Earth-moon Trajectory Optimization Using Solar Electric Propulsion

The optimization of the Earth-moon trajectory using solar electric propulsion is presented. A feasible method is proposed to optimize the transfer trajectory starting from a low Earth circular orbit (500 km altitude) to a low lunar circular orbit (200 km altitude). Due to the use of low-thrust solar electric propulsion, the entire transfer trajectory consists of hundreds or even thousands of orbital revolutions around the Earth and the moon. The Earth-orbit ascending (from low Earth orbit to high Earth orbit) and lunar descending (from high lunar orbit to low lunar orbit) trajectories in the presence of J2 perturbations and shadowing effect are computed by an analytic orbital averaging technique. A direct/indirect method is used to optimize the control steering for the trans-lunar trajectory segment, a segment from a high Earth orbit to a high lunar orbit, with a fixed thrust-coast-thrust engine sequence. For the trans-lunar trajectory segment, the equations of motion are expressed in the inertial coordinates about the Earth and the moon using a set of nonsingular equinoctial elements inclusive of the gravitational forces of the sun, the Earth, and the moon. By way of the analytic orbital averaging technique and the direct/indirect method, the Earth-moon transfer problem is converted to a parameter optimization problem, and the entire transfer trajectory is formulated and optimized in the form of a single nonlinear optimization problem with a small number of variables and constraints. Finally, an example of an Earth-moon transfer trajectory using solar electric propulsion is demonstrated.     

Application of the Conjugate Gradient Method to a Problem on Minimum Time Orbit Transfer

This correspondence considers the problem of optimally controlling the thrust steering angle of an ion-propelled spaceship so as to effect a minimum time coplanar orbit transfer from the mean orbital distance of Earth to mean Martian and Venusian orbital distances. This problem has been modelled as a free terminal time-optimal control problem with unbounded control variable and with state variable equality constraints at the final time. The problem has been solved by the penalty function approach, using the conjugate gradient algorithm. In general, the optimal solution shows a significant departure from earlier work. In particular, the optimal control in the case of Earth-Mars orbit transfer, during the initial phase of the spaceship's flight, is found to be negative, resulting in the motion of the spaceship within the Earth's orbit for a significant fraction of the total optimized orbit transfer time. Such a feature exhibited by the optimal solution has not been reported at all by earlier investigators of this problem.     

Fuel-optimal deorbit scheme of space debris using tethered space-tug based on pseudospectral method

This paper proposes a fuel-optimal deorbit scheme for space debris deorbit using tethered space tug. The scheme contains three stages named respectively as dragging, maintenance and swinging. In the first stage, the tug, propelled by continuous thrust, tows deorbit to a transfer orbit with a tether. Then in the second stage, the combination of the tug and the debris flies unpowered and uncontrolled to a swing point on the transfer orbit. Finally, in the third stage, the tug is propelled at the swing point and the rotation speed of the tethered system increases such that the debris obtains enough velocity increment. The trajectory optimization of the first stage is established considering the total fuel consumption of the three stages, whereas the dynamic model is simplified for computation efficiency. The solution to the optimal problem is obtained using a direct method based on Gauss pesudospectral discretization. Then a model predictive controller is designed to track the open-loop optimal reference trajectories, reducing the states’ deviations caused by model simplification and ignorance of perturbations. Furthermore, it is proved that the fuel-optimal swing point is the apogee of the transfer orbit. The paper analyzes the fuel consumption of a typical scenario and demonstrates effectiveness of the proposed deorbit scheme numerically.     

Tangent-impulse transfer from elliptic orbit to an excess velocity vector

The two-body orbital transfer problem from an elliptic parking orbit to an excess veloc-ity vector with the tangent impulse is studied. The direction of the impulse is constrained to be aligned with the velocity vector, then speed changes are enough to nullify the relative velocity. First, if one tangent impulse is used, the transfer orbit is obtained by solving a single-variable function about the true anomaly of the initial orbit. For the initial circular orbit, the closed-form solution is derived. For the initial elliptic orbit, the discontinuous point is solved, then the initial true anomaly is obtained by a numerical iterative approach; moreover, an alternative method is proposed to avoid the singularity. There is only one solution for one-tangent-impulse escape trajectory. Then, based on the one-tangent-impulse solution, the minimum-energy multi-tangent-impulse escape trajectory is obtained by a numerical optimization algorithm, e.g., the genetic method. Finally, several examples are provided to validate the proposed method. The numerical results show that the minimum-energy multi-tangent-impulse escape trajectory is the same as the one-tangent-impulse trajectory.     

