考虑地球扁率效应的两圆轨道之间的双共切最优转移

两圆轨道之间的双共切转移轨道是其近地点和远地点分别在这两个圆轨道上的椭圆轨道。本文用两次冲量法给出了沿双共切椭圆轨道实现从一圆轨道向另一圆轨道转移的最优方案，并考虑到地球扁率造成的轨道摄动。文中的所谓圆轨道指的是变轨时刻的密切轨道为圆形的轨道，是对近圆轨道的近似替找。     

地月低能轨道转移的混沌控制方法

针对航天器在混沌区域的滑行时间过长，提出一种低能地月轨道转移的混沌控制方法。首先通过地月圆形限制性三体问题(CRTBP)的庞加莱截面图，将混沌区域进行分层并分析其规律，再利用混沌轨道对初始状态高度敏感的特性，在尽可能减少运送时间的前提下实现地月低能轨道转移。该方法的优点是利用混沌区域的固有规律，不需要依靠周期轨道特性。仿真结果表明，本文提出方法仅需施加2~4次脉冲，明显缩短混沌区域的滑行时间，从而实现地月低能转移。     

考虑J_2摄动作用的异面椭圆轨道双冲量交会轨道修正方法

重点研究了地球扁率J2摄动作用对固定时间双冲量异面椭圆轨道交会运动的影响以及相应的轨道修正方法.根据摄动理论,利用Eneke法计算了J2摄动作用引起的实际飞行轨迹与理论标称轨迹之间的位置偏差.在此基础上,提出了通过修正预定的交会位置来修正转移轨道偏差的控制方法.通过仿真计算,对修正前后的位置偏差进行了仿真分析,结果表明,文中提出的轨道修正方法能够有效地减小摄动作用引起的制导误差,且方法简洁、易于实现.     

Inter-orbital low-thrust transfers in an arbitrary field of forces

Low-thrust transfers between preset orbits are considered in the presence of perturbations of different origin. A simple method of finding the transfer trajectory is suggested, based on linearization of motion near reference orbits. The required accuracy of calculations is achieved by way of increasing the number of reference orbits. The method can also be used in the case of a large number of revolutions around the attracting center: no averaging of motion is required in this case. The suggested method is applicable as well, when the final orbit is specified partially and when there are constraints on the thrust direction. The optimal solution to the linearized problem is not optimal for the original problem; closeness of solutions to these two problems is estimated using a numerical example. Capabilities of the method are also illustrated by examples.     

Qualitative Properties of Orbits for Minimum-Fuel Impulsive Transfers between Circular Coplanar Orbits with a Given Launch Time

The coplanar problem of minimizing propellant consumption in impulsive transfer between circular boundary orbits is investigated. The launch time and the initial configuration of objects on the boundary orbits are specified arbitrarily. The qualitative properties of optimal two-impulse trajectories and their optimality in the class of multi-impulse transfers are studied.     

Particle swarm optimization applied to impulsive orbital transfers

The particle swarm optimization (PSO) technique is a population-based stochastic method developed in recent years and successfully applied in several fields of research. It mimics the unpredictable motion of bird flocks while searching for food, with the intent of determining the optimal values of the unknown parameters of the problem under consideration. At the end of the process, the best particle (i.e. the best solution with reference to the objective function) is expected to contain the globally optimal values of the unknown parameters. The central idea underlying the method is contained in the formula for velocity updating. This formula includes three terms with stochastic weights. This research applies the particle swarm optimization algorithm to the problem of optimizing impulsive orbital transfers. More specifically, the following problems are considered and solved with the PSO algorithm: (i) determination of the globally optimal two- and three-impulse transfer trajectories between two coplanar circular orbits; (ii) determination of the optimal transfer between two coplanar, elliptic orbits with arbitrary orientation; (iii) determination of the optimal two-impulse transfer between two circular, non-coplanar orbits; (iv) determination of the globally optimal two-impulse transfer between two non-coplanar elliptic orbits. Despite its intuitiveness and simplicity, the particle swarm optimization method proves to be capable of effectively solving the orbital transfer problems of interest with great numerical accuracy.     

