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.     

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.     

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.     

Multiple continuous coverage of the earth based on multi-satellite systems with linear structure

A new and wider definition is given to multi-satellite systems with linear structure (SLS), and efficiency of their application to multiple continuous coverage of the Earth is substantiated. Owing to this widening, SLS have incorporated already well-recognized “polar systems” by L. Rider and W.S. Adams, “kinematically regular systems” by G.V. Mozhaev, and “delta-systems” by J.G. Walker, as well as “near-polar systems” by Yu.P. Ulybyshev, and some other satellite constellations unknown before. A universal method of SLS optimization is presented, valid for any values of coverage multiplicity and the number of satellites in a system. The method uses the criterion of minimum radius of a circle seen from a satellite on the surface of the globe. Among the best SLS found in this way there are both systems representing the well-known classes mentioned above and new orbit constellations of satellites.     

椭圆轨道卫星对地全球覆盖电推进控制

针对椭圆轨道卫星近/远地点的星下点对全球或特定纬度区域的访问问题,提出一种连续小推力下的对地覆盖控制策略。首先,推导了自然摄动对卫星拱线变化的影响,并探讨了进行小推力覆盖控制的必要性。然后,针对燃料消耗的优化问题,将控制方程展开成含傅里叶级数的形式,用以获得便于星上计算的解析形式的次优解,同时探讨了截取阶数与优化程度的关系。在进行拱线控制的同时,通过合理设置约束,对椭圆轨道的近地点高度进行保护,确保卫星安全运行。仿真结果表明,提出的方法能够以适当的燃料消耗代价实现椭圆轨道的近/远地点的全球覆盖控制或特定纬度区域的反复推扫,且控制力在可接受的范围内。     

Optimal Choice of a Satellite Broadcasting System Based on High-Elliptic Orbits

The problem of the construction of a satellite broadcasting system whose capabilities are supplemented and expanded in comparison with geosynchronous satellites is considered. The optimal orbit of a high-elliptic satellite of the Earth, which provides for a maximal duration of stay of the satellite sighting line within the directional pattern of an antenna motionlessly installed on the Earth's surface, is determined. The advantages of using a satellite system with such orbits are shown.     

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.     

基于T-H方程的卫星轨迹模型参考输出跟踪控制方法

当目标卫星沿椭圆轨道运行时,描述追踪星与目标星相对运动的线性化方程为T-H方程。将描述航天器相对运动的T-H方程变换为周期系统的状态空间形式,并给出卫星轨迹跟踪控制问题的数学描述。基于周期系统的参量Lyapunov方法和模型参考跟踪控制理论,提出了卫星轨迹跟踪控制器的设计方法。利用该方法设计了带有收敛速率保障的反馈镇定控制器和具有自由参数的前馈控制器。对追踪星相对目标星悬停任务进行了数值仿真,仿真结果表明提出的控制方案是有效的。     

Calculation of quasisynchronous orbits of a spacecraft around Phobos for solving the problem of landing on its surface

The problem of selecting quasi-synchronous orbits of a spacecraft around Phobos is considered. These quasi-synchronous orbits are far (with respect to the Hill’s sphere) quasi-satellite orbits with retrograde rotation in the restricted three body problem. The orbit should pass through a given point at a specified time instant. It should also possess a property of minimum distance from the Phobos surface at every passage above the region of planned landing. The equations of dynamics are represented in the form describing the orbit as a combination of motions in two drifting ellipses, inner and outer ellipses. The center of the outer ellipse is located on the inner ellipse. A formula is derived that relates averaged values of half-axes of the inner and outer ellipses. It is used for construction of the first approximation of numerically designed orbit, which makes it possible to simplify and speed up the computing process. The tables of initial conditions obtained as a result of calculations are presented.     

Capabilities of Kinematically Regular Satellite Systems with Symmetry Groups of the Second Type in the Problem of Continuous Single Coverage of the Earth

The problem of a continuous single coverage of the Earth by systems of satellites in circular orbits of equal radii is considered. The results of calculating the characteristics of kinematically regular systems consisting of 6 to 60 satellites and possessing symmetry groups of the second type are presented. It is shown that, when the number of satellites varies from 20 to 38 inclusive, the best systems of this class surpass all currently known systems with respect to their characteristics.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 3, 2005, pp. 215–223.Original Russian Text Copyright © 2005 by Mozhaev.     

A specific case of stability of cylindrical precession of a satellite

In a central Newtonian gravitational field, the motion of a dynamically symmetrical satellite along an elliptical orbit of arbitrary eccentricity is considered. The particular motion of the satellite is known when its axis of symmetry is perpendicular to the orbit plane, and the satellite rotates about this axis with a constant angular velocity (cylindrical precession). A nonlinear analysis of stability of this motion has been performed under the assumption that the geometry of the satellite mass corresponds to a thin plate. At small values of orbit eccentricity e the analysis is analytical, while numerical analysis is used for arbitrary values of e.     

