Collinear invariant shapes for three-spacecraft Coulomb formations

This paper investigates invariant shape conditions for a three-craft collinear formation in deep space controlled solely by electrostatic Coulomb forces. Previous research shows that invariant shape solutions can exist under certain circumstances for a charged three-craft collinear configuration. This paper investigates the structure of the cluster shape solution space. The problem is examined from a mission design perspective, determining whether or not real charges can always be found that will yield a desired invariant collinear shape configuration. The paper proves that for any three-craft collinear invariant shape formations there always exists an infinite set of real open-loop charges that yield a shape equilibrium. Further, the null-space of the feasible charge solutions is analyzed, and a method for determining a charge-optimal solution is presented. The results are demonstrated through use of numerical simulations.     

等质量立体五星库仑编队飞行的分析与控制

分析了立体五星编队在静电力和万有引力作用下的静态构型。分别讨论了五星编队在共线和平面情况下的静态构型,着重研究了五星构成立体双直角六棱锥构型时各个卫星所带的静电荷量。由于地球同步轨道的卫星所受到的作用力不仅是万有引力与静电库仑力,还有空气阻力等摄动力,因此只有对其施加控制,卫星才能在静态平衡点保持编队构型的稳定性。本文采用线性二次型最优控制方法来保持编队的静态构型稳定,并通过Matlab实现了五星立体库伦编队飞行控制仿真。     

Symmetric periodic solutions of the Hill’s problem. I

The planar circular Hill’s problem is considered, as well as its limiting integrable variant called the Hénon problem, for which the original Hill’s problem is a singular perturbation. Among solutions to the Hénon problem there are a countable number of generating solutions-arcs that are uniquely determined by the condition of successive passage through the origin of coordinates—singular point of equations of motion of the Hill’s problem. Using the generating solutions-arcs as “letters” of a certain “alphabet”, one can compose, according to some rules, the “words”: generating solutions of families of periodic orbits of the Hill’s problem. The sequence of letters in a word determines the order of orbit transfer from one invariant manifold to another, while the set of all properly specified words determine the system’s symbolic dynamics.     

Stability of triangle libration points in generalized restricted circular three-body problem

Equilibrium positions of a small-mass body are considered with respect to a precessing dumbbell. The dumbbell represents two rigidly fixed spherical gravitating bodies. Such a system can be considered as a model of a binary asteroid. Stability of relative equilibrium positions with equal distances from the small mass to the attracting centers is studied. By analogy with the classical restricted three-body problem, these positions are referred to as triangle libration points. It is shown that the character of stability of these libration points is determined by three constant parameters: nutation angle and angular velocity of precession, as well as the ratio of masses at the ends of the dumbbell. Stability conditions are derived in the linear approximation, and the regions of stability and instability in the space of problem parameters are constructed. The paper is a continuation of [1].     

Stability of large damped flexible spacecraft with stored angular momentum

Vibrational stability of large flexible structurally damped spacecraft carrying internal angular momentum and undergoing large rigid body rotations is analysed modeling the systems as elastic continua. Initially, analytical solutions to the motion of rigid gyrostats under torque-free conditions are developed. The solutions to the gyrostats modeled as axisymmetric and triaxial spacecraft carrying three and two constant speed momentum wheels, respectively, with spin axes aligned with body principal axes are shown to be complicated. These represent extensions of solutions for simpler cases existing in the literature. Using these solutions and modal analysis, the vibrational equations are reduced to linear ordinary differential equations. Equations with periodically varying coefficients are analysed applying Floquet theory. Study of a few typical beam- and plate-like spacecraft configurations indicate that the introduction of a single reaction wheel into an axisymmetric satellite does not alter the stability criterion. However, introduction of constant speed rotors deteriorates vibrational stability. Effects of structural damping and vehicle inertia ratio are also studied.     

卫星编队飞行的无速度测量非线性鲁棒控制

本文基于带有界干扰的线性动力学模型，研究了卫星编队飞行中的相对位置控制问题。首先，在线性二次型最优控制的基础上，设计了一种非线性控制律，并使用李雅普诺夫稳定性理论证明了系统的稳定性。接着，通过对线性系统状态观测器进行改进，得到了一种非线性速度观测器，观测误差被证明是渐近收敛的。观测器与控制律的结合实现了无速度测量的控制，闭环系统被证明是渐近稳定的。文末的数值仿真验证了理论分析。     

General dynamics in the Restricted Full Three Body Problem

The problem of a binary system and a spacecraft in its gravity field is studied. As the mass distribution of the bodies is considered, the two problems are referred as the Full Two Body Problem (F2BP) and the Restricted Full Three Body Problem (RF3BP), respectively. The conditions for relative equilibria and their stability in the F2BP were derived for an ellipsoid–sphere system. As the non-equilibrium problem is more common in nature, we look at periodic orbits in the F2BP close to the relative equilibrium conditions. It is found that families of periodic orbits can be computed where the minimum energy state of one family is the relative equilibrium state. An approximation method was derived in order to facilitate the computation of periodic orbits near relative equilibria while keeping the interesting dynamical features. The next step is to make the connection between the dynamics of the RF3BP and the F2BP. In the current paper, we solve for the dynamics of the F2BP and substitute this model in the RF3BP. We provide a basic investigation of the dynamics of a particle in the gravitational field of this binary system. We show results in the F2BP and the RF3BP.     

