航天器异面气动力辅助变轨大气飞行段的最优轨迹

本文研究航天器利用气动力辅助变轨实现由远地轨道向近地轨道异面转移问题，就航天器利用大气飞行实现减速及轨道平面机动提出了一种考虑过程约束存在时的优化设计方法。通过方案设计将函数优化问题转换成参数优化问题，并利用美国航天飞机数据进行了模拟计算，得到满意结果。     

Optimal trajectories for the aeroassisted flight experiment

This paper deals with the determination of optimal trajectories for the aeroassisted flight experiment (AFE). The intent of this experiment is to simulate a GEO-to-LEO transfer, where GEO denotes a geosynchronous Earth orbit and LEO denotes a low Earth orbit. Specifically, the AFE spacecraft is released from the Space Shuttle and is accelerated by means of a solid rocket motor toward Earth, so as to achieve atmospheric entry conditions identical with those of a spacecraft returning from GEO. During the atmospheric pass, the angle of attack is kept constant, and the angle of bank is controlled in such a way that the following conditions are satisfied: (a) the atmospheric velocity depletion is such that, after exiting, the AFE spacecraft first ascends to a specified apogee and then descends to a specified perigee; and (b) the exit orbital plane is identical with the entry orbital plane. The final maneuver, not analyzed here, includes the rendezvous with and the capture by the Space Shuttle. In this paper, the trajectories of an AFE spacecraft are analyzed in a 3D space, employing the full system of 6 ODEs describing the atmospheric pass. The atmospheric entry conditions are given, and the atmospheric exit conditions are adjusted in such a way that requirements (a) and (b) are met, while simultaneously minimizing the total characteristic velocity, hence the propellant consumption required for orbital transfer. Two possible transfers are considered: indirect ascent (IA) to a 178 NM perigee via a 197 NM apogee; and direct ascent (DA) to a 178 NM apogee. For both transfers, two cases are investigated: (i) the bank angle is continuously variable; and (ii) the trajectory is divided into segments along which the bank angle is constant. For case (ii), the following subcases are studied; 2, 3, 4 and 5 segments; because the time duration of each segment is optimized, the above subcases involve 4, 6, 8 and 10 parameters, respectively. It is shown that the optimal trajectories of cases (i) and (ii) coalesce into a single trajectory: a two-subarc trajectory, with the bank angle constant in each subarc (bang-bang control). Specifically, the bank angle is near 180° in the atmospheric entry phase (positive lift projection phase) and is near 0° in the atmospheric exit phase (negative lift projection phase). It is also shown that, during the atmospheric pass, the peak values of the changes of the orbital inclination and the longitude of the ascending node are nearly zero; hence, the peak value of the wedge angle (angle between the instantaneous orbital plane and the initial orbital plane) is nearly zero. This means that the motion of the spacecraft is nearly planar in an inertial space.     

连续推力机动轨道优化设计的贝塞尔曲线法

提出一种基于贝塞尔曲线的平面机动轨道设计方法。该方法将贝塞尔曲线方程与轨道形状方程相结合，利用得到的复合函数作为轨道方程来对机动轨道进行数学描述；通过约束条件获得可行的机动轨道族，由控制点设计给出具体的优化变量，将累积速度增量作为优化指标函数；并利用优化算法完成参数优化，从而得到最优机动轨道。最后针对设计的机动轨道推力峰值较大的问题，进一步提出了分段贝塞尔曲线法，在降低推力峰值的同时，可进一步降低燃料消耗，并在平面机动转移轨道设计的基础上，通过梯度下降对自由控制点进行修正，解决了考虑时间约束的平面轨道交会问题。     

The use of three-impulse transfer to insert the spacecraft into the high Moon Artificial Satellite orbits

The problem of the optimal spacecraft’s insertion from the Earth into the high circular polar Moon Artificial Satellite’s orbit (MAS) with a radius of 4000–8000 km has been investigated. A comparison of single- and three-impulse insertion schemes has been performed. The analysis was made taking into account the disturbances from the lunar gravity field harmonics and the gravity fields of the Earth and the Sun, as well as the engine’s limited thrust. It has been shown that the three-impulse transfer from the initial selenocentric hyperbola of the approach into the considered final high MAS orbit is noticeably better with respect to the final mass than the ordinary single-impulse deceleration. The control parameters that implement this maneuver and provide nearly the same energy expenses as in the Keplerian case have been presented. It was found that, in contrast to the Keplerian case, in the considered case of the real gravity field, there is the optimal maximum distance of the maneuver. Recently, the Moon exploration problem became actual again.     

