Rapid design and optimization of low-thrust rendezvous/interception trajectory for asteroid deflection missions

Asteroid deflection techniques are essential in order to protect the Earth from catastrophic impacts by hazardous asteroids. Rapid design and optimization of low-thrust rendezvous/interception trajectories is considered as one of the key technologies to successfully deflect potentially hazardous asteroids. In this paper, we address a general framework for the rapid design and optimization of low-thrust rendezvous/interception trajectories for future asteroid deflection missions. The design and optimization process includes three closely associated steps. Firstly, shape-based approaches and genetic algorithm (GA) are adopted to perform preliminary design, which provides a reasonable initial guess for subsequent accurate optimization. Secondly, Radau pseudospectral method is utilized to transcribe the low-thrust trajectory optimization problem into a discrete nonlinear programming (NLP) problem. Finally, sequential quadratic programming (SQP) is used to efficiently solve the nonlinear programming problem and obtain the optimal low-thrust rendezvous/interception trajectories. The rapid design and optimization algorithms developed in this paper are validated by three simulation cases with different performance indexes and boundary constraints.     

一类最省燃料优先的多圈飞行脉冲交会

通过分析采用多圈飞行Lambert解的双脉冲交会的特征速度与转移轨道半长轴的关系,指出其最优解实际上是2N+1条满足时间约束的转移轨道中燃料较省的,而非最省燃料轨道.提出将双脉冲交会的首次脉冲矢量分解成方向相同的两次脉冲,使得追踪器在特定的滑行轨道飞行N圈以消耗多余的转移时间,利用剩余的转移时间沿最省燃料轨道与目标交会.几何上证明了这种交会的特征速度与最省燃料转移相同,并且给出了解的存在性条件.通过仿真验证了这种交会比采用多圈飞行Lambert解的双脉冲交会更省燃料,解的存在性对转移时间的长度要求更低.     

交会对接自由漂移轨迹安全性判断研究

针对长方形禁飞区下,近距离交会对接过程提出任意初始状态下轨迹安全的判断方法.先分析CW方程描述下相对运动轨迹的性质,通过分析轨迹与禁飞区最可能相交的特征点的分析和轨迹越过禁飞区相交问题的判断,判断轨迹是否安全.仿真结果表明所提出的安全判断方法能准确给出轨迹是否安全的结论,且算法简单、计算量小.     

最优气动力辅助空间拦截和交会

航天器从高轨道向位于低地球圆轨道的靶目标实施拦截或进行交会 ,并用间接求解的直接伴随方法 ,即用D型拉格朗日方法求解其优化问题。拦截条件是指在最终时刻两者的位置相同 ,而交会条件是指不仅位置相同且最终的速度矢量亦相等。文章讨论了最小时间与最小脱靶量 ,或最小时间与最小燃料消耗的复合性能指标 ,以及推力协同机动的优化解。推力协同下 ,对于特定情况 ,如在热流约束边界部分推力弧是奇异的 ,气动力控制是正常的。这种复杂性和奇异问题的求解在拦截和交会问题中都是值得慎重处理的。     

广义多圈Lambert算法求解多脉冲最优交会问题

基于一种高效高精度的Battin多圈Lambert算法提出一种考虑轨道摄动的广义多圈Lambert算法.与现有算法相比,本算法虽然原理复杂但计算流程非常简单,效率极高,分别通过几次内外循环就可满足精度要求.广义多圈Lambert算法结合一种可行解迭代交会模型构成了一个通用的多圈多脉冲交会规划框架,应用两步法求解此多变量的复杂工程优化问题,首先利用高效率的进化全局优化算法以及解析轨道模型作全局搜索,然后利用序列二次规划算法以及简化高精度轨道计算模型作局部搜索,此方法可以保证高效高精度的求解多圈多脉冲交会问题.算例表明此方法特别适用于满足实际工程约束的交会规划问题.     