圆型限制性三体问题相对运动解析研究

针对圆型限制性三体问题共线平动点附近周期/拟周期轨道下的相对运动问题,提出一种新的、通用的解析研究方法。在周期/拟周期轨道近似解析解的基础上,结合微分修正方法,获得了精确的周期/拟周期轨道。对周期/拟周期轨道的单值矩阵进行分析,同时借鉴Floquet理论核心思想,建立了六个相对运动模态,并将相对运动表示为六个相对运动模态的线性组合,获得了相对运动的近似解析解。最后在地-月系统圆型限制性三体问题下,以L1点作为研究对象,分别以Halo轨道、Lissajous轨道和Lyapunov轨道为参考轨道,对相对运动模态和相对运动进行仿真分析,说明了相对运动模态的正确性以及相对运动近似解析解的有效性。     

卫星编队飞行相对位置自适应协同控制

针对卫星编队飞行相对位置协同控制问题,基于编队卫星相对运动非线性动力学方程和一致性理论设计了两种自适应协同控制器。首先,在卫星质量不确定和星间信息交互存在通信时延的条件下,设计了一种全状态反馈自适应协同控制器,并证明了该控制策略对空间摄动力的鲁棒性。其次,进一步考虑速度信息不可测的条件下,采用滤波器设计了一种无速度反馈的自适应协同控制器。最后,以编队构型重构为例对两种自适应协同控制器进行了仿真校验。仿真结果表明：两种自适应协同控制器均可有效应用于卫星编队飞行相对位置的协同控制,能够保证编队卫星对各自期望轨迹跟踪的同时暂态保持编队构型的稳定,具有较高的控制精度。     

Effects of eccentricity of the reference orbit on multi-tethered satellite formations

The paper discusses the relevance of eccentric reference orbits on the dynamics of a tethered formation, when a massive cable model is included in the analysis of a multi-tethered satellite formation. The formations examined in this study are hub-and-spoke (HAS) and closed-hub-and-spoke (CHAS) configurations for in-plane and Earth-facing spin planes. Stability of the formations is studied by means of numerical simulation, together with the evaluation of the effects of eccentricity on tether elongation, agents relative position, and formation orientation and shape.     

追踪星跟踪空间非合作目标的相对轨道设计

对空间非合作目标跟踪飞行可以执行观测或监视等任务。首先从一般性出发对追踪星与非合作目标之间的椭圆轨道相对运动方程进行分析,给出具有任意初始条件的相对运动方程解析表达式。其次,对追踪星沿航向跟踪目标并考虑约束条件时的相对轨道设计进行分析后,给出设计追踪星轨道的方法,该方法使得追踪星在保持对地定向的同时也满足测量敏感器的约束条件。最后通过数学仿真进行了验证。     

On equilibrium stability in the Sitnikov problem

The problem of stability of the trivial equilibrium position in the Sitnikov problem is considered in the first approximation. The first approximation is shown to have the form of a linear second-order equation with time-periodic coefficient (the Hill-type equation). The equilibrium stability was studied on the basis of equation regularization in the vicinity of a singular point with subsequent calculation of the trace a of the monodromy matrix. The equilibrium stability is shown to be stable for almost all values of eccentricity e from the [0, 1] interval. The instability takes place on the discrete set of e values, when the mutipliers are multiple (with non-simple elementary divisors), e = 1 being a point of crowding of this set.     

