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.     

Approximate solutions to minimax optimal control problems for aeroassisted orbital transfer

This paper considers minimax problems of optimal control arising in the study of aeroassisted orbital transfer. The maneuver considered involves the coplanar transfer from a high planetary orbit to a low planetary orbit. An example is the HEO-to-LEO transfer of a spacecraft, where HEO denotes high Earth orbit and LEO denotes low Earth orbit. In particular, HEO can be GEO, a geosynchronous Earth orbit.The basic idea is to employ the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. Hence, this type of flight is also called synergetic space flight. With reference to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The presence of upper and lower bounds on the lift coefficient is considered.The following minimax problems of optimal control are investigated: (i) minimize the peak heating rate, problem P1; and (ii) minimize the peak dynamic pressure, problem P2. It is shown that problems P1 and P2 are approximately equivalent to the following minimax problem of optimal control: (iii) minimize the peak altitude drop occurring in the atmospheric portion of the trajectory, problem P3.Problems P1–P3 are Chebyshev problems of optimal control, which can be converted into Bolza problems by suitable transformations. However, the need for these transformations can be bypassed if one reformulates problem P3 as a two-subarc problem of optimal control, in which the first subarc connects the initial point and the point where the path inclination is zero, and the second subarc connects the point where the path inclination is zero and the final point: (iv) minimize the altitude drop achieved at the point of junction between the first subarc and the second subarc, problem P4. Note that problem P4 is a Bolza problem of optimal control.Numerical solutions for problems P1–P4 are obtained by means of the sequential gradient-restoration algorithm for optimal control problems. Numerical examples are presented, and their engineering implications are discussed. In particular, it is shown that, from an engineering point of view, it is desirable to solve problem P3 or P4, rather than problems P1 and P2.     

基于气动辅助变轨的变气动外形飞行器概念研究--最优控制律问题

从一个天地往返飞行器的上升轨道和再入返回轨道的优化，以及适用不同飞行任务的变轨要求的气动外形问题，提出一项基于气动力辅助变轨的变气动外形飞行器的新概念研究。对于一个固定气动外形飞行器要同时满足上升轨道有效载荷最大和再入轨道热流峰值、过载峰值及机动性能约束下的成本最低往往是困难的。若同时满足不同飞行任务：飞往太空站的运输任务，空间拦截和交会机动巡航任务及星际探测任务，则更为困难，实际上是不可能的。文章研究基于气动力辅助变轨，在热流约束下，气动外形参数变化对最优控制的影响。其结论为：热流约束下的最优控制解，包括考虑推力协同变轨，除了在非约束弧的滚转角不直接受气动外形影响外，其余的控制律，升力系数和滚转角都是气动外形参数和攻角的函数。因而变气动外形可作为一项新技术，即通过气动外形参数变化和相应的变轨策略而获得性能和成本都最佳的用途很广的一种新型飞行器。     

Use of Optical Characteristics to Identify Orbiting Material

Knowledge of the observable properties of orbital debris is necessary to validate debris models for both the low Earth orbit (LEO) and the geosynchronous Earth orbit (GEO). Current methods determine the size and mass of orbital debris based on knowledge or assumption of the material type of the piece. Improvement in the knowledge of material is the goal of the research described herein. The process of using spectral absorption features to determine the material type is explored. A review of the optical measurements of orbital debris as well as current research in the area is discussed. Reflectances of common spacecraft materials are compared. The need for, and advances made possible by obtaining real data are explored. The prospects of the venture are investigated.     

Design of optimal earth pole-sitter transfers using low-thrust propulsion

Recent studies have shown the feasibility of an Earth pole-sitter mission using low-thrust propulsion. This mission concept involves a spacecraft following the Earth's polar axis to have a continuous, hemispherical view of one of the Earth's poles. Such a view will enhance future Earth observation and telecommunications for high latitude and polar regions. To assess the accessibility of the pole-sitter orbit, this paper investigates optimum Earth pole-sitter transfers employing low-thrust propulsion. A launch from low Earth orbit (LEO) by a Soyuz Fregat upper stage is assumed after which solar electric propulsion is used to transfer the spacecraft to the pole-sitter orbit. The objective is to minimize the mass in LEO for a given spacecraft mass to be inserted into the pole-sitter orbit. The results are compared with a ballistic transfer that exploits manifold-like trajectories that wind onto the pole-sitter orbit. It is shown that, with respect to the ballistic case, low-thrust propulsion can achieve significant mass savings in excess of 200 kg for a pole-sitter spacecraft of 1000 kg upon insertion. To finally obtain a full low-thrust transfer from LEO up to the pole-sitter orbit, the Fregat launch is replaced by a low-thrust, minimum time spiral, which provides further mass savings, but at the cost of an increased time of flight.     

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.     

