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。     

最优双冲量交会问题的数学建模与数值求解

基于普适变量法研究了两个共面轨道的最优双冲量交会问题。具体地,基于求解Lambert问题的普适变量法,在将给定时间段划分初始飘移阶段、轨 道转移阶段与终端停泊阶段的前提下,对两圆轨道及两拱线相同的椭圆轨道的最优双冲量交 会问题分别进行了优化数学建模,并利用数学软件Lingo进行了数值求解。数值结果表明,划分给定时间段可以得到更优解。
     

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.     

大范围轨道机动的燃料消耗优化方法

针对航天器大范围轨道交会提出了二冲量燃料最省机动方案的数值寻优算法及多冲量机动方案的啸声境遗传算法.利用共面圆\椭圆轨道间的转移实例对两种算法正确小生境遗传算法.利用共面圆\椭圆轨道间的转移实例对两种算法正确性进行了验证,通过仿真实验,比较了大范围交会轨道机动中不同冲量次数对总燃料消耗的影响,分析得出了非共面轨道交会机动时燃料最省的指导性方案.     

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。
     

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.     

小行星探测最优两脉冲交会轨道设计与分析

小行星探测已经成为新世纪深空探测的一个新热点和未来世界航天发展的一个新方向。转移轨道的设计和探测目标可接近性的分析是小行星探测的关键技术之一。现利用了任意两个非共面非共轴椭圆轨道之间的最优两脉冲转移方法，对我国提出的探测Ivar小行星的交会转移轨道进行了设计与分析，给出了全局最优两脉冲交会轨道的设计参数，并利用此方法对近地小行星的可接近性进行了分析和排序，给出了可接近性较好的40颗近地小行星的转移轨道设计参数。这些研究结果对于近地小行星探测任务的目标选择和发射机会的预测都有重要的参考价值。     

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.     

Biobjective planning of GEO debris removal mission with multiple servicing spacecrafts

The mission planning of GEO debris removal with multiple servicing spacecrafts (SScs) is studied in this paper. Specifically, the SScs are considered to be initially on the GEO belt, and they should rendezvous with debris of different orbital slots and different inclinations, remove them to the graveyard orbit and finally return to their initial locations. Three key problems should be resolved here: task assignment, mission sequence planning and transfer trajectory optimization for each SSc. The minimum-cost, two-impulse phasing maneuver is used for each rendezvous. The objective is to find a set of optimal planning schemes with minimum fuel cost and travel duration. Considering this mission as a hybrid optimal control problem, a mathematical model is proposed. A modified multi-objective particle swarm optimization is employed to address the model. Numerous examples are carried out to demonstrate the effectiveness of the model and solution method. In this paper, single-SSc and multiple-SSc scenarios with the same amount of fuel are compared. Numerous experiments indicate that for a definite GEO debris removal mission, that which alternative (single-SSc or multiple-SSc) is better (cost less fuel and consume less travel time) is determined by many factors. Although in some cases, multiple-SSc scenarios may perform worse than single-SSc scenarios, the extra costs are considered worth the gain in mission safety and robustness.     

卫星数传调度问题的速度可控粒子群优化算法

针对卫星数传调度这一类复杂的约束组合优化问题,提出了一种速度方向和尺度可控的粒子群优化求解算法。为克服粒子群算法的早熟问题,该算法引入了速度更新的方向控制规则和尺度控制规则用于增加群体的多样性,并根据两种控制规则,提出了种群粒子的速度迭代策略,实现了算法运行过程中粒子间吸引和排斥过程的动态调整,同时保证了算法的收敛速度。设计了卫星数传调度问题的编码和解码方式,并证明了该编码方式下最优可行解的存在性。通过仿真实例验证了算法的有效性,并分析了算法控制参数对优化结果的影响。     

Optimal low-thrust transfers between close near-circular coplanar orbits

Four types of optimal solutions are demonstrated to exist for transfers (time of flight is not fixed) between close near-circular coplanar orbits. One solution is realized with the help of fixed orientation of the propulsion system (PS) along a transversal in the orbital coordinate system. Another is reached at fixed orientation of the PS in the inertial coordinate system. The third and fourth types of solutions change the PS orientation in the process of executing the maneuver. Regions of existence are established for all types of solutions, and algorithms for determination of parameters of these maneuvers are suggested. The algorithms were used to calculate parameters of the maneuvers of transfer from a launching orbit to a working Sun-synchronous orbit, and to calculate the maneuvers of supporting the parameters of such an orbit in a specified range.     

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.     

