Optimization of low-thrust orbit transfers with constraints

Approximate numerical methods of optimization are presented for multi-orbit noncoplanar orbit transfers of low-thrust spacecraft. The linear representation of derivatives of boundary parameters is used in the vicinity of a reference trajectory with its discretization into small segments. For each segment a set of pseudo-impulses is introduced, representing possible directions of the thrust vector. In order to solve essentially nonlinear problems, the iterative process of upgrading the reference trajectory is used. At each iteration the linear programming problem of high dimensionality is solved, its boundary conditions being represented in the form of a linear matrix equation. Interval constraints are considered in the form of blocking the propulsion system operation on shadow segments of the orbit, as well as cycling constraints, and constraints on total duration of maneuvers at certain trajectory segments. The results of comparison with solutions obtained by other methods are presented together with examples illustrating the convergence of iterative processes. Optimizations of the trajectories for launching geosynchronous satellites to their orbits and of the trajectories of a noncoplanar transfer from low to high-elliptic Molniya orbit are considered under these constraints.     

共面圆轨道最省燃料小推力多次变轨研究

本文研究两个共面圆轨道之间最节省燃料的多次变轨过程。通过分析，得到滑行段起点和终点之间的解析关系式，解决了变轨次数增加带来的计算问题。给出了从近地圆轨道到同面同步轨道的最优多次变轨的计算结果，并进行了分析和讨论     

面向GEO目标的快速在线在轨服务任务规划

针对地球同步轨道多对多在轨服务任务规划问题,提出了一种基于拍卖算法和先验知识的改进启发式拍卖算法(IHAA)。首先,建立了基于Lambert变轨的任务规划问题表征,设计了给定变轨时长约束下的快速燃料最优估计策略。其次,针对考虑J 2摄动影响的航天器在轨服务规划问题,提出了一种基于拍卖算法的快速求解流程。其中,为确定每一轮拍卖算法任务列表,提出了基于变轨先验知识的目标优先级排序启发式策略,实现了快速的服务时序确定方法;此外,为减少因部分航天器服务能力低导致的分配失败情况,设计了一种基于失败任务再分配的重拍机制。最后,将所提算法与遗传算法、模拟退火算法进行了对比,结果表明IHAA可以快速给出相对适应度较高的规划结果,可用于突发事件星上在线自主规划,亦可提供优化算法初值以提升规划效率。     

运载火箭推力故障下在线计算轻量化任务重构方法

为了避免运载火箭推力下降故障引起发射任务失败,基于径向基神经网络,提出了一种在线计算轻量化的任务重构方法,可快速在线计算最优救援轨道对应飞行轨迹(最优轨迹)的近似解.在离线部分,结合凸优化与自适应配点法产生"故障状态-最优轨迹"数据集.数据集被用来训练径向基神经网络,建立轨迹决策模型来构建故障状态到最优轨迹的动力学关系...     

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。     

Orbital manoeuvres of free flying platforms for retrieval by space shuttle

In a typical future mission a free flying platform will be released to space by Space Shuttle. After performing its active mission, it will have to wait for a suitable later Shuttle flight for retrieval at its original orbital altitude. To allow for the orbital descent during the total mission time of typically several months, one or several orbit raise manoeuvres have to be performed with the platform's own propulsion system. In the paper, the velocity-requirements Δv for these orbital transfers, depending on Sun activity, rendezvous-altitude, ballistic coefficient and longest expected mission time are treated.The simplest manoeuvre, consisting of one initial ascent transfer and one descent transfer at the actual retrieval date, is shown to be not optimal. Up to 25% of Δv can be saved, if several orbit raising transfers in a certain sequence are applied. A straightforward analytical treatment is presented for the optimization, while a computer program with the CIRA-atmosphere model is used for actual mission planning.     

地球同步轨道卫星群在轨加注任务规划

以地球同步轨道卫星群为研究对象,开展“多对多”在轨加注任务规划问题研究。首先建立了任务规划的数学模型,该任务规划属于多目标规划问题,求解过程中需要解决TSP问题。其次,给出了该规划问题的求解方法及流程,采用遗传算法进行求解并设计了相应的遗传算子。最后,选取了14颗地球同步轨道卫星作为目标星进行求解,并在小角度近似条件下对计算结果进行了分析,计算结果验证了算法的有效性。     

Optimal interplanetary rendezvous combining electric sail and high thrust propulsion system

The aim of this paper is to study, from a mission analysis point of view, the performance of a hybrid propulsion concept for a two-dimensional transfer towards a planet of the Solar System. The propulsion system is obtained by combining a chemical thruster, used for the phases of Earth escape and/or target planet capture, with an electric sail, which provides a continuous thrust during the heliocentric transfer. Two possible mission scenarios are investigated: in the first case the sailcraft reaches the target planet with zero hyperbolic excess velocity, thus performing a classical rendezvous mission in a heliocentric framework. In the second mission scenario, a given final hyperbolic excess velocity relative to the planet is tolerated in order to decrease the mission flight time. The amount of final hyperbolic excess velocity is used as a simulation parameter for a tradeoff study in which the minimum flight time is related to the total velocity variation required by the chemical thruster to accomplish the mission, that is, for Earth escape and planetary capture.     