小推力下卫星编队的非自然构型设计与控制

使用小推力控制可以得到许多独特的非自然卫星编队构型,主从星相对位置不变和从星圆形匀速绕飞构型是两类最典型的构型,建立了这两类编队构型的编队参数(主从星距离、空间方位和绕飞速度)与一天内燃料消耗的关系。进一步考虑存在初始误差时控制律的设计,指出PD控制律能够维持小初始误差编队构型,改进的PD控制律能够维持中等初始误差编队构型,而PD控制律和直接法相结合的混合控制律能够维持大初始误差编队构型,仿真结果验证了所设计控制律的有效性。     

Collective trajectory planning for satellite swarm using inter-satellite electromagnetic force

The inter-satellite electromagnetic force presents several significant advantages that help to expand its space applications to the multi-satellite missions gradually. For a satellite swarm, whether the electromagnetic force is applied to enable collective maneuver and how to provide a better performance and broader applications for such swarm highlight an important issue. Considering the trajectory planning problem of satellite swarm using inter-satellite electromagnetic force, a behavior-based collective planning scheme is developed by designing the desired velocity of each satellite as the sum of several different behavioral contributions, which are used to represent the internal and external interactions of the swarm. Therefore, the desired configuration is associated with the equilibrium points of the pre-designed kinematical field. Furthermore, the trajectory planning problem could be translated to a parameter optimization problem considering the swarm dynamics with inter-satellite electromagnetic force. Then based on the analysis of the applicability and advantages triggered by integrating the inter-satellite electromagnetic force into such behavior-based planning scheme, the collective trajectory planning problem with sole electromagnetic force actuation and hybrid actuation with thruster are studied respectively. Numerical simulations are carried out to verify the validity of the proposed algorithm, and the satellite swarm performance enhanced by inter-satellite electromagnetic force is discussed at last.     

基于非线性有限元降阶方法的网格加筋筒壳结构屈曲承载特性研究

非线性有限元数值计算方法是结构屈曲性能评估的主要手段,然而该方法需要基于精细网格迭代求解,降低结构非线性计算规模是其关键技术之一。采用一种结构非线性有限元降阶方法,对均匀轴向压载荷作用下的网格加筋筒壳结构进行了细致的承载稳定性特性分析。该方法将Koiter初始后屈曲理论与Newton弧长法相结合,通过多次使用Koiter摄动展开来跟踪结构非线性平衡路径。计算比较了特征值屈曲载荷和计及几何非线性效应的非线性屈曲载荷值;采用侧向小扰动载荷模拟结构初始几何形状缺陷,分析了缺陷幅度对临界屈曲载荷的影响规律,在验证了非线性有限元降阶方法分析精度的同时,细致考核了该方法在结构非线性屈曲分析以及缺陷敏感性分析中的计算效率优势。     

A vectorial bootstrapping approach for integrated GNSS-based relative positioning and attitude determination of spacecraft

Traditionally in multi-spacecraft missions (e.g. formation flying, rendezvous) the GNSS-based relative positioning and attitude determination problem are treated as independent. In this contribution we will investigate the possibility to use multi-antenna data from each spacecraft, not only for attitude determination, but also to improve the relative positioning between spacecraft. Both for ambiguity resolution and accuracy of the baseline solution, we will show the theoretical improvement achievable as a function of the number of antennas on each platform. We concentrate on ambiguity resolution as the key to precise relative positioning and attitude determination and will show the theoretical limit of this kind of approach. We will use mission parameters of the European Proba-3 satellites in a software-based algorithm verification and a hardware-in-the-loop simulation. The software simulations indicated that this approach can improve single epoch ambiguity resolution up to 50% for relative positioning applying the typical antenna configurations for attitude determination. The hardware-in-the-loop simulations show that for the same antenna configurations, the accuracy of the relative positioning solution can improve up to 40%.     

带充液腔的自旋卫星稳定性问题

本文应用Pfeiffer的思想讨论带轴对称充液腔的卫星系统自旋稳定性。本方法的基本思想为将轴对称腔内的液体旋度平均化,使之与空间位置无关,由此将液体的无限自由度问题离散化为有限自由度问题,从而用线性理论讨论系统的自旋稳定性。用这方法,本文讨论了带充液腔的非轴对称卫星系统、带充液腔的双自旋卫星系统的自旋稳定性,给出了它们的自旋稳定性判据。此外,本文还给出了一些带有不同形状腔体的卫星系统自旋稳定域图,为实际工程设计人员提供理论参考。     

Design of phase-locked loop for communication system via on-board signal processing satellites

The energy inconsistency for a multiple access system via an active satellite with simple repeating of signals is claimed. The on-board ideal signal processing algorithm resolving this inconsistency is considered and the optimal group signal processing algorithm in a manner of digital signals shape transformation followed by their time compression is suggested. The necessity for individual clock synchronization of ground stations is shown and the synchronous multiple access system block diagram with an optimal on-board signal processing is discussed.A phase disturbance dynamics of a two-loops clock synchronization system with variable time delay is investigated. A nonlinear differential-difference equation is obtained and for the first order PLL with time delay the exact solutions are found in cases of relay and linear shapes phase discriminator's characteristics. Phase errors' expressions are derived and the main factors of accuracy limiting caused by PLL's feedback time delay are established.     

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。