Analysis and implementation of in-plane stationkeeping of continuously perturbed Walker constellations

The stationkeeping of symmetric Walker constellations is analyzed by considering the perturbations arising from a high order and degree Earth gravity field and the solar radiation pressure. These perturbations act differently on each group of spacecraft flying in a given orbital plane, causing a differential drift effect that would disrupt the initial symmetry of the constellation. The analysis is based on the consideration of a fictitious set of rotating reference frames that move with the spacecraft in the mean sense, but drift at a rate equal to the average drift rate experienced by all the vehicles over an extended period. The frames are also allowed to experience the $J_2$-precession such that each vehicle is allowed to drift in 3D relative to its frame. A two-impulse rendezvous maneuver is then constructed to bring each vehicle to the center of its frame as soon as a given tolerance deadband is about to be violated. This paper illustrates the computations associated with the stationkeeping of a generic Walker constellation by maneuvering each leading spacecraft within an orbit plane and calculating the associated velocity changes required for controlling the in-plane motions in an exacting sense, at least for the first series of maneuvers. The analysis can be easily extended to lower flying constellations, which experience additional perturbations due to drag.     

大型低轨航天器与星座卫星的碰撞风险研究

针对商业小卫星星座迅猛发展对航天器飞行安全造成潜在威胁的问题，以600 km高度星座和大型低轨航天器为研究对象，通过区域方法(BOX)和碰撞概率风险评估方法，分析了星座与大型低轨航天器的碰撞风险。根据星座轨道演化分析表明，整个星座卫星与大型低轨航天器可能发生碰撞的时间相对集中，持续时间约 1~ 2年。BOX方法计算结果表明，每颗卫星与大型低轨航天器交会，并进入红色预警门限的交会次数约10次左右。碰撞概率计算结果表明，约有5%的卫星进入红色预警门限，星座如果在寿命末期采取无控再入将对大型低轨航天器在1~2年内产生较大的威胁。     

Post-disposal orbital evolution of satellites and upper stages used by the GPS and GLONASS navigation constellations: The long-term impact on the Medium Earth Orbit environment

The long-term evolution and environmental impact in MEO of all the abandoned spacecraft and upper stages associated with the GPS and GLONASS navigation constellations were analyzed. The orbits of the disposed objects, as of 1 May 2011, were propagated for 200 years and snapshots of their evolving distribution were obtained, together with an estimation of the changing collision probability with the spacecraft of the operational navigation systems existing or planned in MEO, i.e., GLONASS, GPS, Beidou and Galileo. The probability that the abandoned objects considered will collide with the operational spacecraft of the navigation constellations is very low, even taking into account the intrinsic eccentricity instability of the disposal orbits. Assuming the present or envisaged configuration of the constellations in MEO, the probability of collision, integrated over 200 years, would be <1/300 with a GLONASS spacecraft, <1/15,000 with a GPS or Beidou spacecraft, and <1/250,000 with a Galileo spacecraft. The worst disposal strategy consists in abandoning satellites and upper stages close to the altitude of the operational constellation (GLONASS), while a re-orbiting a few hundred km away (GPS) is able to guarantee an effective long-term dilution of the collision risk, irrespective of the eccentricity instability due to geopotential and luni-solar perturbations. The disposal strategies applied so far to the GPS satellites should be able to guarantee for at least a few centuries a sustainable MEO environment free of collisions among intact objects. Consequently, there would be no need to adopt disposal schemes targeting also the optimal value of the eccentricity vector. However, it should be pointed out that the GPS disposal strategy was devised well in advance of the Beidou constellation announcement, so most of the abandoned satellites were re-orbited fairly close to the altitude of the new Chinese system. A new re-orbiting approach will be therefore needed in the future.     

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。     

一种低轨卫星星座覆盖性能通用评价准则

针对不同构形卫星星座的统一评价问题,提出了一种低轨星座覆盖性能的通用评价准则,可对不同构形和不同高度的星座对地覆盖性能进行统一评价。该准则将星座的对地仰角特性转化为具有相同覆盖能力的标准卫星数,以之同星座中实际卫星数的比值作为星座覆盖性能指数对星座实施评价。利用该评价准则,计算了Iridium、Globalstar、Celestri和NeLS四种星座构形覆盖性能的评价指数并提出了改进方法。     

Cubature Kalman filtering for relative spacecraft attitude and position estimation

A novel relative spacecraft attitude and position estimation approach based on cubature Kalman filter is derived. The integrated sensor suit comprises the gyro sensors on each spacecraft and a vision-based navigation system on the deputy spacecraft. In the traditional algorithm, an assumption that the chief?s body frame coincides with its Local Vertical Local Horizontal (LVLH) frame is made to construct the line-of-sight observations for convenience. To solve this problem, two relative quaternions that map the chief?s LVLH frame to the deputy and chief body frames are involved. The general relative equations of motion for eccentric orbits are used to describe the positional dynamics. The implementation equations for the cubature Kalman filter are derived. Simulation results indicate that the proposed filter provides more accurate estimates of relative attitude and position over than the extended Kalman filter.     