变比冲发动机作用下共面燃料最优轨道转移

以国外目前正在研制中的变比冲磁等离子体火箭发动机(VASIMR)为背景,研究了变比冲发动机作用下的同平面燃料最优轨道转移。推力方向角和比冲为控制变量,发动机总功率为常值,发动机可多次开关机。采用经典最优控制理论,运用庞德里亚金最小值原理将问题转化为两点边值问题,并通过非线性规划算法求解,得到了受精确开关函数控制的最优比冲时间历程。给出的VASIMR发动机应用算例结果表明,采用VA-SIMR发动机有益于提高航天器有效载荷所占比例。     

Two-maneuver indirect contingency return from a low lunar orbit

The problem of contingency return from the low lunar orbit is studied. A novel two-maneuver indirect return strategy is proposed. By effectively using the Earth’s gravity to change the orbital plane of the transfer orbit, the second maneuver in the well-known three-maneuver return strategy can be removed, so the total delta-v is reduced. Compared with the single-maneuver direct return, our strategy has the advantage in that the re-entry epoch for the minimum delta-v cost can be advanced in time, with a minimum delta-v value similar to that of the direct return. The most obvious difference between our strategy and the traditional single- or multiple- maneuver strategies is that the complete transfer orbit is a patch between a two-body conic orbit and a three-body orbit instead of two conic orbits. Our strategy can serve as a useful option for contingency return from a low lunar orbit, especially when the delta-v constraint is stringent for a direct return and the contingency epoch is far away from the return window.     

基于大幅值Lyapunov轨道的地月转移轨道设计研究

基于平面圆形限制性三体问题模型,利用与绕月轨道相切的大幅值Lyapunov周期轨道,提出了一种新的地月转移轨道设计方法。根据Poincaré截面与限制性三体问题动力学系统对称性计算得到的大幅值Lyapunov轨道,通过与绕月轨道拼接,将地月转移问题转化为地球到大幅值Lyapunov轨道的转移问题。为保证探测器能够从近地轨道（LEO）切向逃逸到达大幅值Lyapunov轨道,通过计算其稳定流形,采用最近点作为Poincaré截面的终止条件求解探测器的初始状态,并根据初始状态完成地月轨道的设计。仿真结果表明,该地月转移策略相比于Hohmann转移,在同样只需要两次速度增量的前提下,约节约100 m/s的速度增量,该研究为地月转移轨道的设计提供了一种新思路。     

电推进在静止轨道空间碎片减缓中的应用

研究了电推进在静止轨道空间碎片减缓中应用的可行性和效果。通过分析电推进中离子推进的技术特点、发展和应用,阐明了用电推进将静止轨道卫星在寿命末期移高到“垃圾轨道”是可行的。提出了电推进采用沿飞行方向的常值推力,以多次双脉冲变轨方式工作的方案,并通过仿真计算,得出了该方案中推力大小、工作时间、特征速度、燃料消耗量等参数的确定方法和量化性指标,验证了电推进应用在空间碎片减缓中的作用和效果。探讨了电推进以脉冲方式工作的工程实现方案．     

广义轨道根数空间的轨道机动可达性

在由动量矩矢量和偏心率矢量定义的广义轨道根数度量空间内,研究了在初始轨道的任意点施加幅值固定的单脉冲后卫星的可达区域,包括脉冲施加的位置任意、方向固定和位置固定、方向任意2种情况,给出了广义轨道根数空间中轨道机动的可达性判据.通过比较脉冲作用前后的广义轨道根数,评估了单脉冲对广义轨道根数的影响,并且利用数值仿真分析了脉冲作用位置、方向与广义轨道根数空间中度量的关系.最后,在广义轨道根数空间中给出了轨道到轨道的机动策略,验证了广义轨道根数的可行性.     

