The Libration Points in Photogravitational Restricted Three-Body Problem

The phologravilational restricled three-body problem in which the mass reduclionfactors of two primaries q_1 q_2( -∞, 1] are siudied and an analytic meihod toesli,;iale the number of libralion points ana io calculate lheir hoalion is given in thispaper. The results show lhal in phologravilalional reslricled three-body problem, thenumber of librafion poinis is .from one to seven for different q_1 and q_2. As application,the motion of dust grain like comet tail in the solar syslern is also discussed.

Improved semi-analytical computation of center manifolds near collinear libration points

In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semianalytical computation of the center manifolds and the associated canonical transformation are valuable tools for exploring the design space of libration point missions. This paper deals with the refinement of reduction to the center manifold procedure. In order to reduce the amount of calculation needed and avoid repetitive computation of the Poisson bracket, a modified method is presented. By using a polynomial optimization technique, the coordinate transformation is conducted more efficiently. In addition, an alternative way to do the canonical coordinate transformation is discussed, which complements the classical approach. Numerical simulation confirms that more accurate and efficient numerical exploration of the center manifold is made possible by using the refined method.

A station-keeping strategy for collinear libration point orbits

Spacecrafts in periodic or quasi-periodic orbits near the collinear libration points are proved to be excellent platforms for scientific investigations of various phenomena.Since such periodic or quasi-periodic orbits are exponentially unstable,the station-keeping maneuver is needed. A station-keeping strategy which is found by an analytical method is presented to eradicate the dominant unstable component of the libration point trajectories.The inhibit force transforms the unstable component to a stable component.In this method,it is not necessary to determine a nominal orbit as a reference path.

A new control law based on characteristic exponent assignment for libration point orbit maintenance

A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields an unstable linear parameter-varying system with periodic coefficients. Given the variational equations, an innovative control law based on characteristic exponent assignment is introduced for libration point orbit maintenance. A numerical simulation choosing the Richardson＇s third order approximation for a halo orbit as a nominal orbit is conducted, and the results demonstrate the effectiveness of this control law.

Motion modeling and formation form analysis of spacecraft near collinear libration points

To meet the increasing research demand for deep space exploration,especially for the second libration point (L2) conditional periodic orbit (Halo orbit) in the Sun-Earth system,the methods to get analytical Halo orbit and differential-correction Halo orbit were described firstly,and the corresponding orbits accuracy was analyzed.Then,based on the results of third-order and differential-correction Halo orbits,the formation form was studied.Analysis was carried out to discuss the influence of system amplitude,initial phase,and phase difference on the formation form,as well as that of initial orbit values on form accuracy.Finally,some simulation results demonstrate the validity of the proposed methods.

Lissajous Orbits at the Collinear Libration Points in the Restricted Three-Body Problem with Oblateness

In the present work, the collinear equilibrium points of the restricted three-body problem are studied under the effect of oblateness of the bigger primary using an analytical and numerical approach. The periodic orbits around these points are investigated for the Earth-Moon system. The Lissajous orbits and the phase spaces are obtained under the effect of oblateness.

Libration Points in the R3BP with a Triaxial Rigid Body as the Smaller Primary and a Variable Mass Infinitesimal Bod

The paper deals with the existence of the coplanar libration points in the restricted three-body problem when the smaller primary is a triaxial rigid body and the infinitesimal body is of variable mass. Following small parameter method, the coordinates of collinear libration points are established whereas the coordinates of triangular libration points are established by classical method. It is found that the mass reduction factor has small effect but triaxiality parameters of the smaller primary have great effects on the coordinates of the libration points.

Multi-modes control method for spacecraft formation establishment and reconfiguration near the libration points

This paper studies Multi-modes control method for libration points formation establishment and reconfiguration. Firstly, relations between optimal impulse control and Floquet modes are investigated. Method of generating modes is proposed. Characteristics of the mode coefficients stimulated at different time are also given. Studies show that coefficients of controlled modes can be classified into four types, and formation establishment and reeonfiguration can be achieved by multi-impulse control with the presented method of generating modes. Then, since libration points formation is generally unstable, mutli-modes keeping control method which can stabilize five Floquet modes simultaneously is proposed. Finally, simulation on formation establishment and reconfiguration are carried out by using method of generating modes and mutli-modes keeping control method. Results show that the proposed control method is effective and practical.