基于脉冲初值的小推力转移轨道优化研究

针对小推力转移轨道优化过程往往忽略初值多样性的现状,研究了基于不同脉冲初值的小推力转移轨道优化问题。基于直接法的离散思想建立了小推力转移轨道优化模型,提出了基于粒子群和序列二次规划的组合优化算法,以地球1∶1共振近地小行星2016HO3交会任务为例,将3种典型的脉冲轨道作为初值设计了燃料最优小推力转移轨道。仿真结果表明:3种初值轨道优化得到了2个小推力转移发射窗口,两者燃料消耗差距不超过6%。不同的初值对小推力轨道的整体性能指标影响较小,但开关机时刻和推力方向的变化会产生较大差异,从而得到不同的最优控制曲线。     

太阳系边际探测飞行任务规划

针对太阳系边际探测任务，开展了星际多目标飞越的任务规划，采用小推力混合优化设计方法完成了基于借力飞行及电推进技术的行星际转移轨道联合优化设计，对比研究了面向日球层鼻尖和尾部探测的星际多目标探测飞行方案。研究表明，探测器在2024-2025年发射，可飞抵日球层鼻尖区域，在2027-2030年发射可飞抵日球层尾部区域，并可在2049年1月1日前飞离日心100 AU，实现太阳系边际空间的科学探测。其中日球层鼻尖探测任务探测器飞抵100 AU的位置位于鼻尖中心区域，可与旅行者1号、2号探测器形成有效互补。文章所用任务规划方法，可为太阳系边际探测的自主任务规划技术提供基础，相关研究成果能够为未来中国首次太阳系边际探测任务的实施提供有价值的参考。     

Electric transfer optimization for mars sample return mission

The aim of this paper is to analyse an alternative scenario for Mars Sample Return Orbiter mission, where electric propulsion is used for Earth-Mars and Mars-Earth heliocentric cruises and for Mars orbit insertion / escape transfers, whereas chemical propulsion is used for final Mars rendezvous. The problem consists in minimizing the initial vehicle mass to obtain a specific final dry mass in reasonable time. The planetocentric phases correspond to continuous low-thrust trajectories, spiraling around Mars between a low orbit and the influence sphere altitude. The heliocentric phases consist of a succession of low-thrust and coasting arcs with specific departure and arrival conditions at the Earth. For these two types of transfer, efficient optimal control tools exist based on Pontryagin's maximum principle. Thanks to the coordination between planetocentric and heliocentric phases, the solution obtained with these two separate tools gives a good upper bound of the optimal solution in terms of propellant consumption and duration. This optimization procedure is described and finally applied to the proposed mission. The numerical results are presented and compared with the baseline chemical mission solution. The electric option could allow to decrease the spacecraft departure mass but may lead to rather long mission duration.     

Mission analysis and systems design of a near-term and far-term pole-sitter mission

This paper provides a detailed mission analysis and systems design of a near-term and far-term pole-sitter mission. The pole-sitter concept was previously introduced as a solution to the poor temporal resolution of polar observations from highly inclined, low Earth orbits and the poor high-latitude coverage from geostationary orbit. It considers a spacecraft that is continuously above either the north or south pole and, as such, can provide real-time, continuous and hemispherical coverage of the polar regions. Being on a non-Keplerian orbit, a continuous thrust is required to maintain the pole-sitter position. For this, two different propulsion strategies are proposed, which result in a near-term pole-sitter mission using solar electric propulsion (SEP) and a far-term pole-sitter mission where the SEP thruster is hybridized with a solar sail. For both propulsion strategies, minimum propellant pole-sitter orbits are designed. In order to maximize the spacecraft mass at the start of the operations phase of the mission, the transfer from Earth to the pole-sitter orbit is designed and optimized assuming either a Soyuz or an Ariane 5 launch. The maximized mass upon injection into the pole-sitter orbit is subsequently used in a detailed mass budget analysis that will allow for a trade-off between mission lifetime and payload mass capacity. Also, candidate payloads for a range of applications are investigated. Finally, transfers between north and south pole-sitter orbits are considered to overcome the limitations in observations due to the tilt of the Earth's rotational axis that causes the poles to be alternately situated in darkness. It will be shown that in some cases these transfers allow for propellant savings, enabling a further extension of the pole-sitter mission.     