嫦娥五号平动点拓展任务轨道方案研究

中国嫦娥五号探测器成功实现月球采样返回任务,为最大限度利用任务资源,研究了利用嫦娥五号轨道器的平动点拓展任务轨道方案,设计了平动点轨道及其转移轨道.首先,给出了任务轨道设计的轨道动力学模型,包括圆型限制性三体问题模型和精确力模型.其次,基于嫦娥二号和嫦娥5T1平动点拓展任务设计经验,介绍了平动点轨道直接转移与入轨等轨道...     

Optimal aeroassisted return from high earth orbit with plane change

This paper gives a complete analysis of the problem of aeroassisted return from a high Earth orbit to a low Earth orbit with plane change. A discussion of pure propulsive maneuver leads to the necessary change for improvement of the fuel consumption by inserting in the middle of the trajectory an atmospheric phase to obtain all or part of the required plane change. The variational problem is reduced to a parametric optimization problem by using the known results in optimal impulsive transfer and solving the atmospheric turning problem for storage and use in the optimization process. The coupling effect between space maneuver and atmospheric maneuver is discussed. Depending on the values of the plane change i, the ratios of the radii, $\text{n =}\text{r}{}_1\text{r}{}_2$ between the orbits and $\text{a =}\text{r}{}_2\text{R}$ between the low orbit and the atmosphere, and the maximum lift-to-drag ratio E1 of the vehicle, the optimal maneuver can be pure propulsive or aeroassisted. For aeroassisted maneuver, the optimal mode can be parabolic, which requires only drag capability of the vehicle, or elliptic. In the elliptic mode, it can be by one-impulse for deorbit and one or two-impulse in postatmospheric flight, or by two-impulse for deorbit with only one impulse for final circularization. It is shown that whenever an impulse is applied, a plane change is made. The necessary conditions for the optimal split of the plane changes are derived and mechanized in a program routine for obtaining the solution.     

CHANG'E-2 lunar escape maneuvers to the Sun–Earth L2 libration point mission

This paper addresses lunar escape maneuvers of the first Chinese Sun–Earth L2 libration point mission by the CHANG'E-2 satellite, which is also the world's first satellite to reach the L2 point from a lunar orbit. The lunar escape maneuvers are heavily constrained by the remaining propellant and the condition of telemetry, track and command, among others. First, these constraints are analyzed and summarized to design a target L2 Lissajous orbit and an initial transfer trajectory. Second, the maneuver mathematical models are studied. The multilevel maneuver schemes which consist of phasing maneuvers and a final lunar escape maneuver are designed for actual operations. Based on the scheme analysis and comparison, the 2-maneuver scheme with a 5.3-h-period phasing orbit is ultimately selected. Finally, the mission status based on the scheme is presented and the control operation results are discussed in detail. The methodology in this paper is especially beneficial and applicable to a future multi-mission instance in the deep space exploration.     

航天器近距离视觉制导自主机动轨道优化

研究具有视觉导引路径约束的航天器近距离机动轨道优化数值计算问题。首先,给出了带路径约束的椭圆参考轨道航天器近距离轨道机动最优化问题数学模型。利用高斯伪谱法将上述最优化问题转化为非线性规划问题,优化参数为配点上的状态量和控制量。然后,利用MATLAB的SNOPT软件包对非线性规划问题进行求解。最后通过数值仿真验证了方法的有效性和鲁棒性。     

月球软着陆的二次型最优制导方法

为实现在月球表面指定区域的精确软着陆,研究了月球软着陆的线性二次型最优制导方法。利用简化的轨道动力学模型,给出了一种基于状态和能耗最优的软着陆二次型制导方法。由于制导律要求同时提供3个方向的时变推力,所以需要通过变推力发动机和姿态机动来实现。该制导方法虽能满足精确软着陆的需要,但对姿态变化的要求超出了着陆器姿态机动能力。因此,本文修正了二次型最优制导方法,取消了对轨道参数的过程约束,仅对其终端进行约束,通过求解着陆指定目标点的能耗最优两点边值问题,得到了发动机推力大小和方向的显式表达式。研究结果表明,利用一定的姿态机动能力,修正的制导方法能够满足精确软着陆的需要。     

