多航天器协同探测星簇构型探测效能的评价方法

为定量评估不同星簇构型设计的探测效能以进行各航天器的轨道设计,基于空间四面体构型的体张量定义,分析现有空间四面体构型的评价参量,并采用将空间五航天器构型分解为“五个四面体”和“主四面体加第五点问题”这两种方法定量评价空间五点协同探测星簇构型的探测效能。最后利用项目组已有的五个航天器在一个轨道周期内的模拟轨道数据对所提出的方法进行仿真,结果表明所提出的方法可以较好地评价空间五点构型的探测效能。     

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。     

Fuel consumption and collision avoidance strategy in multi-static orbit formations

This paper analyses the fuel consumption of interferometric radar missions employing small satellite formations like, e.g., Cross-track Pendulum, Cartwheel, CarPe, or Trinodal Pendulum. Individual analytic expressions are provided for each of the following contributions: separation from a simultaneously injected master satellite, formation set-up, orbit maintenance, formation maintenance, and distance maintenance. For this, a general system of equations is derived describing the relative motion of the small satellites in a co-rotating reference frame. The transformation into Keplerian elements is carried out. To evaluate fuel consumption, three master satellites are assumed in different orbital heights, which are typical for Earth observation missions. The size of the exemplarily analysed formations is defined by remote sensing aspects and their respective fuel requirements are estimated. Furthermore, a collision avoidance concept is introduced, which includes a formation separation and formation set-up after a desired time period.     

小卫星编队绕飞构型运动学设计与分析研究

基于运动学的相对运动数学模型,利用物理意义更明确的绕飞方程进行了小卫星绕飞轨道的设计.根据绕飞轨道方程,重点分析了4类常用的绕飞编队构型:同绕飞轨道编队、同面同绕飞中心编队、异面同绕飞中心编队和多绕飞中心编队,总结分析了各种编队轨道设计的约束条件,获得了一般规律性结论.最后通过仿真验证了所提出的绕飞编队轨道设计方法和结论的正确性.     

Control of satellite imaging formations in multi-body regimes

Libration point orbits may be ideal locations for satellite imaging formations. Therefore, control of these arrays in multi-body regimes is critical. A continuous feedback control algorithm is developed that maintains a formation of satellites in motion that is bounded relative to a halo orbit. This algorithm is derived based on the dynamic characteristics of the phase space near periodic orbits in the circular restricted three-body problem (CR3BP). By adjusting parameters of the control algorithm appropriately, satellites in the formation follow trajectories that are particularly advantageous to imaging arrays. Image reconstruction and coverage of the (u, v) plane are simulated for interferometric satellite configurations, demonstrating potential applications of the algorithm and the resulting motion.     

SAR干涉测高分布式小卫星编队构形优化设计

SAR干涉（InSAR）测高是分布式卫星目前一个重要的应用方向。星间基线是系统高程理论精度的决定性因素之一，而基线是由编队构形决定的，因此构形设计是InSAR测高分布式小卫星系统顶层设计的一个关键内容。针对设计变量与目标函数之间的关系非常复杂，没有简单明确的解析形式的特点，选择遗传算法作为优化算法进行构形的优化设计，给出了编码方法和适应度函数。以典型雷达卫星参数为初始条件，对几种不同构形进行了仿真，结果表明在一个轨道周期内，双星空间编队约有一半时间能够满足精度优于1m的要求，是进行InSAR测高的首选构形。     

一种星间相对状态估计方法

编队自主导航是实现分布式遥感系统星间协同观测的基础。为实现分布式遥感系统星间相对状态的精确确定，提出一种基于MEMS激光雷达与纳型星罗盘的星间相对状态估计方法。借助相对姿态、轨道运动学方程建立了星间相对状态的无迹卡尔曼滤波(UKF)算法，解决了MEMS激光雷达测量与参考航天器姿态耦合的问题，并利用预定入轨参数及高精度轨道外推(HPOP)对方法进行仿真校验。结果表明，该方法具有可行性和实用性，估计精度满足分布式遥感任务需求，能够较好解决中远距离星间相对状态估计问题。     

基于DEM和GMTI的收发同置分布式InSAR编队构型设计

针对多星收发同置分布式干涉合成孔径雷达(InSAR),建立了基线的空间几何模型,基于高程测量(DEM)和动目标检测(GMTI)任务设计卫星编队构型。给出了多星收发同置分布式InSAR的基线参数与构型参数的转换关系,在任务对基线的约束下,以小于某指标的测高和测速误差的轨道运行时间为优化目标,设计构型参数并仿真分析,获得了三种不同编队构型的基线稳定性和测量误差。     