载人登月着陆器奔月窗口搜索方法

对环月轨道共面交会的载人登月任务中,着陆器(LM)奔月零窗口与轨道参数精确快速设计方法进行了研究。任务采用人货分离奔月模式,着陆器于载人飞船到达环月轨道前抵达环月共面交会轨道,着陆器近月点一次共面减速完成近月制动。提出一种三层快速精确奔月窗口搜索方法:第一层采用地心二体轨道理论解析计算月窗口及奔月轨道参数初值,作为正确性基本参考;第二层采用改进的双二体解析动力学模型求解月窗口内奔月轨道参数变化规律;第三层采用高精度轨道动力学模型和SQP_Snopt优化求解奔月零窗口及轨道参数精确解。仿真结果表明,本文提出的三层逐级奔月窗口搜索方法能快速精确求解载人登月任务中着陆器奔月窗口及精确轨道参数,也揭示了影响着陆器奔月窗口的主次因素和规律,为中国未来载人登月工程提供参考。     

小卫星星座的最优脉冲变轨研究

针对小卫星星座,进行星座发射中的最优脉冲式变轨研究,给出了形成星座的脉冲式变轨的基本原理;基于卫星相对运动状态转移方程,推导出了星座参脉冲式变轨的理论解,即所要施加的脉冲控制量的解析式,利用遗传算法,对双脉冲式变轨的脉冲控制量进行了优化计算,求得了使总变轨脉冲最小的最优变轨时间,最后,探讨了星座脉冲式变轨的工程实现现途径,为工程应用和研究提供参考。     

负升力返回时航天器的再入走廊与轨迹研究

研究了较大升阻比航天器采用负升力返回时的再入走廊与最优轨迹，通过数字仿真并与正升力再入时的结果比较，得到结论：采用负升力再入时的返回走廊前１／３段比采用正升力的相应部分宽度有较大增加；离轨点所耗燃料质量与热防护系统质量之和较正升力再入时的情况有一定减少。由此可见，负升力再入概念在提高有效载荷上明显优越于正升力再入概念。     

天/地基多平台空间目标光电观测时效性分析

针对如何部署光学探测设备才能更好实现对空间目标的高精度高频度监视问题,考虑光照条件、相对关系及探测性能,构建了天/地基空间目标探测与成像仿真模型;按照轨道特征选取了94颗LEO（Low Earth Orbit,低地球轨道）卫星、63颗GEO（Geosynchronous Earth Orbit,地球同步轨道）卫星和18颗大椭圆轨道卫星,选用春夏秋冬典型季节的特定时间长度,仿真分析了国内地基、南北极科考站、LEO卫星、准GEO卫星等多平台光电手段的位置探测和成像观测能力;比对分析地基平台纬度和季节、天基平台轨道高度和倾角对探测能力的影响得出：南北极科考站相比于国内站点可提高重点季节的探测时效性,98°倾角LEO平台对低轨目标成像时效性方面更具优势,等.在此基础上,提出了我国空间目标光电观测设备天地一体的布局构想.     

动能拦截器助推段导引方案研究

针对大气层外高速飞行的目标, 提出了一种可用于动能拦截器助推段的导引方法.建立了拦截器和目标的运动模型, 在分析可拦截约束条件的基础上推导出转移轨道计算方法, 同时通过对拦截器可发射区域中的转移轨道优化得到满足约束条件的有效发射区域, 并以点火时刻待增速度为性能指标来寻优计算获得发射参数.仿真结果表明, 该方法能有效实现拦截器助推段的制导控制.      

The Dawn Ion Propulsion System

Dawn??s ion propulsion system (IPS) is the most advanced propulsion system ever built for a deep-space mission. Aside from the Mars gravity assist it provides all of the post-launch ??V required for the mission including the heliocentric transfer to Vesta, orbit capture at Vesta, transfer to various Vesta science orbits, escape from Vesta, the heliocentric transfer to Ceres, orbit capture at Ceres, and transfer to the different Ceres science orbits. The ion propulsion system provides a total ??V of nearly 11 km/s, comparable to the ??V provided by the 3-stage launch vehicle, and a total impulse of 1.2×10⁷ N?s.     

基于人工免疫算法的载人登月任务地月转移双脉冲中止策略研究彭 坤,果琳丽,向开恒,王 平,杨 雷

载人登月任务中,任务中止策略设计是确保航天员安全返回的重要基础。首先结合"星座"计划飞行方案分析了载人登月任务各飞行阶段的中止策略;其次针对地月转移巡航段进行了双脉冲中止策略设计,以速度增量数值、方位角以及变轨时间间隔为控制变量,加入轨道同向、近地点高度、偏心率以及飞行时间约束,提出双脉冲变轨计算流程;最后采用人工免疫算法对该问题进行了求解和优化。仿真算例表明,双脉冲中止策略存在多组解,其全局分布特性为:飞行时间越短速度增量需求越大;飞行时间相近时,大偏心率中止轨道对应的速度增量小;故障点离地月加速点越近,所需速度增量越小。同时也验证了人工免疫算法求解双脉冲中止策略问题的有效性。     