低轨大规模星座对空间碎片环境的影响及其应对措施（英文）

Large constellations have developed rapidly in recent years because of their unique advantages, but they will inevitably have a major negative impact on the space debris environment, leading to its deterioration. The key to mitigate the impact is the success rate and duration of the post-mission disposal(PMD) process. Aiming at solving this problem, this paper further studies the impact of large constellations on other space assets under different PMD strategies through simulation, and proposes corresponding strategies and suggestions for mitigation.According to OneWeb's large constellation launch plan, the dangerous intersection of the large constellation with existing space assets at different stages of the constellations life cycle is calculated by simulation. Based on this, the influence of the large constellation operation on existing space assets at different times and strategies of PMD is analyzed. The conclusion shows that in the PMD stage, large constellations have the greatest impact on existing space assets; the PMD duration and number of satellites performing PMD at the same time are key factors to the degree of negative impact. The faster the PMD is, the less threat it poses to other spacecraft. More results and conclusions are still being analyzed.     

卫星星座的相对几何和区域覆盖重复周期

研究了在设计δ星座或者由几个δ星座的某些卫星构成的星座时经常需要考虑的三个问题：任意两颗卫星是否在同一条星下点轨迹上，同一条星下点轨迹上的卫星通过某一区域的相对顺序和星座对某特定区域或地点覆盖重复周期的计算。首先对δ星座中卫星之间的相对几何关系做了详细的分析，给出了第一个问题的判断准则，并进一步导出了位于同一条星下点轨迹上的卫星通过某一指定地区的相对顺序以及相应的时间间隔的计算方法。在解决前两个问题的基础上，针对由一个或几个δ星座(或子星座)构成的设计星座，给出了计算其区域覆盖重复周期的方法。     

Nonlinear relative position control of precise formation flying using polynomial eigenstructure assignment

A nonlinear relative position control algorithm is designed for spacecraft precise formation flying. Taking into account the effect of J₂ gravitational perturbations and atmospheric drag, the relative motion dynamic equation of the formation flying is developed in a quasi-linear parameter-varying (QLPV) form without approximation. Base on this QLPV model, polynomial eigenstructure assignment (PEA) is applied to design the controller. The resulting PEA controller is a function of system state and parameters, and produces a closed-loop system with invariant performance over a wide range of conditions. Numerical simulation results show that the performance can fulfill precise formation flying requirements.     

空间停靠动力学和控制

本文研究空间停靠是广义的，它包括停留和靠近两个内容。本文首先研究空间靠近动力学方程；其次讨论保持点的动力学特性和保持点轨迹稳定的必要条件；最后介绍靠近段安全可靠的控制策略，其中包括主动稳定保持点轨迹的控制方案。     

低轨Walker星座构型演化及维持策略分析

针对低轨(LEO)Walker星座构型维持问题，分析在地球非球形引力和大气阻力摄动下卫星的运动规律及星座构型演化特性。结果表明，低轨Walker星座构型发散主要体现在由初始轨道参数不一致引起的轨道高度衰减和相位漂移，国内首例低轨Walker星座实测轨道数据验证了理论分析的正确性。结合星座任务特性与构型发散特点，提出了基于基准卫星的相对相位维持策略，选取一颗卫星作为基准卫星，使星座中其它所有卫星相对于基准卫星的相位漂移量累加值最小，通过对目标卫星实施一次相对基准卫星的轨道高度抬升/降低，维持星间的相对位置关系。实际工程应用表明了此策略的有效性，不仅降低星座构型维持的复杂度及频次，节约燃料，且轨控时间短，为我国今后卫星星座的构型维持提供参考。     