飞船在大气层外飞行段的主要参数对轨道的影响

飞船返回地球时再入速度很大,过大的过载和气动加热率尤其对载人飞船带来安全性问题。如果利用航天器在大气层外及其边缘处多次再入运动,可降低速度、耗散热量。文章主要分析了载人飞船在大气层外多次再入飞行时的各主要参数对飞船轨道和轨道终点的影响。在分析过程中,首先建立了飞船在大气层外飞行的数学模型,进而通过大量的数值仿真得到一条基准轨道,在此基础上分别改变轨道起始点参数（倾角、偏航角和飞行速度）的初始值,分析轨道的特性及轨道的终点误差。最后根据起始点参数值和对应的轨道终点误差值的关系,得到了飞船在大气层外飞行时的起始参数对飞行轨道及轨道终点影响的敏感度,从而为工程上轨道的设计提供一个有效的参考依据。     

A preliminary study of pulse-laser powered orbital launcher

An air-breathing pulse-laser powered orbital launcher has been proposed as an alternative to conventional chemical launch systems. The aim of the present study is to assess its feasibility through the estimation of its achievable payload mass per unit beam power and launch cost. A transfer trajectory from the ground to a geosynchronous Earth orbit (GEO) is proposed, and the launch trajectory to its geosynchronous transfer orbit (GTO) is computed using the realistic performance modeled in the pulsejet, ramjet, and rocket flight modes of the launcher. Results show that the launcher can transfer 0.084 kg of payload per 1 MW beam power to a geosynchronous earth orbit. The cost becomes a quarter of existing systems if one can divide a single launch into 24,000 multiple launches.     

天基照相跟踪空间碎片批处理轨道确定研究

随着国内外天基观测空间碎片研究的展开,文章提出了利用跟踪卫星的CCD(Charge
Coupled Device)相机对空间碎片进行轨道探测的方法,首先建立了CCD照相观测模型和基于 照相观测 的空间碎片批处理轨道确定模型。通过对CCD相机底片归算方法的分析可知,利用
CCD相机所获得的观测数据与跟踪卫星的姿态无关,且其精度只与测量和坐标转换计算的精 度有关,在测量和计算中可获得较高的精度。分别对分布密度较高的低轨道和地球同步 轨道区域的空间碎片进行了定轨分析。仿真结果表明,定轨时采用两个跟踪弧段的照相数据 定轨精度大大高于一个弧段照相数据的定轨精度;跟踪卫星距离空间碎片越近,定轨精度越 高;低轨道空间碎片的定轨精度高于地球同步轨道上的空间碎片定轨精度。
     

Nonlinear feedback control of low-thrust orbital transfer in a central gravitational field

This paper investigates the problem of continuous-thrust orbital transfer using orbital elements feedback from a nonlinear control standpoint, utilizing concepts of controllability, feedback stabilizability and their interaction. Gauss's variational equations (GVEs) are used to model the state-space dynamics of motion under a central gravitational field. First, the notion of accessibility is reviewed. It is then shown that the GVEs are globally accessible. Based on the accessibility result, a nonlinear feedback controller is derived which asymptotically steers a spacecraft form an initial elliptic orbit to any given elliptic orbit. The performance of the new controller is illustrated by simulating an orbital transfer between two geosynchronous Earth orbits. It is shown that the low-thrust controller requires less fuel than an impulsive maneuver for the same transfer time. Closed-form, analytic expressions for the new orbital transfer controller are given. Finally, it is proven, based on a topological nonlinear stabilizability test, that there does not exist a continuous closed-loop controller that can transfer a spacecraft onto a parabolic escape trajectory.     

Single crystal mo solar thermal thruster for microsatellites

One potentially attractive propulsion concept offering significant payload gains for orbit transfer from LEO to higher orbits, station keeping and attitude control of spacecraft is thermal propulsion using light gas (typically hydrogen) as propellant and various kinds of heat energy. Solar Thermal Propulsion (STP) is a typical thermal propulsion with high Isp (500 – 1,000 s) in an appropriate thrust magnitude range and provides possibly much less space pollution than conventional chemical propulsion.

This paper presents the test results of a 30 mm dia. (medium-sized) windowless type of single crystal Mo thruster for orbit transfer of 50 kg class microsatellites. The cavity dia. is 20 mm, double the size of the previous model, and can apply to a primary solar reflector of up to 3.5 m dia., which is the maximum size containable in the H-II rocket fairing without segmentation. The performed mission analyses indicate that this size of STP is suitable to orbit transfer of 50 kg class microsatellites, such as LEO to GEO, or only multiple apogee kicks from GTO to GEO or deep space missions.     