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。     

伴随卫星轨道保持

文中利用伴随轨道方程推导出伴随卫星相对运动状态转移方程。基于这一状态转移方程，研究了双脉冲校正中的伴随运动状态的变化，并得出需要的脉冲控制量的解析式。利用遗传算法对脉冲控制量进行了优化设计，求得使总脉冲最小的最优变轨时间，脉冲控制量和轨迹。     

考虑在轨运动可靠性的空间机械臂关节力矩优化方法

提出一种考虑在轨运动可靠性的冗余度空间机械臂关节力矩优化方法。首先将机械臂操作空间中点到点的转移任务从笛卡尔空间转换至关节空间,利用七次多项式插值法对各关节变量进行参数化处理,获得粒子群算法的优化控制参数;与传统路径规划方法不同,将机械臂各关节力矩的均值和最小作为粒子群算法优化求解的目标函数;依据该目标函数以及相应优化控制参数,利用粒子群算法对空间机械臂运行轨迹进行优化求解,得到机械臂关节力矩均值和最小的运行路径。仿真实验表明,相比传统路径规划方法及以关节力矩二范数为目标函数的关节力矩优化方法,在降低冗余度空间机械臂关节力矩均值方面,文中方法分别减小了33.57%和10.47%;在降低关节力矩最大值方面,分别减小了43.25%和6.19%。     

基于混合量子粒子群优化算法的三维航迹规划

针对粒子群优化算法(PSO)存在的早熟收敛问题,通过将种群的繁殖机制引入量子粒子群优化算法(QPSO),提出了一种混合量子粒子群优化算法(HQPSO),将该算法应用于无人飞行器的三维航迹规划。同时,运用统计学方法,通过仿真实验比较了HQPSO算法与QPSO算法以及带动态变化惯性权系数的PSO算法的性能。仿真实验结果表明,HQPSO不但比QPSO和PSO具有更强的全局搜索能力,而且比QPSO和PSO具有更快的收敛速度。     

一种基于EPSO的航天器交会轨迹优化方法

研究了航天器在固定时间内燃料最省的多脉冲交会问题,提出了一种基于种群熵粒子群优化 (Population Entropy based Particle Swarm Optimization,EPSO)算法的交会轨迹优化设计方法。采用线性化C\|W方程描述航天器的相对运动,以能耗最优为控制目标,得到了基于连续推力的最优转移轨迹,用于确定脉冲点的位置。考虑工程实用性,采用多脉冲控制方法,利用脉冲点的位置参数建立了以脉冲点时间间隔为决策变量的优化目标函数,并用EPSO算法进行求解。在EPSO中,种群熵描述粒子在搜索空间中位置分布的混乱程度,并通过上一代的种群熵确定下一代的搜索空间,从而减少搜索空间的浪费,提高了算法的搜索速度和收敛精度。仿真结果表明,算法本身具有良好的优化性能,适用于航天器轨迹优化。     

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.     

Optimum low-thrust limited power transfers between neighbouring elliptic non-equatorial orbits in a non-central gravity field

A complete first-order analytical solution is developed for the problem of optimum low-thrust limited power transfers between neighbouring elliptic non-equatorial orbits in a non-central gravity field. The optimization problem is formulated as a Mayer problem of optimal control with Cartesian elements as state variables. After applying the Pontryagin maximum principle and determining the optimal thrust acceleration, an intrinsic canonical transformation is performed: the Cartesian elements are changed by suitable orbital elements. Hori's method is applied in determining a first-order analytical solution. Simple analytical solutions are obtained explicitly for long-time transfers.     

空间交会相对状态测定与控制

阐述航天器交会对接最终逼近段相对状态测定与控制算法。测定算法适用于计算机视觉系统,根据标志点构型几何特征,建立非线性测距方程组并构造加权目标函数。对非共面标志点构型（如3点T型与5点锥型）和共面标志点构型（如正方形、矩形、菱形）,目标函数均含标志点间距比率关系项;对共面构型,目标函数还包含共面条件项。按最小二乘法,采用Gauaa-Newton数值迭代法求解测距最佳值;对共面标志点四边形构型,利用对角线交点的虚影像坐标确定测距求解迭代初值。获得测距后即可应用四元数估算法确定相对姿态与相对位置。对相对姿态控制算法,给出相对姿态运动学与动力学方程,讨论相平面法与四元数反馈法的控制设计方法。相平面控制法应用常值推力,针对小姿态角机动的特点,将相对姿态通道解耦为三个独立的二阶子系统,设计相平面推力方向切换函数;四元数反馈法应用本征轴旋转的线性二阶系统瞬态响应特性,选择相对四元数与相对角速率反馈增益系数,确定控制力矩。对相对位置控制算法,将实际位移对标称位移之差作为控制变量,阐述所需速度增量最小的双冲量机动。大量模拟计算结果表明相对状态测定与控制算法是有效的。