航天器集群构形控制的虚拟弹簧阻尼网络方法

针对航天器集群质心相对运动构形控制问题,提出了一种基于虚拟弹簧阻尼网络的分布式控制方法。航天器间以虚拟的弹簧阻尼器相互连接,弹簧的原长根据期望的相对运动构形来设定。各航天器的控制输入是与其相连的所有弹簧阻尼器的合力。在线性动力学模型和拓扑结构连通且固定的假设下,基于代数图论的方法推导出了闭环系统稳定性条件。对近地轨道上100个航天器形成格点相对运动构形和20个航天器形成时变距离的椭圆构形的实例进行了仿真,考虑了轨道摄动的影响,结果表明,集群通过虚拟弹簧阻尼网络控制可实现期望构形,并能达到厘米量级的构形保持控制精度。该控制方法不改变集群的质心,只需施加很小的控制加速度;仅基于局部的邻居交互,能够适应大规模集群对分布式控制的要求。     

一种绕飞编队卫星星间链路系统的总体设计方法

为了建立高精度相对定位编队卫星的星间链路,提出了一种基于GPS的绕飞编队卫星星间链路系统设计方法。针对我国首次以InSAR为背景的任务,以某绕飞编队星座星间链路系统总体方案为例,利用STK/MATLAB分析软件,对天线覆盖区与组阵进行了仿真分析,并根据分析结果做了系统优化,包括星间轨道构型、天线设计组阵图、天线安装位置、链路预算、星间通信措施设计分析以及电磁兼容性分析等。结果表明:基于GPS的编队卫星能够从系统角度优化设计建立星间链路,从而完成编队跟飞、绕飞期间的星间通信与测量任务,为卫星建立星座构型、相对定位测量提供了可靠、稳定的传输通道。该设计方法可为同类卫星或其他类型卫星星间链路系统设计提供参考。     

考虑地球扁率的大椭圆轨道编队飞行优化设计

大椭圆轨道上卫星编队的相对运动特性及其所受摄动力的影响给编队轨道设计者提出了新的挑战.本文总结了大椭圆轨道卫星编队的五种基本形式,利用数值积分法计算了主星轨道倾角、近地点角和平近点角初值对地球扁率作用下基本编队形式相对位置极值点漂移量的影响规律.结合零J2项摄动条件,提出基于主星平近点角初值的J2项编队相对轨道优化设计方法,进而获得瞬时根数描述的编队初始条件.仿真算例表明：优化设计结果可以明显降低大椭圆轨道编队卫星的相对漂移量,与平根数描述的编队初始条件的设计结果相比,相对距离极大值点的漂移量降低约81.8681%,验证了基于主星平近点角初值的大椭圆轨道编队优化设计方法的可行性.     

分布式卫星群构形初始化控制策略

构形初始化是分布式卫星控制的重要内容。在绕飞构形归一化描述的基础上，提出了两次脉冲速度增量实现绕飞的两种方案。在一种分层控制结构下，通过两种初始化方案的合理组合，可保证卫星群整体的初始化可在一个轨道周期内完成，从而降低了初始化误差。在对导航和误差特性进行分析后，通过数值仿真，证明了所提方法的可行性。     

Application of SDRE technique to orbital and attitude control of spacecraft formation flying

This paper proposes the application of a nonlinear control technique for coupled orbital and attitude relative motion of formation flying. Recently, mission concepts based on the formations of spacecraft that require an increased performance level for in-space maneuvers and operations, have been proposed. In order to guarantee the required performance level, those missions will be characterized by very low inter-satellite distance and demanding relative pointing requirements. Therefore, an autonomous control with high accuracy will be required, both for the control of relative distance and relative attitude. The control system proposed in this work is based on the solution of the State-Dependent Riccati Equation (SDRE), which is one of the more promising nonlinear techniques for regulating nonlinear systems in all the major branches of engineering. The coupling of the relative orbital and attitude motion is obtained considering the same set of thrusters for the control of both orbital and attitude relative dynamics. In addition, the SDRE algorithm is implemented with a timing update strategy both for the controller and the proposed nonlinear filter. The proposed control system approach has been applied to the design of a nonlinear controller for an up-to-date formation mission, which is ESA Proba-3. Numerical simulations considering a tracking signal for both orbital and attitude relative maneuver during an operative orbit of the mission are presented.     