地月空间NRHO与DRO在月球探测中的应用研究

针对地月系统三体问题低能往返轨道转移在月球探测中的应用研究，结合天体借力飞行技术与混合优化技术，系统分析了不同目标轨道与借力方位对任务飞行时间与燃料消耗等关键参数的影响，给出了往返轨道设计初值的选择策略。针对轨道设计初值猜想问题，首先采用遗传算法与二体Lambert转移快速确定轨迹拼接点初值。在同时考虑近月点与近地点多约束条件下，基于序列二次规划算法与多重打靶法进一步对燃料最优的地月往返轨道进行研究，并推导了约束方程解析梯度提高设计效率。最后分析近月点高度、不同目标轨道的转移时间与燃耗变化特性，对于考虑月球借力的地月空间轨道往返转移设计及参数选取具有重要的参考价值。     

Design of transfer trajectories between resonant orbits in the Earth–Moon restricted problem

The application of dynamical systems techniques to mission design has demonstrated that employing invariant manifolds and resonant flybys enables previously unknown trajectory options and potentially reduces the ΔV$\mathrm{\Delta }V$ requirements. In this investigation, planar and three-dimensional resonant orbits are analyzed and cataloged in the Earth–Moon system and the associated invariant manifold structures are computed and visualized with the aid of higher-dimensional Poincaré maps. The relationship between the manifold trajectories associated with multiple resonant orbits is explored through the maps with the objective of constructing resonant transfer arcs. As a result, planar and three-dimensional homoclinic- and heteroclinic-type trajectories between unstable periodic resonant orbits are identified in the Earth–Moon system. To further illustrate the applicability of 2D and 3D resonant orbits in preliminary trajectory design, planar transfers to the vicinity of L₅ and an out-of-plane transfer to a 3D periodic orbit, one that tours the entire Earth–Moon system, are constructed. The design process exploits the invariant manifolds associated with orbits in resonance with the Moon as transfer mechanisms.     

从地球到日-火系平动点轨道的转移

平动点轨道特殊的空间位置及动力学特征,使其在深空探测中具有重要的应用。以日-火系平动点轨道(Lissajous与Halo轨道)任务为目标,结合平动点轨道的不变流形理论,研究了小推力转移问题。首先给出了圆型限制性三体动力学模型下平动点附近不变流形(稳定和不稳定流形)高阶分析解以及相应的计算实例。接着以流形分析解为基础,建立了初始小推力轨道优化模型,并利用改进的协作进化算法求解初始小推力轨道。最后将初始轨道离散,采用多点打靶法将最优控制问题转化为参数优化问题,并用序列二次规划方法(SQP)求解。仿真结果证明轨道设计方法的有效性。     

Applications of multi-body dynamical environments: The ARTEMIS transfer trajectory design

The application of forces in multi-body dynamical environments to permit the transfer of spacecraft from Earth orbit to Sun–Earth weak stability regions and then return to the Earth–Moon libration (L₁ and L₂) orbits has been successfully accomplished for the first time. This demonstrated that transfer is a positive step in the realization of a design process that can be used to transfer spacecraft with minimal Delta-V expenditures. Initialized using gravity assists to overcome fuel constraints; the ARTEMIS trajectory design has successfully placed two spacecrafts into Earth–Moon libration orbits by means of these applications.     

A new universal equation for the time of transfer between two points of the central gravitational field

The paper presents the derivation of two new equations for calculating the time of transfer between two points of the central gravitational field: for hyperbolic orbits and the universal equation for elliptical and hyperbolic orbits. In the paper we have used as an independent variable, instead of the linear elements (semimajor axis, focal parameter of orbit or a chord connecting the ends of boundary radii of transfer), the angular parameter—the angle between the radius vector of an initial point of transfer and the vector of initial velocity of transfer. Paper’s material is a continuation of that presented in the “Space research“ Journal, vol. 2, March–April, 2009.     