Designing nonuniform satellite systems for continuous global coverage using equatorial and polar circular orbits

We present a method for designing nonuniform satellite systems for continuous global coverage using a combination of equatorial and near-polar satellite segments in circular orbits. Equations are derived to determine the basic design parameters of the satellite system itself and the conditions of its closure at the joint of near-polar and equatorial segments. We analyze specific features of near-polar and equatorial satellite systems and their advantages and disadvantages compared with existing classes of near-polar phased and kinematically correct satellite systems. We estimate the minimum required number of spacecrafts in satellite systems for a given fold of coverage and present calculated dependences for classes of near-polar phased and equatorial satellite systems with different types of closure. For the class of kinematically correct satellite systems, we analyze the characteristics of systems with a minimum spacecraft flight height and reveal that the number of satellites in the orbital plane depends on the flight height for different folds of coverage. We bring examples of the best near-polar equatorial satellite systems of global coverage for different folds and a class of satellite systems with a fixed number of spacecrafts and orbital planes in them.     

Orbit lifetime for microparticles in highly elliptical orbits with low perigee

On the basis of numerical experiments, we have shown the principal possibility of long (more than 1 month) and extremely long (more than 1 year) orbit lifetime of technogenic microparticles with radii from 1 to 100 μm injected into the near-Earth space in highly elliptical orbits with low perigee, including the case of an orbit with parameters corresponding to the orbital parameters of the Molniya satellite. Calculations are performed taking into account the perturbing effect on the orbital microparticle motion in the near-Earth space of gravitational perturbation caused by the Earth’s polar oblateness, the solar pressure force (calculated using methods of the Mie theory), and the drag force of neutral component of the background gas under conditions of low, medium, and high levels of solar and geomagnetic activities.     

椭圆轨道交会、悬停与绕飞的全状态反馈控制

面向大椭圆轨道航天器交会对接、编队伴飞以及在轨操控等空间应用的需求,对大椭圆轨道上航天器间的相对运动进行了分析与建模,采用幂级数法分别在脉冲推力和常值推力作用两种情况下对系统进行了近似求解。通过对系统解的变换以及对系统状态的重构,给出了大椭圆轨道上的三种交会制导律。脉冲推力作用假设下的脉冲制导类似近圆轨道的Hill制导方法。常值推力作用假设下的全状态反馈制导律则在交会制导、相对悬停和循迹绕飞控制的过程中实现了对相对位置和相对速度的同步控制。通过构造新的系统状态,改进的变系数全状态反馈制导律提高了相对速度的制导精度,降低了相对制导过程中的最大轨控加速度。三种制导律的制导效果通过数学仿真进行了校验和比较,文中给出的方法实现了椭圆轨道上相对交会制导、悬停保持和循迹绕飞控制。     

卫星对地球覆盖情况的判据及算法探讨

在多颗卫星轨道的设计过程中，经常要考虑卫星对地球的覆盖情况。本文针对多颗卫星在某一时刻是否对地球进行了全球覆盖进行了探讨，并同了一种简单的判定方法及其对应的算法，同时对这一方法进一步推广为判定是否多颗卫星同时对地球进行了Ｎ次覆盖。本文给出的方法对于卫星网设计有一定的帮助。     

The Solution of Some Problems of Optimizing the Processes of a Flexible Correction of Motion of Satellite Systems: I

The first of a series of problems of the optimization of correction of satellite systems, moving over near-circular orbits, is considered. The correction is accomplished by means of low-thrust engines and is supposed to be flexible, where only the parameters of the relative motion of satellites must be corrected. The problem has a large dimension, but is invariant with respect to renumbering of satellites. This allows us to decompose the problem, i.e., to find new variables, linearly dependent on old ones, in which the problem breaks down into a series of independent subproblems of low dimension. The decomposition is accomplished by means of the technique [1] based on the theory of linear representations of groups.     

The dive and ascent satellite program for lower ionosphere research

Lower ionosphere is a transition region from outer-space to low atmosphere and had been unexplored on a continuous basis before Atmosphere Explorer satellites flew in the region. Purpose of a new aeronomy satellite, DAS (Dive and Ascent Satellite) having a capability to control orbits and flying at the very low perigee altitude less than 130 km is to explore the bottomside of ionosphere spreading over between 100 and 300 km altitudes. Preliminary study on the new aeronomy satellite is conducted at National Aerospace Laboratory in cooperation with Radio Research Laboratories and Meteorological Research Institute.This paper reviews the mission design, orbit decay and transfer analysis, typical orbit profile, aerodynamic characteristics and satellite configuration study, aerodynamic heating and thermal control analysis, attitude control analysis, on-board propulsion and power subsystems, and operation analysis with emphasis on their technical feasibility.     

偶数重连续覆盖的Walker星座设计方法

针对期望覆盖重数为偶数重时连续覆盖Walker星座的构型设计问题,提出一种基于覆盖带理论的构型设计方法。首先分析同轨道卫星组成覆盖带时的构型设计特例,随后将结论推广,改进了传统Walker星座的构型表征形式并提出覆盖带构型参数。基于轨道参数的相平面映射,给出了异轨卫星组成覆盖带时特征宽度的计算方法。通过分析相平面上覆盖带的拼接情况,给出了轨道倾角的优化策略和偶数重覆盖任意纬度的Walker星座设计步骤。所提出方法能显著提高构型枚举效率,且能满足不同纬度范围的覆盖需求。仿真表明,该方法能减少约10%覆盖所需的卫星数量,并能通过调整构型参数进一步优化轨道面数量。