Quasi-periodic orbits of small solar sails with time-varying attitude around Earth–Moon libration points

This paper proposes new quasi-periodic orbits around Earth–Moon collinear libration points using solar sails.By including the time-varying sail orientation in the linearized equations of motion for the circular restricted three-body problem(CR3BP),four types of quasi-periodic orbits(two types around L1 and two types around L2)were formulated.Among them,one type of orbit around L2 realizes a considerably small geometry variation while ensuring visibility from the Earth if(and only if)the sail acceleration due to solar radiation pressure is approximately of a certain magnitude,which is much smaller than that assumed in several previous studies.This means that only small solar sails can remain in the vicinity of L2 for a long time without propellant consumption.The orbits designed in the linearized CR3BP can be translated into nonlinear CR3BP and high-fidelity ephemeris models without losing geometrical characteristics.In this study,new quasi-periodic orbits are formulated,and their characteristics are discussed.Furthermore,their extendibility to higher-fidelity dynamic models was verified using numerical examples.

A symplectic moving horizon estimation algorithm with its application to the Earth-Moon L2 libration point navigation

Accurate state estimations are perquisites of autonomous navigation and orbit maintenance missions.The extended Kalman lter(EKF)and the unscented Kalman lter(UKF),are the most commonly used method.However,the EKF results in poor estimation performance for systems are with high nonlinearity.As for the UKF,irregular sampling instants are required.In addition,both the EKF and the UKF cannot treat constraints.In this paper,a symplectic moving horizon estimation algorithm,where constraints can be considered,for nonlinear systems are developed.The estimation problem to be solved at each sampling instant is seen as a nonlinear constrained optimal control problem.The original nonlinear problem is transferred into a series of linear-quadratic problems and solved iteratively.A symplectic method based on the variational principle is proposed to solve such linear-quadratic problems,where the solution domain is divided into sub-intervals,and state,costate,and parametric variables are locally interpolated with linear approximation.The optimality conditions result in a linear complementarity problem which can be solved by the Lemke's method easily.The developed symplectic moving horizon estimation method is applied to the Earth-Moon L2 libration point navigation.And numerical simulations demonstrate that though more time-consuming,the proposed method results in better estimation performance than the EKF and the UKF.

地月空间天基时空基准的构建与传递

地月空间正在逐渐成为人类太空探索活动的热点区域。高精度时间、空间基准的构建和传递是确保地月空间任务规划与实施的重要基础,既是地球时空基准的体系化拓展,也是提升地月空间时空信息保障水平的重要手段。随着GNSS系统的发展和稳定服务,地球区域时空基准设施相对完备。月球区域的导航系统与地球类似,国内外也提出了多种方案,但地月空间还包括地球、月球区域以外的区域,其时空基准实施的构建需要充分考虑空域大、动力学特殊等因素,在高效益实现时空信息服务的同时,将地球和月球的时空基准进行有机衔接。立足当前发展需求,开展了地月空间时空基准架构的设计,并针对地球、月球区域之外地月区域特点,研究并提出基于地月平动点的天基时空基准构建、溯源和传递方案,可支持实现地月空间时空基准信息服务,为地月空间时空基准的一体化构建与发展提供参考。

地月历表误差对共线平动点周期轨道的误差影响分析

基于圆形限制性三体问题下地月平动点的3阶轨道解析解,分析不同初值条件下的轨道演化特性,并基于误差传播理论研究地月历表误差对地月共线平动点周期轨道在不同初值及初值误差时的影响。结果表明:1)轨道误差与地月历表误差在同一个量级,当地月历表误差均值不为0时,其峰值大约为地月历表误差的2.5倍,轨道误差随时间变化的无量纲周期约为轨道无量纲周期的0.5倍;2)在同一条轨道的不同位置,地月历表误差影响存在较大差异,平面Lyapunov轨道、Halo轨道和垂直Lyapunov轨道误差的峰值点分别位于或接近X向最大值与最小值处、Z向最大值与最小值处和z=0处。