空天飞行器弹道/轨道一体化设计

弹道/轨道一体化设计是解决空天飞行器发射入轨和轨道转移问题的一种全新思路。针对目前存在的空天飞行器弹道/轨道一体化设计问题,通过改进非开普勒轨道方程的方法建立飞行器在连续推力、气动力、引力以及摄动力等多种力作用下的弹道/轨道一体化设计动力学模型;提出基于轨道设计反方法的弹道/轨道一体化设计方法。其创新点主要体现在：通过整合连续推力、气动力、引力以及摄动力等多种作用力达到了统一弹道/轨道模型的目的;提出了基于傅里叶级数形状方法的轨道设计方法,该方法相比于之前的逆多项式法,可以处理带推力约束的轨道设计问题;由于在弹道段采用类似于轨道设计反方法的设计思想设计弹道,使得弹道和轨道两段轨迹的设计方法也达到了统一,致使从模型和设计方法的角度都体现了弹道/轨道设计的统一性,解决了传统分段设计方法是在不同段采用不同的模型和方法,很难体现出一体化设计思想的问题。仿真分析表明本文提出的弹道/轨道一体化设计方法是可行和有效的。     

Spacecraft telemetry link performance in a transfer orbit

There are several critical periods early in the mission of a geo-stationary communication satellite. The first is the period from launch vehicle ignition until the upper stage final successful burn. The second is after the above span until the vehicle reaches its final altitude of a synchronous orbit. For a nominal low thrust apogee boost ascent subsystem during that later time, almost continuous telemetry is mandatory. This is especially true during the crucial periods of main engine burns and attitude correction phases. Maintaining a strong telemetry link throughout this phase requires an adequate RF signal link from the spacecraft to a ground station in the telemetry RF channel. An analysis of this link performance during each orbit until final position has two major aspects. One, the location of the spacecraft in relation to the ground tracking station at each moment in the mission is a matter of geometry and Keplerian physics. The other is the RF signal and its supporting subsystems, both on the ground and aboard the vehicle. The fundamental theoretical considerations or both the orbit parameters and radio link components are examined and then the individual parameter sensitivities are analyzed. Next, a nominal cast for a generic mission is studied. This survey considers the telemetry performance during each major stage of the flight from the launch through the transfer orbit to the postinjection period to the final orbit. Then abnormal situations due to both orbit and RF faults are examined. Finally, some design and operation concepts which may lessen the impact of the previous anomalies, are presented     

连续地月转移系统动力学研究与能量分析

为了研究新型连续地月转移系统的动力学及能量需求,采用Lagrange方法,在系绳为刚性杆假设的前提下,同时忽略第三体引力、地球扁率和系绳轴向变形等扰动因素的影响,建立了驱动型动量交换绳系卫星(MMET)系统的三维刚性动力学模型。对所建立的动力学模型进行了数值仿真及对比分析,仿真结果验证了所建模型的正确性。研究表明,外力矩对系统轨道运动参数影响甚小,对姿态运动参数影响明显。采用MMET方式进行载荷转移,推导出了实现载荷地月轨道转移所需的入口速度条件以及时间周期条件,并求解出了载荷在2次任务之间的时间间隔。给定初始条件下,当MMET系统以0.231 6 rad/s的旋转角速度绕其质心旋转1 448.5圈,其绕地心刚好运行5圈时,载荷可顺利进入地月转移轨道。最后,对连续地月转移系统实现载荷的地月转移进行了能量对比分析,结果表明,相同条件下,MMET载荷转移方式相比于传统脉冲变轨方式在载荷转移过程中消耗更少的能量。     

月球卫星精密定轨

随着空间应用需求的日益增大,深空探测已成为现实,而月球显然是人类走向深空的首选目标。发射月球探测器通常分3个阶段,其运动状态分别对应3种不同类型的轨道:近地停泊轨道、地月转移轨道和绕月轨道。月球是1个慢自转天体且无大气,就轨道解而言这些因素导致环月卫星的运动与地球卫星有所差别。本文针对月球探测任务的特点,从月球与地球的差别入手,在仔细分析月球卫星的受力状况前提下,着重阐述月球探测器在环月段精密定轨的方法原理和具体实现过程。