小推力轨道保持方法

对小推力轨道保持方法进行了研究。用快、慢变量控制器分别控制轨道要素的快慢变量,基于推导的经典轨道要素与2个推力方向角和最佳变轨位置的关系,给出了最优推力方向角的解析表达式。用Lyapunov反馈控制实现卫星轨道机动的轨道转移,并引入相位调整,实现了卫星的站位保持。仿真结果表明:基于Lyapunov的反馈控制可实现小推力轨道的转移和保持。     

太阳帆日心定点悬浮转移轨道设计

研究了太阳帆航天器日心定点悬浮轨道(HFDO)的转移轨道设计问题,以球坐标形式建立了太阳帆的动力学模型,基于该模型给出在日心悬浮轨道基础上实现定点悬浮的条件,提出了一种实现日心定点悬浮的转移轨道设计方法。首先,确定定点悬浮的位置;然后,设计经过该位置的绕日极轨轨道;最后,实施轨道减速实现定点悬浮,并给出了解析形式的轨道控制律。结合太阳极地观测任务,设计了定点悬浮在太阳北极1AU处的太阳帆转移轨道。仿真结果表明:该轨道转移方案总耗时3.5年,太阳帆定点到黄北极距日心1AU处,此后只要保持太阳光垂直照射帆面,即可维持稳定的悬浮状态。     

MDO approach for early design of aerobraking orbital transfer vehicles

This paper presents a new multidisciplinary design optimization (MDO) methodology for preliminary design of an aeroassisted orbital transfer vehicle (AOTV) performing a two-way transfer between a low-Earth “parking” orbit and a high-energy orbit. This work has been performed in the frame of Onera's CENTOR [N. Bérend, C. Jolly, F. Jouhaud, D. Lazaro, Y. Mauriot, C. Monjaret, J.M. Moschetta, M. Parlier, J.L. Pastre, Y. Servouze, J.L. Vérant, Project CENTOR: Preparing the design of future orbital transfer vehicles; IAC-07-D.2.3.07, in: 58th International Astronautical Congress, 24–28/09/2007, Hyderabad, India] project whose objective is to prepare tools and methodology for studying and designing future space transportation systems for new kinds of missions such as on-orbit servicing (OOS), payload ferrying, or in-situ observation of space-debris. Using simplified models and an appropriate low-dimension formulation for the optimization problem the method makes possible to obtain rapidly and easily a global view of the trade-off between the payload mass and the total mass. It also makes possible to discuss the feasibility of the vehicle with regard to different multidisciplinary constraints and technology hypotheses for the heat shield. This approach is illustrated by eight different AOTV design studies, considering two different missions (LEO–MEO and LEO–GEO), two different propulsion technologies (LOX-LH2 and LOX-CH4) and two different thermal protection system (TPS) characteristics. In each case, we discuss the feasibility and characteristics of the lightest vehicle carrying a prescribed 100 kg payload, and, conversely, a heavy vehicle with a prescribed 18 ton total mass, carrying the heaviest possible payload.     

Analysis of the orbital motion of the asteroid Apophis’ satellite

We have analyzed the orbital disturbed spacecraft motion near an asteroid. The equations of the asteroidocentric spacecraft motion have been used with regard to three perturbations from celestial bodies, the asteroid’s nonsphericity, and solar radiation pressure. It has been shown that the orbital parameters of the main spacecraft and a small satellite with a radio beacon can be selected such that the orbits are rather stable for a fairly long period of time, i.e., a few weeks for the main spacecraft with an orbit initial radius of ~0.5 km and a few years before approaching Apophis with the Earth in 2029, for a small satellite at an orbit initial radius of ~1.5 km. The initial orientation of the spacecraft orbital plane perpendicular to the sunward direction is optimal from the point of view of the stability of the spacecraft flight near an asteroid.     

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 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.     

低轨Walker星座构型演化及维持策略分析

针对低轨(LEO)Walker星座构型维持问题，分析在地球非球形引力和大气阻力摄动下卫星的运动规律及星座构型演化特性。结果表明，低轨Walker星座构型发散主要体现在由初始轨道参数不一致引起的轨道高度衰减和相位漂移，国内首例低轨Walker星座实测轨道数据验证了理论分析的正确性。结合星座任务特性与构型发散特点，提出了基于基准卫星的相对相位维持策略，选取一颗卫星作为基准卫星，使星座中其它所有卫星相对于基准卫星的相位漂移量累加值最小，通过对目标卫星实施一次相对基准卫星的轨道高度抬升/降低，维持星间的相对位置关系。实际工程应用表明了此策略的有效性，不仅降低星座构型维持的复杂度及频次，节约燃料，且轨控时间短，为我国今后卫星星座的构型维持提供参考。     

气动辅助空间交会最优轨道设计与闭环导引律

给出了同平面HEO-LEO实现空间交会的必要条件;研究了基于气动辅助轨道转移技术实现同平面HEO-LEO的空间交会方案,通过设计一条标准的同平面HEO-LEO气动辅助轨道转移的最优轨迹,得到了轨道转移飞行器(OTV)与目标实现交会必须满足的标准相角;最后对大气飞行段设计了非线性最优闭环导引律,通过引入Lyapunov最陡下降函数,对函数中相应参数进行适当调整,使应用闭环导引律得到的大气内飞行轨迹与最优轨迹充分接近,仿真结果表明该气动辅助空间交会方法正确、可行。