近月空间广域观测星座设计与效能分析

为满足近月空间广域观测及地月转移目标跟踪观测需求,设计一种运行于地月平动点L1/L2点轨道及DRO轨道的三星广域观测星座。首先分析了近月空间目标特性与重点区域范围,并根据观测需求和维持代价优选系统轨道。接着根据观测对象特性完成对近月空间环扫覆盖探测与地月转移目标跟踪观测的工作模式设计。最后根据视星等公式对不同相位角和观测距离的目标亮度进行仿真分析得出载荷探测能力需求,并推导得出载荷探测视场需求。通过效能仿真分析,该星座对近月空间覆盖率周期为8天,可在1.5个周期内实现对近月空间的100%覆盖,单周期观测近月目标不少于14次、观测弧长不少于3.5 min,对典型地月转移目标观测弧段时长可占转移周期80%以上。满足近月空间广域观测和对近月目标及地月转移目标编目定轨需求。

平动点导航星座下的月面接收机自主完好性监测

为了减少月球探测复杂环境对导航的影响和提升平动点导航星座的可靠性,提出了一种基于多假设解分离的月面接收机自主完好性监测方法。该方法利用了地月空间引力不对称性,仅需3颗平动点卫星测量信息就可以实现月面用户级完好性监测。为使月球背面更多区域的可见星数达到完好性监测所需卫星数,增加L2点Halo轨道卫星数并采用多种群遗传算法优化Halo轨道振幅和初始相位。最后采用解分离算法验证了基于3颗卫星进行完好性监测的可行性。仿真表明,在2颗可见星条件下可实现故障检测,平面短周期轨道卫星故障更容易检测;在3颗可见星条件下可实现故障排除,故障偏差达到20σ~30σ(σ=1 m)时,故障检测率和排除率开始上升到100%。首次分析了基于平动点导航星座的完好性监测可行性并提出了解决方法,该方法可应用于探月任务导航领域,为未来探月任务完好性监测算法和平动点导航星座设计提供了有益参考。

地月L1点低能转移轨道设计与优化

针对地月空间平动点周期轨道与近地轨道之间的低能转移问题,提出一种地月L1(Earth-Moon L1,EML1)点Halo轨道到地球静止轨道(geostationary Earth orbit,GEO)的四脉冲低能转移轨道的设计方法。所提方法在扰动流形和Lambert弧段拼接的三脉冲转移轨道设计基础上,从分析轨道雅可比常数变化与速度增量关系的角度出发设计四脉冲低能转移轨道。数值仿真结果表明,四脉冲优化模型比三脉冲模型效率更高,可以得到更优的转移方案,有效解决了优化过程中由于搜索空间大、极值数量多而导致的优化结果不佳的问题。所提设计方法可以用于EML1其他周期轨道族与各类近地轨道的相互转移问题研究。

一种面向限制性三体问题的轨道-姿态运动模态构建方法

针对平动点附近的具有强非线性和耦合性的轨道-姿态动力学机理分析,以及如何利用其动力学特性完成相关任务操作等问题,提出了基于Floquet理论的轨道-姿态运动模态构建方法,并探讨了所构建模态的典型应用。首先,在平动点轨道-姿态周期解的基础上,对轨道-姿态状态转移矩阵进行分块,根据分块矩阵特征值特点,建立了姿态模态和姿轨耦合模态,与轨道模态共同构成完整的轨道-姿态运动模态。然后,对模态特性进行了相空间分析。最后,以平动点相对轨道-姿态运动解析、平动点轨道-姿态稳定性控制和平动点轨道附近姿轨编队设计为应用案例,相应数值仿真表明了所提出模态的正确性,以及在典型航天任务设计与控制中的应用价值。