Optimal ballistically captured Earth–Moon transfers

The optimality of a low-energy Earth–Moon transfer terminating in ballistic capture is examined for the first time using primer vector theory. An optimal control problem is formed with the following free variables: the location, time, and magnitude of the transfer insertion burn, and the transfer time. A constraint is placed on the initial state of the spacecraft to bind it to a given initial orbit around a first body, and on the final state of the spacecraft to limit its Keplerian energy with respect to a second body. Optimal transfers in the system are shown to meet certain conditions placed on the primer vector and its time derivative. A two point boundary value problem containing these necessary conditions is created for use in targeting optimal transfers. The two point boundary value problem is then applied to the ballistic lunar capture problem, and an optimal trajectory is shown. Additionally, the problem is then modified to fix the time of transfer, allowing for optimal multi-impulse transfers. The tradeoff between transfer time and fuel cost is shown for Earth–Moon ballistic lunar capture transfers.     

航天器轨道机动的闭环控制精度分析

利用线性协方差分析法对航天器在闭环控制作用下轨道机动的精度问题进行了研究。首先,分析了存在的主要误差,给出了误差影响下航天器轨道机动闭环控制的系统框图。然后建立了开环和闭环控制系统协方差分析的数学模型,并根据轨道方程线性化给出了脉冲速度修正算法。对赤道大椭圆轨道卫星开环和闭环控制下轨道机动的精度问题进行了分析,与Monte Carlo仿真结果与一致,校验了方法的有效性与正确性。     

不完备轨道信息下的LEO轨道面内机动检测方法

针对某些因轨道信息不完整而无法直接外推的LEO轨道飞行器的机动检测问题,提出了一种基于轨道摄动影响的面内机动检测方法。该方法将半长轴和偏心率作为检测量,通过分析大气阻力摄动和J 2 项摄动对 LEO 飞行器轨道的影响,从而确定目标飞行器的轨道参数允许边界值,再通过和实际轨道参数进行比较来判定被检测数据点参数是否超出正常范围。最后,采用这种方法对X\|37B飞行器轨道数据进行了仿真验证,共检测出10个机动点,结果表明该方法可以较为准确地利用有限轨道信息检测目标的轨道机动情况。     

热流限制下的最优气动力辅助变轨

以变轨能量消耗最小为优化目标，应用极大值原理研究了飞行过程受热流限制和升力系统约束下的气动力辅助共面变轨问题，飞行过程成分第一自由弧段，约束弧段，第二自由弧段三个部分，讨论了升力系数的最优表达式，分析了飞行过程中两种约束的相互作用，给出了约束弧起始位置的角点条件和终端的横截条件下，对不同的初值选取方法讨论了三种计算策略，并给出了数值算例。     

基于参数优化的脉冲轨道设计

基于参数优化设计了一种可处理各类脉冲轨道优化的一般方法,并给出了两种确定最优脉冲数的方法。以脉冲矢量与脉冲施加时刻为未知参数,将脉冲轨道优化设计转为非线性参数优化,用合适的非线性规划算法求解。主矢量理论对所得解最优性的验证表明该方法可行。     

Spacecraft Injection into a Heliocentric Terrestrial Orbit

We consider the problem of injection of a spacecraft into the heliocentric Earth's orbit ahead and/or behind the Earth by 60° and 120° in heliographic longitude. The range of solar and astrophysical problems for which these orbits are necessary is reviewed. The variants of injection into heliocentric orbits work from a low around-Earth orbit with one turn-on of the engine in this orbit and one turn-on at the end of the injection trajectory. In this case, it turns out to be more profitable to put spacecraft into orbit for three or even four revolutions of the Earth about the Sun. The velocities necessary for the start from a low around-Earth orbit, the velocities at the final point of injection, and the fuel mass (relative to the spacecraft mass) necessary for injection are estimated. The problems for which injection to similar orbits is executed, using the low-thrust engine and with a combined regime of injection, are also considered.     

