分布式航天系统在干涉测量、遥感成像、互联网通信等空间任务中发挥了重要作用。近年来，低轨巨型星座由于其全覆盖、高带宽、低时延的通信能力受到广泛关注。低轨巨型星座的星间距离尺度远大于传统编队集群，同时庞大的卫星数量增加了地面集中测控规划的压力，带来了分布式航天系统动力学与控制的新难题。亟需探索不受空间尺度约束的卫星相对运动模型，发展卫星在轨协同的控制能力。针对任意空间尺度下相对运动高精度建模问题，本文基于一阶位形分解模型，创新地提出了广域不变相对轨道根数的概念，揭示了大空间尺度下扭曲椭圆的相对运动几何特征，推导了广域不变相对轨道根数与轨道根数差、相对位置速度之间的转换关系，分析了 摄动对广域相对运动的长期影响，为大规模分布式航天系统动力学分析与控制奠定了理论基础。针对构型约束下卫星编队构型重构自组织控制问题，本文基于相对轨道根数建立了构型重构势函数，基于李雅普诺夫方法和高斯变分方程，对势函数控制稳定性进行了严格证明，提出了二体引力环境下二次型引力势函数变量选取准则，实现了分布式航天系统的低能耗自组织构型控制。针对有界飞行约束下卫星集群边界重构自组织控制问题，本文基于极值原理建立了适用于任意空间尺度的星间相对运动边界模型，基于边界模型建立了边界重构势函数和星间避碰势函数，实现了卫星向满足边界约束的相对运动轨道的自发收敛，利用蒙特卡洛仿真，验证了所提方法的能耗优势。针对低轨巨型星座的自组织控制问题，本文解析建立了低轨巨型星座连续覆盖约束，该约束可表示为共面卫星的升交点赤经约束和共面相邻卫星的星间相对运动边界约束。分别设计了面外控制、边界控制和半长轴控制势函数，制定了共面卫星自组织控制规则，并在GW-2星座上对星座自组织控制方法进行了仿真验证。最后，讨论了采用电推进的故障卫星替换问题。本文提出的广域不变相对轨道根数对于大规模分布式航天系统构型设计和构型受摄演化具有重要意义，提出的在轨自组织控制方法仅依赖局部观测信息，改进了现有分布式航天系统地面集中的运行模式与控制架构，为未来大规模工程应用提供了更为优化的解决方案。
Distributed space system is playing an important role in many space applications, such as interferometry, remote sensing, Internet communication, etc. In recent years, low-Earth-orbit mega constellations have received widespread attention, due to their potential to provide full-coverage, high-bandwidth and low-latency telecommunication services. The inter-satellite distance of mega constellations is much larger than that of close formations and clusters, and the numerous satellites increases the TT&C requirements on the ground, that brings new problems in relative motion dynamics and control. There is an urgent need to establish the relative motion model that is accurate for arbitrary inter-satellite range, and to develop the on-orbit coordinated control capability.For the problem of high-precision modeling of relative motion with arbitrary inter-satellite range, the dissertation innovatively proposes the scale-independent relative orbital elements, that demonstrate the twisted elliptical characteristic of large-range relative motion. The relationships between relative orbital elements, orbital element differences and relative position and velocity are deduced. The secular influence of perturbation on the large-range relative motion is analyzed. The above achievements lay the theoretical foundation for relative motion analysis and control of large-scale distributed space systems. For the self-organizing reconfiguration control problem of close formation flying, the dissertation establishes the reconfiguration artificial potential functions in terms of relative orbital elements. Based on the Lyapunov method and Gaussian variation equation, the stability of the proposed artificial potential functions is proved, and the selection criterion of the state variables in the quadratic attractive potential function under two-body condition is proposed. The self-organizing reconfiguration control is realized for close formations with low control consumption.For the self-organizing bounded flight control problem of satellite clusters, the dissertation establishes the boundary model between satellites based on the extreme value principle, that is suitable for different inter-satellite ranges. The corresponding artificial potential functions for bounded flight control and collision avoidance are designed based on the proposed boundary model. Satellites can be controlled to relative trajectories that satisfy the boundary constraints autonomously. The low control consumption of the proposed control method is verified by Monte Carlo simulation.For the self-organizing control problem of mega constellations, the dissertation analytically establishes the continuous coverage constraint for low-Earth-orbit mega constellations. It can be expressed as the right ascension of ascending node constraint of coplanar satellites and the boundary constraint between coplanar adjacent satellites. The out-of-plane control, boundary control and semi-major axis control are discussed by means of artificial potential functions, and the self-organizing control rules between coplanar satellites is proposed. The self-organizing control method is simulated and verified on the GW-2 constellation. Finally, the replacement of failure satellites using electric propulsion is studied.In this dissertation, the proposed scale-independent relative orbital elements are of great significance for configuration design and analysis of large-scale distributed space systems. The proposed on-orbit self-organizing concept relies on local observation information only, that changes the ground centralized operation mode and control architecture of the existing distributed space systems, and gives a better solution for future large-scale engineering applications.