Autonomous navigation to quasi-periodic orbits near translunar libration points

Libration-point missions have been very useful and successful. Due to the unstable natures of most of these orbits, the long-time stationkeeping demands frequent maneuvers and precise orbit determinations. Earth-based tracking will have to undertake much more responsibilities with the increasing number of libration missions. An autonomous navigation system could offer a better way to decrease the need for Earth-based tracking. Nevertheless, when an autonomous navigation system is applied, there are three important factors affecting autonomous navigation accuracy, i.e., the accuracy of initial conditions, the accuracy of measurements, and the accuracy of onboard dynamics for propagation. This paper focuses on analyzing the influence from the third factor and finding an appropriate navigation dynamics, which can satisfy the requirement of estimation accuracy but not cause too much burden for onboard computation. When considering the restricted three-body model and the bicircular restricted four-body model as navigation dynamics, the astrin- gency is not shown during the simulations. Meanwhile, when considering the influences of the Sun＇s direct and indirect perturbations and the eccentricity of the Moon＇s orbit, a new navigation dynamic model with the standard ephemerides is proposed. The simulation shows the feasibility of the proposed model.

Trajectory design for the Moon departure libration point mission in full ephemeris model

The lunar probe may still have some remaining fuel after completing its predefined Moon exploration mission and is able to carry out some additional scientific or technological tasks after escaping from the Moon orbit.The Moon departure mission for the lunar probe is the focus of this paper.The possibility of the spacecraft orbiting the Moon to escape the Moon's gravitational pull is analyzed.The trajectory design for the Earth-Moon system libration point mission is studied in a full ephemeris dynamical model,which considers the non-uniform motion of the Moon around the Earth,the gravity of the Sun and planets and the finite thrust of the onboard engine.By applying the Particle Swarm Optimization algorithm,the trajectory design for the transfer from the Moon-centered orbit to the L1 halo orbit,the station-keeping strategies for the Earth-Moon halo orbit and the construction of homoclinic and heteroclinic orbits are investigated.Taking the tracking conditions and engineering constraints into account,two feasible schemes for the Moon departure libration point mission for the lunar probe are presented.

地月远距离逆行轨道脉冲调相方法

地月远距离逆行轨道(DRO)在月球探测、地月空间开发等任务中具有重要价值。针对地月DRO的脉冲调相机动问题,提出了直接调相和间接调相两种调相方法。首先,通过数值方法构建了地月DRO直接调相策略的可行集,分析了调相机动起点和终点位置选择对调相性能的影响,得到了双脉冲最优和次优调相机动策略。针对相位差较大的调相问题,进一步提出了双脉冲弧段组合调相策略。其次,利用地月平动点周期轨道及其同宿、异宿转移轨道,构造了地月DRO间接调相方法,并分析了不同雅可比常数下间接调相策略的燃耗和飞行时间。最后,分析对比了间接调相轨道与直接调相轨道的性能,给出了两者的适用条件。研究结果将为地月DRO的广泛应用开发提供理论基础。

Trajectory correction for lunar flyby transfers to libration point orbits using continuous thrust

Trajectory corrections for lunar flyby transfers to Sun–Earth/Moon libration point orbits(LPOs)with continuous thrusts are investigated using an ephemeris model.The lunar flyby transfer has special geometrical and dynamical structures;therefore,its trajectory correction strategy is considerably different from that of previous studies and should be specifically designed.In this paper,we first propose a control strategy based on the backstepping technique with a dead-band scheme using an ephemeris model.The initial error caused by the launch time error is considered.Since the perturbed transfers significantly diverge from the reference transfers after the spacecraft passes by the Moon,we adopt two sets of control parameters in two portions before and after the lunar flyby,respectively.Subsequently,practical constraints owing to the navigation and propellant systems are introduced in the dynamical model of the trajectory correction.Using a prograde type 2 orbit as an example,numerical simulations show that our control strategy can efficiently address trajectory corrections for lunar flyby transfers with different practical constraints.In addition,we analyze the effects of the navigation intervals and dead-band scheme on trajectory corrections.Finally,trajectory corrections for different lunar flyby transfers are depicted and compared.