椭圆轨道拱线相位调节方法研究

分析了两个大小相同、拱线不同的椭圆轨道问的轨道转移,研究了单脉冲转移和双脉冲对称转移方法。用遗传算法解决了对称转移方法中最优变轨点的位置确定,获得了对称转移问题的数值解。仿真结果表明：对称转移较单脉冲转移更省能量。     

A low-thrust transfer between the Earth–Moon and Sun–Earth systems based on invariant manifolds

A low-energy, low-thrust transfer between two halo orbits associated with two coupled three-body systems is studied in this paper. The transfer is composed of a ballistic departure, a ballistic insertion and a powered phase using low-thrust propulsion to connect these two trajectories. The ballistic departure and insertion are computed by constructing the unstable and stable invariant manifolds of the corresponding halo orbits, and a complete low-energy transfer based on the patched invariant manifolds is optimized using the particle swarm optimization (PSO) algorithm on the criterion of smallest velocity discontinuity and limited position discontinuity (less than 1 km). Then, the result is expropriated as the boundary conditions for the subsequent low-thrust trajectory design. The fuel-optimal problem is formulated using the calculus of variations and Pontryagin's Maximum Principle in a complete four-body dynamical environment. Then, a typical bang–bang control is derived and solved using the indirect method combined with a homotopic technique. The contributions of the present work mainly consist of two points. Firstly, the global search method proposed in this paper is simply handled using the PSO algorithm, a number of feasible solutions in a fairly wide range can be delivered without a priori or perfect knowledge of the transfers. Secondly, the indirect optimization method is used in the low-thrust trajectory design and the derivations of the first-order necessary conditions are simplified with a modified controlled, restricted four-body model.     

水平推力作用下共面椭圆轨道的最优转移

本文研究在两次水平推力作用下共面椭圆轨道的转移问题,给出了冲量大小和作用点位置的计算公式,文中还讨论了圆到圆、椭圆到圆这两种特殊情况的轨道转移,并给出了数值例子。     

长征三号甲系列运载火箭高适应性发展——从总体与导航制导控制的视角

从总体与导航制导控制的视角,对长征三号甲系列运载火箭发展与成就进行了分析和小结。长征三号甲系列运载火箭,在长征三号运载火箭解决我国发射高轨道卫星有无问题的基础上,历经基本能力、适应能力、高适应能力的发展,具备了高轨道大型卫星运载能力,突破了从单一轨道面到三维空间各种轨道发射、从高轨卫星转移轨道到工作轨道发射、从地球轨道到地月轨道发射以及从航天技术试验到高可靠工程应用发射等关键技术,使我国运载火箭整体能力取得了地球全轨道发射、星际轨道发射等跨越发展。航天重大工程和国际商业发射表明,该系列运载火箭已进入世界高轨道航天器发射的运载火箭前列,并奠定了进一步开拓发展的基础。     

Optimal low-thrust transfer between neighbouring quasi-circular orbits around an oblate planet

The problem of optimal low-thrust, limited power transfer between quasi-circular orbits (e 0) around an oblate planet is analysed. It is assumed that the orbital changes due to thrust acceleration and Earth oblateness are of the same order. A first order solution to the problem is obtained by application of Pontryagin's Maximum Principle. Subsequently, by application of Hori's method for generalized canonical systems, a first order solution in a small parameter ε is derived. Finally, three particular cases of long-time transfer and the orbit maintenance manoeuvre are considered. The results obtained are in agreement and represent an extension of the work done by Marec.     

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。
     

Ground assisted rendezvous with geosynchronous satellites for the disposal of space debris by means of Earth-oriented tethers

Previous studies have shown that extended length Earth-oriented tethers in the geosynchronous (GEO) region can be used to re-orbit satellites to disposal orbits. One such approach involves the extension of a GEO based tether, collection of a debris object, and retraction of the tether, which transfers the retracted configuration to a higher energy orbit for debris disposal. The re-extension of the tether after debris disposal returns the configuration to the near-GEO altitude. The practical feasibility of such a system depends on the ability to collect GEO debris objects, attach them to a deployed tether system, and retract the tethers for transfer to the disposal orbits.This study addresses the collection and delivery of debris objects to the deployed tether system in GEO. The investigation considers the number, type and the characteristics of the debris objects as well as the collection tug that can be ground controlled to detect, rendezvous and dock with the debris objects for their delivery to the tethers system.A total of more than 400 objects are in drift orbits crossing all longitudes either below or above the geostationary radius. More than 130 objects are also known to librate around the stable points in GEO with periods of libration up to five or more years. A characterization of the position and velocity of the debris objects relative to the collection tug is investigated. Typical rendezvous performance requirements for uncooperative GEO satellites are examined, and the similarities with other approaches such as the ESA's CX-OLEV commercial mission proposal to extend the life of geostationary telecommunication satellites are noted.     

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...