo轨道维持的线性周期控制策略

共线型平动点附近的Halo轨道具有指数不稳定性,轨道维持是必不可少的。推导了基于Halo轨道的误差动力学方程,并证明其一阶近似即为线性周期系统。以一次维持的作用时间为离散步长,并通过定常变换,将所得误差动力学化为线性离散定常系统;则仅需通过极点配置,即可实现Halo轨道镇定。研究结果表明,利用Halo轨道周期性设计的线性周期控制策略,可以满足轨道维持任务的需要。

基于不变流形的小推力Halo轨道转移方法研究

利用动力系统理论中的不变流形概念设计向halo轨道转移的小推力轨道。首先,根据小推力发动机是否工作将转移轨道划分为上升段和滑行段。两个轨道段分别采用不同的动力学模型描述;并通过不变流形和Lyapunov反馈控制原理将整段轨道参数化;最后进行参数优化获得最优转移轨道。这种方法通过合理选择坐标系和利用反馈控制的方法,避免了由三体动力学模型以及最优控制问题的共轭方程所具有的极强的非线性带来的求解困难。具有很强的收敛性;优化过程的每一步中不包含迭代过程,计算速度快。并以从地球停泊轨道向日-地L2点halo轨道转移为例验证了此方法的有效性。这种方法对小推力动平衡点任务设计有着重要的实际意义。