Aeroshell design techniques for aerocapture entry vehicles

A major goal of NASA's In-Space Propulsion Program is to shorten trip times for scientific planetary missions. To meet this challenge arrival speeds will increase, requiring significant braking for orbit insertion, and thus increased deceleration propellant mass that may exceed launch lift capabilities. A technology called aerocapture has been developed to expand the mission potential of exploratory probes destined for planets with suitable atmospheres. Aerocapture inserts a probe into planetary orbit via a single pass through the atmosphere using the probe's aeroshell drag to reduce velocity. The benefit of an aerocapture maneuver is a large reduction in propellant mass that may result in smaller, less costly missions and reduced mission cruise times. The methodology used to design rigid aerocapture aeroshells will be presented with an emphasis on a new systems tool under development. Current methods for fast, efficient evaluations of structural systems for exploratory vehicles to planets and moons within our solar system have been under development within NASA having limited success. Many systems tools that have been attempted applied structural mass estimation techniques based on historical data and curve fitting techniques that are difficult and cumbersome to apply to new vehicle concepts and missions. The resulting vehicle aeroshell mass may be incorrectly estimated or have high margins included to account for uncertainty. This new tool will reduce the guesswork previously found in conceptual aeroshell mass estimations.     

分布式卫星系统在轨操作的多目标分配

针对空间在轨操作目标分配问题,以分布式卫星系统为研究对象,提出了一种基于粒子群算法的在轨操作多目标分配方法。以分布式卫星机动所消耗的总能量最省为目标函数,建立了在轨操作多目标分配的数学模型。基于固定时间拦截理论,以机动时刻和对应的速度增量作表征,设计实现了单颗卫星最优机动方案。通过合理设计粒子位置与目标分配解的对应关系,采用粒子群算法对问题进行了求解,并详细阐述了算法的实现步骤。算例分析结果表明,建立的模型和算法能够快速得到正确的可行解,可有效解决多约束条件下空间在轨操作的多目标分配问题。     

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。     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: I

The problem of optimal control is considered for the motion of the center of mass of a spacecraft in a central Newtonian gravitational field. For solving the problem, two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems. Both the variants have a quaternion variable among the phase variables. In the first variant this variable characterizes the orientation of an instantaneous orbit of the spacecraft and (simultaneously) the spacecraft location in this orbit, while in the second variant only the instantaneous orbit orientation is specified by it. The suggested equations are convenient in the respect that they allow the general three-dimensional problem of optimal control by the motion of the spacecraft center of mass to be considered as a composition of two interrelated problems. In the first variant these problems are (1) the problem of control of the shape and size of the spacecraft orbit and (2) the problem of control of the orientation of a spacecraft orbit and the spacecraft location in this orbit. The second variant treats (1) the problem of control of the shape and size of the spacecraft orbit and the orbit location of the spacecraft and (2) the problem of control of the orientation of the spacecraft orbit. The use of quaternion variables makes this consideration most efficient. The problem of optimal control is solved on the basis of the maximum principle. Several first integrals of the systems of equations of the boundary value problems of the maximum principle are found. Transformations are suggested that reduce the dimensions of the systems of differential equations of boundary value problems (without complicating them). Geometrical interpretations are given to the transformations and first integrals. The relation of the vectorial first integral of one of the derived systems of equations (which is an analog of the well-known vectorial first integral of the studied problem of optimal control) with the found quaternion first integral is considered. In this paper, which is the first part of the work, we consider the models of motion of the spacecraft center of mass that employ quaternion variables. The problem of optimal control by the motion of the spacecraft center of mass is investigated on the basis of the first variant of equations of motion. An example of a numerical solution of the problem is given.     

基于序优化理论的晕轨道转移轨道设计

利用晕轨道的稳定流形可以设计从地球到晕轨道的转移轨道。但由于小幅度晕轨道的稳 定流形与地球停泊轨道无法相交,因此需采用两脉冲转移。微分修正法是求解两脉冲转移常 用的优化方法,虽然收敛速度快,但很难获取全局最优解,而且收敛半径小,如果初始猜想 与最优解相差很远,该方法可能会不收敛。将序优化理论与微分修正法相结合,利用序优化 思想缩小搜索空间,得到足够好的初始猜想,然后利用微分修正法快速收敛到满足终端精度 要求的解。仿真结果表明该方法有很好的收敛性,且计算量小。