能量最优与燃料最优Lambert交会问题

Lambert双脉冲交会问题是航天工程中轨道转移和在轨交会等领域的重要问题,而能量最优和燃料最优Lambert交会问题是针对典型应用背景和工程需求衍生的一类Lambert优化问题。针对能量最优与燃料最优Lambert双脉冲交会问题提出一种基于矢量形式的解析计算方法,给出能量最优和燃料最优Lambert交会问题的矢量形式解析解,同时对2种最优交会问题求解的性质与特点进行了分析对比。仿真结果验证了计算的正确性及燃料最优轨道相比能量最优轨道燃料消耗较少的事实。      

月球探测器发射机会分析

发射月球探测器实际上是使探测器与月球交会的问题,由于月球位置的变化,选择不同的交会日期相应的地月转移轨道是不相同的。文章分析了月球在一个恒星月内位置变化与相应的地月转移轨道升交点赤经和近地点幅角变化的关系,在这个基础上讨论了发射机会和发射窗口问题。     

Optimal two-impulse rendezvous with terminal tangent burn considering the trajectory constraints

The two-impulse orbital rendezvous problem with a terminal tangent burn between coplanar elliptical orbits is studied by considering a lower bound on perigee radius and an upper bound on apogee radius for the transfer orbit. This problem requires that two spacecraft arrive at the rendezvous point with the same arrival flight-path angle after the same flight time. The admissible range of the final true anomaly that meets the perigee and apogee constraints is obtained in closed form. The revolution number of the transfer orbit is expressed as a function of the true anomaly and the revolution numbers of the initial and final orbits. All the feasible solutions are obtained with a bound on the revolution number of the final orbit. Then, the minimum-fuel one is determined by comparing their costs. Finally, two numerical examples are provided to obtain all the feasible solutions for given initial impulse points and the optimal solution with the initial coasting arc. Numerical results show that the minimum-fuel solution for the terminal tangent burn rendezvous is close to that for the cotangent rendezvous when the rendezvous time is long enough; however, the cotangent rendezvous may not exist when the rendezvous time is short.     

燃料受限的时间最优多脉冲交会问题

主要研究了时间最优多脉冲交会问题中最优交会时间和最优脉冲数随各因素的变化规律.建立了考虑路径约束的数学模型,并利用遗传算法对问题进行了求解.在此基础上通过大量的数值计算研究了共面圆轨道间交会问题中各因素(包括轨道半径比、初始相位差、燃料以及路径约束)对最优交会时间和最优脉冲次数的影响,并总结出了最优交会时间和最优脉冲数随各因素的变化规律.根据最优交会时间随各因素变化的曲线较为"平缓"(均为单调或只有一个极值)的事实,指出可以利用较少的特征点通过插值的方法来快速求解最优交会策略.结论对于空间营救和在轨规避等实际任务的轨道设计具有一定的参考价值.     

Trajectory optimization of multiple asteroids exploration with asteroid 2010TK7 as main target

In this study, the Earth’s Trojan asteroid 2010 TK₇ is selected as the rendezvous target. The multiple flyby sequence of asteroid exploration was proposed by optimizing the probe’s orbit. Impulsive maneuvers and low-thrust propulsion were used respectively to design the trajectories of the multiple asteroids exploration mission. Under impulsive maneuvers, gravity assist technique was adopted to reduce fuel consumption. First a reference orbit with only 2010 TK₇ as the rendezvous target was designed. Then five asteroids near the reference orbit were selected as candidates. Finally, we obtained a multiple asteroids exploration sequence of three asteroids based on gravity assist technique and genetic algorithm, and an additional velocity impulse of 0.4?km/s was required. In the subsequent section, a sixth-degree inverse polynomial shape-based method is applied to the low-thrust trajectory design of 2010 TK₇, and the exploration sequence under the action of low-thrust propulsion was provided.     