Rosetta: The ESA comet rendezvous mission

Rosetta was selected in November 1993 for the ESA Cornerstone 3 mission, to be launched in 2003, dedicated to the exploration of the small bodies of the solar system (asteroids and comets). Following this selection, the Rosetta mission and its spacecraft have been completely reviewed: this paper presents the studies performed the proposed mission and the resulting spacecraft design.

Three mission opportunities have been identified in 2003–2004, allowing rendezvous with a comet. From a single Ariane 5 launch, the transfer to the comet orbit will be supported by planetary gravity assists (two from Earth, one from Venus or Mars); during the transfer sequence, two asteroid fly-bys will occur, allowing first mission science phases. The comet rendezvous will occur 8–9 years after launch; Rosetta will orbit around the comet and the main science mission phase will take place up to the comet perihelion (1–2 years duration).

The spacecraft design is driven (i) by the communication scenario with the Earth and its equipment, (ii) by the autonomy requirements for the long cruise phases which are not supported by the ground stations, (iii) by the solar cells solar array for the electrical power supply and (iv) by the navigation scenario and sensors for cruise, target approach and rendezvous phases. These requirements will be developed and the satellite design will be presented.     

微纳卫星星座的Kuhn-Munkres匹配部署优化方法

针对将半长轴、升交点赤经、纬度辐角均不同的低轨微纳卫星群部署到同一轨道面不同目标相位的星座部署问题，提出一种基于Kuhn Munkres(KM)匹配的星座部署优化方法。通过KM算法实现卫星和目标纬度辐角的优化匹配，充分利用J 2摄动，使升交点赤经借助半长轴和纬度辐角的部署而得到同步修正，从而节约燃料。仿真结果表明，相比于传统部署方法，在相同约束下，优化后的部署方法使各星平均燃耗减少，各星燃耗量均衡性提高。弥补了传统同轨星座部署中将各星初始位置简化为空间一点且忽略部署过程中的升交点赤经漂移的不足。采用有限常值推力实现轨道机动，适用于携带微推力推进系统的微纳卫星。     

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.     

登月舱用深度变推下降级发动机系统方案研究

在我国的载人登月技术方案中,为实现软着陆,登月舱需要一种大推力、高性能、多次起动,能够大范围变推力的泵压式发动机.通过研究国外登月用下降级发动机技术发展现状和趋势,基于我国氢氧发动机和低温推进剂空间贮存水平,进行了深度变推发动机的系统方案研究;通过分析比对燃气发生器循环和膨胀循环系统优缺点,确定发动机系统方案为涡轮串联闭式膨胀循环;采用空间可长时间贮存的液氧/甲烷推进剂组合,可满足任务周期要求;根据推力深度调节时对各组合件性能要求,确定喷注器燃烧稳定技术和燃烧室身部传热技术是深度变推发动机研制的核心关键技术.     

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.     

Optimization of transfer trajectories to the Apophis asteroid for spacecraft with high and low thrust

The problem of optimization of a spacecraft transfer to the Apophis asteroid is investigated. The scheme of transfer under analysis includes a geocentric stage of boosting the spacecraft with high thrust, a heliocentric stage of control by a low thrust engine, and a stage of deceleration with injection to an orbit of the asteroid’s satellite. In doing this, the problem of optimal control is solved for cases of ideal and piecewise-constant low thrust, and the optimal magnitude and direction of spacecraft’s hyperbolic velocity “at infinity” during departure from the Earth are determined. The spacecraft trajectories are found based on a specially developed comprehensive method of optimization. This method combines the method of dynamic programming at the first stage of analysis and the Pontryagin maximum principle at the concluding stage, together with the parameter continuation method. The estimates are obtained for the spacecraft’s final mass and for the payload mass that can be delivered to the asteroid using the Soyuz-Fregat carrier launcher.     

不同月球借力约束下的地月Halo轨道转移轨道设计

针对地月系L2点不同任务需求下的低耗能转移轨道设计问题,基于不变流形理论与混合优化技术,深入研究了不同月球借力约束与不同幅值Halo轨道的入轨点（简称HOI点）对转移轨道飞行时间与燃料消耗的影响,给出了HOI点选择策略。首先结合任务要求并考虑月球引力影响,在月球借力点施加不同约束条件,通过微分修正算法调整Halo轨道的稳定流形,设计月球到Halo轨道的转移轨道。采用遗传算法与微分修正算法相结合的混合优化策略,在同时考虑地球停泊轨道高度、倾角、升交点赤经与航迹角等多约束条件下,对燃料最优的地月转移轨道进行研究。最后,分析月球借力高度、借力方位角和不同HOI点对平动点转移轨道飞行时间与燃耗变化量的影响,对于考虑月球借力的地月平动点转移轨道设计与应用具有重要的参考价值。     

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。