Robust decentralized attitude control of spacecraft formations under time-varying topologies,model uncertainties and disturbances

This paper investigates the robust decentralized attitude control problem for spacecraft formations under uncertain communication topologies. Based on modified Rodrigues parameters representation and a Lagrange-like model, a class of decentralized attitude control schemes designed by the use of sliding mode control approach is proposed to steer the attitude of the spacecraft formation to a time-varying reference states with no assumption on the information exchange graph. By taking into account the model uncertainties and external disturbances simultaneously, the proposed robust control strategies are proven effective to overcome these unexpected phenomena. Finally, numerical examples are included to demonstrate the effectiveness and robustness of the developed control schemes.     

Elimination of relative secular drift of orbits of two satellites caused by polar oblateness of the Earth

A method of elimination of relative secular drifts in satellite formations is suggested for the case of influence of a perturbation due to polar oblateness of the Earth. The method is applied to eliminate relative secular drifts in the case when a satellite is controlled using an engine mounted along its orientation axis (the satellite is supplied with a passive magnetic attitude control system) and with the help of a solar sail installed on one of the satellites. Analytical results are confirmed by numerical simulation.     

Optimal reconfigurations of two-craft Coulomb formations along manifolds

Coulomb formations refer to swarms of closely flying spacecraft, in which the net electric charge of each vehicle is controlled. Active charge control is central to this concept and enables a propulsion system with highly desirable characteristics, albeit with limited controllability. Numerous Coulomb formation equilibria have been derived, but to maintain and maneuver these configurations, some inertial thrust is required to supplement the nearly propellant-less charge control. In this work, invariant manifold theory is applied to two-craft Coulomb equilibria, which are admitted in a linearized two-body gravity model. The manifolds associated with these systems are analyzed for the first time, and are then utilized as part of a general procedure for formulating optimal reconfigurations. Specifically, uncontrolled flows along the manifolds are sought which provide near continuous transfers from one equilibrium to another. Control is then introduced to match continuity, while minimizing inertial thrusting. This methodology aims to exploit uncontrolled motions and charge control to realize the shape-changing ability of these formations, without large inertial control efforts. Some variations in formulating and parameterizing the optimal transfers are discussed, and analytical expressions are derived to aid in establishing control parameter limits, under certain assumptions. Numerical results are provided, as demonstrative examples of the optimization procedure, using relatively simple control approximations. Finally, Particle Swarm Optimization, a novel stochastic method, is used with considerable success to solve the numerically difficult parameter optimization problems.     

Out-of-plane stability analysis of collinear spinning three-craft Coulomb formations

The results of a stability analysis focusing on the out-of-plane motion of collinear three-craft Coulomb formations with set charges are discussed. Such a formation is assumed to be spinning in deep space without relevant gravitational forces present. Assuming in-plane motion only with circular relative trajectories and initial position and velocity perturbations confined to the orbital plane, the previous work analytically proves marginal stability in the linear sense and numerically shows marginal stability in the short term. In this paper, the equations of motion are presented in the cylindrical coordinate frame in order to analyze the out-of-plane motion in more detail. The out-of-plane motion is shown to decouple to first order from the marginally stable in-plane motion. A simple control law is developed and applied, which directly controls the out-of-plane motion only within specified deadbands. For a wide variety of out-of-plane perturbations, the control law succeeds in preserving the in-plane variant shape despite some out-of-plane motion. A trend between the settling time and deadband, which defines the largest out-of-plane errors allowed before the controller is turned on, is determined, which illustrates how large the deadband may be before the in-plane motion is affected.     

深空探测中利用静止轨道卫星编队连续导航精度分析

针对我国难以全天候24小时对探测器连续测控和通信，以及建立全球性深空网络困难的问题，提出利用地球静止轨道卫星编队进行深空导航的构想。两个静止轨道卫星编队相距一定角度，可以完成对深空探测器进行全天候连续导航定位。卫星编队采用无源反向导航的方法，多颗卫星协同工作，共同完成导航任务。分析表明该天基导航系统的几何参数精度因子受时间测量误差均方差和基线长度变化影响较大。编队的构型对定位精度有很大影响，其中基线长度不能过小，时间测量误差均方差不能过大，否则定位误差会急剧增加，伴随卫星椭圆轨道偏心率也存在一定界限。增加伴随卫星数量也有利于提高系统的定位精度。