Four-body cislunar quasi-periodic orbits and their application to ballistic lunar transfer design

Examining the properties of quasi-periodic orbits provides insight into the Sun-perturbed environment in cislunar space. In this investigation, quasi-periodic trajectories and their properties are explored in the Sun-Earth-Moon four-body problem. Computation and the stability characteristics of families of invariant tori are detailed. Furthermore, this investigation offers a framework for construction of ballistic lunar transfer trajectories in the four-body problem. The framework leverages manifold trajectories to supply a set of initial conditions for construction of periapsis Poincaré maps. Periapsis maps reduce the dimensionality of the space and illuminate solutions of interest as a basis to produce feasible families of transfers. Through a continuation process, families of ballistic transfers and families of transfers that include powered lunar flybys are constructed. Ultimately, these solutions supply an initial guess for transition to the Sun-Earth-Moon ephemeris model.     

天舟二号货运飞船全相位自主快速交会对接技术和在轨验证

介绍天舟二号货运飞船全相位自主快速交会对接技术和在轨飞行结果.介绍21世纪以来交会对接发展的两个趋势：自主和快速;给出天舟二号货运飞船全相位自主快速交会对接方案,以及主要技术特点;给出天舟二号货运飞船5~8 h飞控实施方案和推迟一天发射的飞控实施方案,以及在轨执行效果.天舟二号货运飞船入轨自主快速交会对接是世界上首次进行的全自主快速交会对接任务,为我国空间站工程后续任务奠定了坚实的技术基础.     

基于时域映射的多无人机系统给定时间分布式最优集结

针对多无人机系统给定时间最优集结问题,建立了基于时域映射的分布式优化框架。首先,引入一类特殊的时域映射,将原时域的给定时间决策问题转化为了无限域中的渐近稳定问题,简化了分析设计流程。其次,进一步设计了给定时间梯度下降算法,其收敛时间与系统初始条件及其他参数无关,能够被预先给定,且算法时变增益的使用消除了参数选择过程,在全局信息严重匮乏的情况下仍然适用。仿真结果表明:所提方法能够在给定时间内实现多无人机分布式最优集结,并保证任务时间内闭环系统全局有界。      

Phasing with near rectilinear Halo orbits: Design and comparison

In the next future, space agencies are planning to return to the Moon. The objective is to assemble an orbiting space station, called Gateway, on a Near Rectilinear Halo Orbit around the Moon as a base for future Moon and deep space missions. Within this framework, multiple side missions will be planned to sustain the Gateway (Artemis mission). The proposed work is thought in framework of the preliminary design of future cargo missions, in particular on the design of an efficient phasing trajectory, under the Circular Restricted Three body problem hypotheses, to bring a cargo vehicle from the end of the Earth-Moon transfer to the beginning of the proximity operations such as rendezvous and docking with the space station. The work aims covering the lack of literature in phasing trajectories with the NRHO by proposing three different strategies to connect the Earth-Moon transfer trajectory with the proximity operations. The three strategies are classified based on the choice of the parking orbits or the choice of the manifolds. Two strategies use butterfly and Halo orbits to park the vehicle before transferring to the target orbit. The third strategy, instead, uses manifolds to allow a direct phasing. In the paper, the three innovative strategies are designed and compare in a specific scenario.     

环月轨道交会的载人登月任务轨道与窗口规划

针对环月轨道(Low Lunar Orbit,LLO)共面交会支持的"人货分离"载人登月任务,提出了一种任务窗口与轨道一体化规划方法。分析了基于LLO共面交会的"人货分离"载人登月任务的基本流程和工程约束;针对任务各阶段窗口与轨道求解问题,提出了以动力下降时刻为迭代初值的窗口规划策略,并建立了高精度模型下的环月轨道、双二体模型下的人员和货物运输轨道规划模型。以载人月球探测中国科学家命名的环形山为假想背景,给出仿真实例,仿真结果验证了文章所提方法的正确性,为探月工程任务提供了一种有效的窗口与轨道设计工具。     

空间交会策略回顾及自主快速交会方案研究

介绍了已实施的几种典型的空间交会策略.通过分析现在的2~3d交会方案以及国外最新发展的4圈快速交会方案,总结了实现快速交会所要解决的主要技术问题.针对中国空间交会技术的发展需求,提出了一种自主快速交会方案.对比现有的4圈快速交会方案,该方案所允许的追踪航天器和目标航天器的初始相位角范围大大增加,但燃料消耗基本保持不变,这对开展实际工程有较好的指导意义.     

