Design of satellite constellations with continuous coverage on elliptic orbits of <Emphasis Type="Italic">Molniya</Emphasis> type

New methods of choosing the structures of satellite constellations (SC) on elliptical orbits of the Molniya type are presented. The methods, using critical inclination and putting the orbit apogee in the Earth’s hemisphere with an area of continuous coverage, are based on geometrical analysis of two-dimensional representation of the coverage conditions and SC motion in the space of inertial longitude of the orbit ascending node and time. The coverage conditions are represented in the form of a certain region. Dynamics of all satellites in this space is represented by uniform motion along a straight line approximately parallel to the ordinate axis, while the satellite system forms a grid. The problem of choosing a minimal (as far as the number of satellites is concerned) SC configuration can be formulated as a search for the most sparse grid. The contemporary advanced methods of computational geometry serve as an algorithmic basis for the problem solution. Design of SC for continuous coverage of latitude belts with the use of kinematically regular systems is considered. A method of analyzing single-track systems for continuous coverage of arbitrary geographic regions is described, which makes a region at any time instant observable by at least one satellite of the system. As an example, SC on elliptical orbits are considered with periods of ～4, 12, and 24 hours.     

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.     

基于轨道摄动解的卫星编队飞行

用完全不同的方法推导出一种两颗卫星相对运动的表达式.首先,它描述的是一颗真实的卫星相对一颗在理想轨道上运动的虚拟卫星的运动,而这正是研究编队飞行所必须的;其次,这个表达式将真实卫星相对虚拟卫星的三维位置表示成虚拟卫星的Brouwer平根数及两卫星轨道根数之差的函数.据此便可以充分应用已有的关于轨道摄动的研究成果.作为一个基本模型,首先讨论了一颗真实卫星相对虚拟卫星形成椭圆型地面轨迹的飞行方式.基于轨道长期摄动的已有结果可以很容易地揭示这种飞行方式的长期变化,从而可以毫无困难地制定出轨道调整的策略.最后还研究了三颗卫星以同一条椭圆轨迹飞行的轨道设计和控制问题,该椭圆以虚拟卫星为中心.     

Mapping orbits with low station keeping costs for constellations of satellites based on the integral over the time of the perturbing forces

The present paper is concerned with the search for orbits that have potential to require low fuel consumption for station-keeping maneuvers for constellations of satellites. The method used to study this problem is based on the integral over the time of the undesired perturbing forces. This integral measures the change of velocity caused by the perturbation forces acting on the satellite, so mapping orbits that are less perturbed, which generates good candidates for orbits that requires low fuel consumption for station-keeping maneuvers. The integral over the time depends only on the orbit of the spacecraft and the dynamical system considered. The type of engine and the control technique applied to the spacecraft are not considered to search for those orbits. It can be a good strategy to be applied for a first mapping of orbits. For this search, it is analyzed the integral of orbits with different values of the Keplerian elements in order to find the best ones with respect to this criterion. The perturbations considered are the ones caused by the third body, which includes the Sun and the Moon, and the J₂ term of the geopotential. The results presented here show numerical simulations to obtain the integral of those perturbing forces for different orbits. The GPS and the Molniya constellations are used as examples for those calculations.     

空间太阳能电站的准对日定向姿态

针对空间太阳能电站的俯仰姿态运动,提出一种能追踪太阳运动的准对日定向(QSP)姿态方案。此方案的太阳能电池阵列在万有引力梯度力矩的作用下,始终在垂直于太阳光的方向附近作幅值约为18.8°的振动,且几乎不需要姿态控制力矩。准对日定向姿态方案解决了大型太阳能电池阵列对日定向所需的巨大俯仰姿态控制力矩问题。准对日定向姿态的发电效率为对日定向姿态的97.3%,对Abacus空间太阳能电站而言每年可节省燃料约36791 kg。通过数值方法得到了准对日定向姿态的精确初始条件。随后,设计了比例-微分控制器,保证了系统存在初始姿态误差的条件下收敛到准对日定向姿态。最后研究了轨道、姿态和结构振动对准对日定向姿态的影响,并发现准对日定向姿态下的结构振动幅值比对日定向姿态减小约40倍。     

基于改进遗传算法的移动目标成像侦测任务规划问题研究

基于先验信息调用成像侦察卫星监控陆地或海洋移动目标动态信息是卫星成像侦察面临的新 课题。在已知移动目标位置等先验信息基础上,动态构造目标可变潜在区域及其运动预测模 型,利用STK辅助构造其候选成像观测活动集合;在此集合及目标运动预测模型基础上 对动态可变区域成像卫星调度问题进行建模,并设计了一种基于模拟退火算法及遗传算法的 改进遗传算法对问题进行求解,得到近最优的移动目标成像侦测方案。最后通过实例及算法 对比验证了规划模型及算法对解决该类问题的合理性和有效性。
     