共面快速受控绕飞轨迹设计与控制

绕飞运动在航天器在轨服务与在轨支援、辅助航天员舱外活动、航天器编队飞行、空间交会对接等空间活动中具有重要应用。分析了快速受控绕飞的可行性和主要过程，建立了适用于目标航天器运行在圆轨道上的共面快速绕飞和进入绕飞与退出绕飞的轨迹设计模型，采用多速度脉冲控制方法和等角度，等时间控制方式对绕飞轨迹进行控制。仿真计算结果表明所提出的快速受控绕飞轨迹设计模型和控制方法可以实现对圆轨道目标航天器的共面快速受控绕飞。     

GPS在航天器编队飞行任务中的基础性作用

GPS正在改变航天器的测控格局 ,拓宽卫星和星座控制技术 ,从而构成空间编队飞行定时、测量和控制的技术基础。国内外已开发出对航天器编队飞行任务进行精确定位和导航的GPS方案。GPS将充当一大类多航天器编队飞行任务的导航系统。在当前开发的空间编队飞行技术中 ,编队航天器的测量和控制、星间链路通信、任务综合与验证、编队飞行试验台、分散式控制、高轨道航天器的相对导航等 ,无一不与GPS息息相关     

单航天器无需机动对星座多星交会轨道全解

文献[1,2]已研究了单航天器无需变轨对Walker星座多星交会的轨道设计,在此基础上,依据交会点必是轨道交点的轨道特性,提出了轨道全解的解析法,可给出该轨道所能够交会卫星的最大数目,研究结果可为单航天器无需大机动变轨对星座多星接近的轨道应用提供理论参考。     

Research on constellation refueling based on formation flying

A new scheme for refueling satellite constellation is proposed in this paper. Compared with the traditional research, where the satellite refueling is implemented through spacecraft rendezvous and docking, the new pattern studied here is based on formation flying, and it is more feasible, safer and more reliable. On the grounds of the proposed pattern, two refueling strategies are studied. The first is called single supplier refueling (SSR) based on formation flying. In this scenario, one fuel-sufficient satellite called a supplier, departs from its parking orbit, and after a series of orbit maneuvers, arrives at the target constellation that consists of multiple fuel-deficient satellites called workers. It then transfers equal fuel to each worker within the prescribed mission time. The second strategy is called double suppliers refueling (DSR) based on formation flying. This time two suppliers take charge of refueling half of the workers respectively in the same way as SSR. Using a genetic algorithm, the orbit of a supplier with a minimum consumption of fuel can be obtained once the mission time is fixed. Simulation results indicate that DSR is superior to SSR and that this dominance will be more distinct as the number of workers increases and the mission time decreases.     

Orbital evolution of the first upper stages used for the new European and Chinese navigation satellite systems

The solutions adopted for the disposal of the upper stages used to put in orbit the first satellites of the new European (Galileo) and Chinese (Beidou) navigation constellations were analyzed. The orbit evolution of the rocket bodies was modeled for 200 years, taking into account all relevant perturbations, and the chosen disposal options were evaluated in terms of their long-term consequences for the debris environment. The results obtained, when applicable, were also discussed in the context of the eccentricity instability problem, pointed out in previous studies. In addition, the long-term evolution of the fragments resulting from a Beidou rocket body breakup, and of simulated high area-to-mass ratio objects released in the disposal orbits of the first two Galileo upper stages, was investigated.Eight out of ten Beidou upper stages were found to have an orbital lifetime <25 years and the other two resulted in a dwell time of approximately 6 years below 2000 km. It was also found that the perigee heights of the two upper stages used to deploy the first Galileo test spacecraft will remain more than 169 km above the constellation nominal altitude, never crossing the existing or planned navigation systems. In spite of an inclination resonance possibly leading to the exponential growth of the eccentricity over several decades, the optimal choice of the disposal orbital elements was able to prevent such an outcome, by maintaining the orbit nearly circular. Therefore, the upper stage disposal strategies used so far for Beidou and Galileo have generally been quite successful in averting the long-term interference of such rocket bodies with the navigation constellations, provided that accidental breakups are prevented.     

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.     

航天器编队飞行和空间演示验证技术——有人照料空间实验室与平动-转动物理仿真器

航天器编队飞行是近年来国内外航天领域研究的热点问题,同时也是空间技术今后一个重要发展方向。为此文章首先讨论航天器编队飞行特点;其次研究编队飞行今后能否获得顺利成功应用,有关它的各种算法和软件空间飞行演示验证技术和方法;最后介绍了美国麻省理工学院空间系统实验室（MITSSL）对航天器编队飞行算法软件空间演示验证的方法和实验。