A new class of intermediate thrust arcs in the restricted three-body problem

The Mayer’s variational problem of determining spacecraft optimal trajectories in the context of a classical restricted three-body problem is considered. Integrability of differential equations of a controllable motion in the non-central gravitational field represents well known and challenging task. It is shown that in the absence of sufficient number of first integrals, an explicit dependability of unknown integrals on certain variables can be used to explore the existence of previously unknown particular integrals and solutions of these equations utilizing Dokshevich’s method of analytical dynamics. A new class of extremal analytical solutions of the problem for intermediate thrust arcs is presented. An illustrative example of utilizing these solutions in minimizing the spacecraft characteristic velocity of a transfer from a specified initial position to some final position in the Earth-Moon system is discussed.     

多冲量近程交会最优化模型

文章基于Lawden方程对椭圆参考轨道的近程最优交会问题进行了研究,并提出了一种混合遗传算法求解最优近程交会问题。首先在一定假设条件下给出了目标在椭圆参考轨道的近距离相对运动模型——Lawden方程,构建了多脉冲最优交会问题模型并进行了理论分析。性能指标选为轨道交会过程中燃料消耗和时间消耗加权最小的多目标优化指标,优化参数为脉冲大小和脉冲施加时刻,终端状态受到相对位置和相对速度的约束。然后介绍了具有较强全局和局部寻优能力的混合遗传算法。最后以四脉冲为例进行仿真计算。仿真结果表明,是否考虑第一次脉冲位置,总燃料消耗变化不明显。因此,追踪航天器一旦捕获到目标信息即可施加第一次脉冲。仿真结果还证明了混合遗传算法在求解最优交会问题时的有效性。因此,混合遗传算法对基于Lawden方程的椭圆参考轨道近程最优交会问题的求解可行。     

基于引导型人工免疫算法的最优Lambert变轨

主要研究了燃料最省的Lambert双脉冲变轨问题.首先对普适变量法进行改进以避免奇异,并将其用于Lambert双脉冲变轨问题的求解.然后针对只给定初始时刻追踪航天器和目标航天器的轨道要素及总时间约束的交会问题,引入调相时间的概念,并将其和转移时间作为Lambert变轨的优化变量.最后采用引导型人工免疫算法GAIA(Guiding Artificial Im-mune Algorithm)对该优化问题进行寻优.仿真算例表明,与自适应遗传算法AGA(Adaptive Ge-netic Algorithm)相比,GAIA具有更强的寻优能力和更快的寻优速度,从而验证了GAIA用于最优Lambert变轨的有效性.     

Two-segment lunar free-return trajectories design using the pseudostate theory

Accurate initial solutions for two-segment Earth-Moon free-return trajectories, with midcourse transfer opportunities for favorable lunar targeting, are developed analytically by using the pseudostate theory. A constrained flight-path angle quasi-Lambert problem is formulated to determine the lunar-orbiting phase of the free-return trajectory. Gradient and direct-shooting algorithms are used to correct the initial estimates of certain two-body parameters. Numerical simulations with a high-fidelity model are undertaken to verify the accuracy of the pseudostate solutions and to illustrate the efficiency of the proposed algorithm. Perilune altitude errors for the pseudostate method are less than 10% of their corresponding values for the patched conic technique. The differences between the pseudostate and the high-fidelity solutions can be eliminated rapidly.