分布式卫星编队飞行队形保持协同控制

针对分布式卫星编队飞行队形保持控制问题提出一种分布式协同控制算法,并给出该协同控制算法与编队卫星星间信息传递拓扑结构之间的关系。该协同控制算法以模型预测控制为基础,利用分布式编队卫星的自然特性以及编队卫星之间的信息传递拓扑结构,采用分布式的算法结构,设计分布式的模型预测协同控制算法。该控制算法是一种在线滚动优化控制算法,同时能够较好地解决存在状态约束、控制输入约束等情形下的各种控制问题。最后通过数值仿真验证了结果的有效性。仿真结果表明,当编队卫星星间信息传递拓扑结构中存在生成树时,提出的分布式协同控制算法能够有效地应用到编队卫星队形保持控制问题上来。     

Decay of high eccentricity satellite orbits with air drag using uniformly regular KS canonical elements

A non-singular analytical theory for the motion of high eccentricity satellite orbits under the influence of air drag is developed in terms of the Uniformly Regular Kustaanheimo and Stiefel (URKS) canonical elements, by assuming the atmosphere to be oblate with variation of density scale height with altitude. The series expansions include up to fourth-order terms of an independent variable Δ=λ² (function of eccentric anomaly) and c (a small parameter dependent on the flattening of the atmosphere). Only two of the nine equations are solved analytically due to symmetry in the equations of motion. Comparison of the important orbital parameters semi-major axis and eccentricity up to 1000 revolutions, obtained with the present analytical solution and the KS theory, shows the superiority of the present solution over the KS elements analytical solution. The theory can be used effectively for the orbital decay of aero-assisted orbital transfer orbits during mission planning.     

Reconstruction of spacecraft rotational motion using a Kalman filter

Quasi-static microaccelerations of four satellites of the Foton series (nos. 11, 12, M-2, M-3) were monitored as follows. First, according to measurements of onboard sensors obtained in a certain time interval, spacecraft rotational motion was reconstructed in this interval. Then, along the found motion, microacceleration at a given onboard point was calculated according to the known formula as a function of time. The motion was reconstructed by the least squares method using the solutions to the equations of satellite rotational motion. The time intervals in which these equations make reconstruction possible were from one to five orbital revolutions. This length is increased with the modulus of the satellite angular velocity. To get an idea on microaccelerations and satellite motion during an entire flight, the motion was reconstructed in several tens of such intervals. This paper proposes a method for motion reconstruction suitable for an interval of arbitrary length. The method is based on the Kalman filter. We preliminary describe a new version of the method for reconstructing uncontrolled satellite rotational motion from magnetic measurements using the least squares method, which is essentially used to construct the Kalman filter. The results of comparison of both methods are presented using the data obtained on a flight of the Foton M-3.     

Navigation Solution to Maneuver a Spacecraft Relative to a Sphere Centered on a Cooperative Satellite

A differential correction algorithm is presented to deliver an impulsive maneuver to a satellite to place it within a sphere, with a user defined radius, centered around a non-maneuvering satellite within a constrained time. The differential correction algorithm develops and utilizes the State Transition Matrix along with the Equations of Motion and multiple satellite?s state information to determine the optimum trajectory to achieve the desired results. The results from the differential correction algorithm are very accurate for prograde orbits, as presented. The results allow for orbit design trade-offs, including satellites? initial inclinations, semi-major axes, as well as the ballistic coefficients. The results also provide an empirical method to determine the optimum ΔV$\mathrm{\Delta }V$ solution for the provided problem. Understanding that the minimum fuel solution lies with a semi-major axis ratio of 1, a very accurate empirical approximation is presented for semi-major axis ratio values less than and greater than 1. This work ultimately provides the generalized framework for applying the algorithm to a unique user defined maneuvering spacecraft scenario.     

A Retrospective Geometric Analysis of the Long-Term Evolution of Orbits and the Ballistic Lifetime for Satellites of the Prognoz Series

We consider the applied aspects of the geometrical analysis of solutions in a restricted circular double-averaged three-body problem that are concerned with the design of high-apogee satellite orbits. Based on the analysis of the long-term evolution and the ballistic lifetime for orbit families of the Prognoz satellites launched into their orbits in the period 1972–1995, we suggest some practical suggestions for choosing long-lived high-apogee orbits with taking into account various requirements for the domain of evolution of the orbital elements.     

摄动椭圆参考轨道的相对运动状态转移方程

当面质比不同的主从卫星在近地轨道上作编队飞行时,大气阻力摄动和J2项摄动就成为影响编队队形的两个最主要的因素,这样描述相对运动的状态转移方程必须考虑这两项摄动。该文利用相对轨道要素法推导了包含J2项摄动和大气阻力摄动参考轨道为椭圆的卫星编队相对运动较精确的状态转移方程。当主从卫星的面质比相等时大气阻力摄动对卫星编队队形的影响很小而可以忽略,这样上面的状态转移方程可以化为更简单的形式。仿真结果表明该状态转移方程能较精确的预测编队飞行的相对运动。     

星载GPS的毫米级编队卫星相对定位

在比较分析编队卫星相对定位与陆地相对定位技术的基础上,结合陆地相对定位技术和 卫星精密定轨技术提出了基于GPS进行编队卫星相对定位的方法及原理。文章采用2004年4月 1日到10日的GRACE卫星实测数据进行了相对定位计算,并采用KBR观测数据对本文相对定位 结果和JPL单独定轨结果进行了外部检核,检核结果表明：1. 与直接采用单独定轨结果相 比,该方法可以明显提高卫星的相对位置精度。2. 利用本文方法计算的两颗GRACE卫星相 对位置精度约为4.5 mm。
     

Evaluation of a satellite constellation for active debris removal

This paper analyzes an example of a three-dimensional constellation of debris removal satellites and proposes an effective constellation using a delta-V analysis that discusses the advisability of rendezvousing satellites with space debris. Lambert?s Equation was used to establish a means of analysis to construct a constellation of debris removal satellites, which has a limit of delta-V injection by evaluating the amount of space debris that can be rendezvoused by a certain number of removal satellite. Consequently, we determine a constellation of up to 38 removal satellites for debris removal, where the number of space debris rendezvoused by a single removal satellite is not more than 25, removing up to 584 pieces of debris total. Even if we prepare 38 removal satellites in their respective orbits, it is impossible to remove all of the space debris. Although many removal satellites, over 100 for example, can remove most of the space debris, this method is economically disproportionate. However, we can also see the removal satellites are distributed nearly evenly. Accordingly, we propose a practical two-stage strategy. The first stage is to implement emergent debris removal with the 38 removal satellites. When we find a very high probability of collision between a working satellite and space debris, one of the removal satellites in the constellation previously constructed in orbit initiates a maneuver of emergent debris removal. The second stage is a long-term space debris removal strategy to suppress the increase of space debris derived from collisions among the pieces of space debris. The constellation analyzed in this paper, which consists of the first 38 removal satellites, can remove half of the over 1000 dangerous space debris among others, and then the constellation increases the number of the following removal satellites in steps. At any rate, an adequate orbital configuration and constellation form is very important for both space debris removal and economic efficiency. Though the size of constellation of debris removal satellites would be small originally, such a constellation of satellites should be one of the initial constellations of removal satellites to ensure the safety of the future orbital environment.     

High-precision single-input control of relative motion in spacecraft formation

A Newton-type method is proposed to improve the accuracy of control for relative motion of two satellites in close formation. We assume that the deputy satellite is equipped with a passive attitude control system that provides one-axis stabilization, and one or two orbit control thrusters are installed along the stabilized axis. Previous studies show that it is possible to construct periodic relative trajectories both in case of passive magnetic and spin stabilization. However, the accuracy of the numerically obtained control is quite low due to modeling errors caused by linearization of the equations of relative motion. Therefore, a correction procedure is required to compensate for nonlinear effects. To this end we suggest a recently developed algorithm based on the Newton method for solving nonlinear systems with geometric constraints. Being implemented, this algorithm allows decreasing the modeling error by up to ten times. The previously found control and trajectory of the linearized system are used as initial approximations.     

Quasistatic Microaccelerations onboard the Foton Satellite during Its Flight at High-Altitude Orbits

The level of quasistatic microaccelerations onboard the Foton-M satellite is predicted for its flights in two orbits: the planned orbit with the altitudes in perigee h = 262 km and in apogee h = 304 km and the orbit with h = 262 km and h = 350 km. The prediction is based on mathematical simulation of the satellite motion with respect to its center of mass under the action of gravitational and aerodynamic moments. The model is represented by the system of equations of the satellite rotational motion. Parameters of this system are chosen from the condition of coincidence of the motion of preceding Foton satellites (h 220 km and h 400 km) calculated using this model with the results of determination of actual rotational motion of the Foton-11 and Foton-12 satellites. With the help of the model thus calibrated, a calculation is made of the rotational motion of the Foton-M satellite and of the quasistatic microaccelerations onboard it. As is shown by the results of simulation, the use of the first and the second orbits will result in reductions of microaccelerations by 30% and 60%, respectively.     

通信卫星灵活载荷技术综述

通信卫星逐步由高轨地球同步轨道卫星向高、中、低轨结合的全球覆盖卫星方向发展,多业务和多重覆盖的发展趋势对通信卫星的灵活性提出了更高的要求。通信卫星配备灵活载荷已经成为重要发展方向,对面向个人用户的高通量通信卫星及高、中、低轨结合的组网通信卫星来说尤为重要。配备灵活载荷的通信卫星能实现端到端业务,能灵活调整覆盖区,实现灵活组网,并提升资源利用率。分析了国内外通信卫星灵活载荷的发展动态,介绍了通信卫星灵活载荷的技术特点,并给出了有效载荷方案,最后阐述了通信卫星灵活载荷发展的关键技术及发展思路。     

编队飞行卫星群的轨道动力学特性与构形设计

编队飞行卫星群由一些相对距离近的小卫星组成,在严格的条件下,若干颗伴随卫星环绕一颗中心卫星作相对运动,相对轨道为特别性质的椭圆,本文研究了编队飞行卫星群的轨道动力学特性,提出了编队飞行的轨道构形设计的原则和方法。