【作者】 张大力；

【导师】 王常虹； 夏红伟；

【作者基本信息】 哈尔滨工业大学 ， 控制科学与工程， 2023， 博士

【摘要】 地球静止轨道（Geostationary Earth Orbit,GEO）卫星对地观测范围广、应用效益高,广泛应用于军、民、商等领域,具有极高的战略价值。然而,受技术水平和空间环境等因素的影响,GEO卫星在轨故障频发,严重影响卫星性能甚至导致卫星失效,带来巨大的经济损失和不利的社会影响。同时,不断增长的空间碎片占据了大量轨道资源,严重威胁GEO卫星的安全运行和轨道空间的可持续发展。为了维护轨道环境,保护GEO空间资产的安全,亟需开发面向GEO卫星的在轨服务技术。其中,高可靠、低成本、高精度的实现对GEO目标的近程交会是顺利开展在轨服务任务的前提和关键。为了满足任务需求,近程交会过程中服务星的运行轨迹在任何情况下均应保证自身和目标的绝对安全,并且该阶段的相对导航技术需要具备较高的精度和可靠性。本文以GEO卫星在轨服务过程中的近程交会阶段为研究背景,以交会任务中存在的轨迹优化和相对导航问题为主要研究对象,探讨多摄动影响下的GEO卫星相对运动建模、GEO卫星安全交会轨迹优化设计、仅测角条件下的相对导航方法和混合推力机动目标相对导航方法等理论问题,并基于一套地面半物理仿真系统对本文理论方法进行验证。主要完成以下内容:（1）研究了多摄动影响下的卫星相对运动建模问题。详细分析了主要摄动力对GEO卫星的影响;提出一组扩展的准非奇异平均相对轨道根数描述两星相对运动,在此基础上提出一种包含主要摄动力的相对运动建模方法,并分别推导地球非球形引力摄动J₂和J₃项、第三体引力摄动和太阳光压（Solar Radiation Pressure,SRP）摄动对相对运动影响的系统矩阵,进而给出了解析的相对运动模型;给出了平均和瞬时相对轨道根数以及相对位置/速度的线性变换关系,避免了复杂的迭代计算。在给定的初始条件下对两个典型的GEO任务场景进行仿真,分析了不同摄动因素对相对轨道根数的影响规律,并将改进模型应用于GEO卫星相对位置保持控制,结果表明所提模型具备较高的准确性。（2）研究了GEO卫星安全交会轨迹优化设计问题。考虑导航和控制偏差,提出了一种量化的安全性评价指标,并给出了计算方法。从目标函数、优化变量和约束条件三个方面出发,构建了兼顾燃料和安全性最优的安全交会轨迹优化模型,其中引入一种代数判据对被动安全约束进行判定,避免了数值迭代的巨大计算量。通过数值仿真,分析并总结了燃料消耗与安全性指标之间的关系,给出了可用于实际交会任务的建议方案。无推力自由飞行段的仿真表明,仅考虑燃料最优得到的交会方案存在潜在的碰撞风险,而考虑了安全性指标的优化方案能够保证交会轨迹的安全性。（3）研究了仅测角条件下的相对导航问题。采用相机偏置安装的方式提高系统的可观性,给出了仅测角导航观测模型,并通过“类线性”变换的可观性分析方法,给出相对距离可观测的相机偏置安装条件。为了解决粒子滤波算法固有的样本贫化问题,提出一种改进萤火虫算法对其重采样过程进行优化,并对优化算法收敛性进行证明,在此基础上提出一种改进粒子滤波算法,有效提高了算法的估计性能,为解决仅测角相对导航问题提供了参考方案。（4）研究了GEO混合机动目标的相对导航问题。考虑GEO卫星的常见推力配置,分析了其典型的机动特性。针对交互多模型（Interacting Multiple Model,IMM）算法对混合机动目标模型较难匹配的问题,建立考虑无机动、脉冲机动和有限推力机动三种情况的交互模型集,覆盖了GEO目标典型机动特性。进一步的,针对IMM算法模型转移概率近似的问题,提出一种基于加速度估计的自适应修正模型转移概率计算方法,增强了匹配模型的作用。所提改进算法的性能较传统IMM算法有较大提高,能够有效实现对GEO混合推力机动目标的相对导航。（5）研究了理论方法的地面仿真验证问题。基于已有实验条件设计搭建了一套空间交会地面半物理仿真系统,详细论述了系统功能和需求,给出了系统具体组成和工作原理,并根据系统缩比仿真原理,给出了系统缩放比例与仿真能力的对应关系。基于所搭建的仿真平台,分别设计了安全交会轨迹优化方法、仅测角相对导航方法和混合推力机动目标相对导航方法的仿真方案,并对本文所提仅测角相对导航方法进行试验,证明了理论方法以及平台设计的正确性。论文围绕GEO卫星交会任务中的轨迹优化和相对导航问题做了较为系统的理论分析和研究,所提方法和取得的成果对未来面向GEO目标的在轨维护、空间碎片清除和空间攻防等任务具有重要的现实意义。更多还原

【Abstract】 Due to the wide range of earth observation and high application efficiency,Geostationary Earth Orbit（GEO）satellites are widely used in military,civil and commercial fields,which have high strategic value.However,influenced by technical level and space environment and other factors,GEO satellites have frequent on-orbit failures,which seriously affect the performance of satellites and even lead to the failure of satellite functions,bringing huge economic losses and adverse social impacts.Meanwhile,the growing space debris occupies a large amount of orbital resources,which seriously threatens the safe operation of GEO satellites and the sustainable development of orbital space.In order to maintain the orbital environment and protect the safety of GEO space assets,it is urgent to develop the on-orbit service technology for GEO satellites,among which a high reliability,low cost and high accuracy to achieve the proximity rendezvous to GEO targets is the prerequisite and the key to successfully carrying out the on-orbit service mission.In order to meet the mission requirements,the trajectory of the service satellite during the proximity rendezvous should be absolutely safe under all circumstances,and the relative navigation technology in this phase should have high accuracy and reliability.This thesis takes the proximity rendezvous phase of the on-orbit service mission of GEO satellites as the research background,and takes the trajectory optimization and relative navigation problems existing in the rendezvous mission as the main research objects.It investigate the theoretical problems such as relative motion modeling of GEO satellites under the influence of main perturbations,the optimization design of GEO satellites safe rendezvous trajectory,the angles-only relative navigation method and the relative navigation approach of hybrid thrust maneuvering target.Based on a set of ground semi-physical simulation system,the theoretical methods in this thesis are validated.The following are mainly accomplished.（1）The relative motion modeling of GEO satellites under the influence of multiple perturbations is studied.A detailed analysis of the influence of the main perturbations on the GEO satellites is presented.An extended set of quasi-nonsingular mean relative orbital elements is proposed to describe the relative motion of the two satellites.On this basis,a relative motion modeling method including the main perturbations is proposed,and the systematic matrices of the relative motion effects of the Earth non-spherical gravitationalJ₂,J₃ term perturbations,the third-body perturbations and the solar radiation pressure（SRP）perturbation are derived respectively,and then an analytical relative motion model is given.The linear transformation from the mean relative orbital elements to the osculating relative orbital elements and from the osculating relative orbital elements to the relative position/velocity are given,avoiding complicated iterative calculations.Under the given initial conditions,two typical GEO mission scenarios are simulated by using the derived relative motion model,and the influence mechanism of different perturbations on the mean relative orbital elements is obtained.The improved model is applied to the GEO satellites relative position keeping control,and the results show that the proposed model has high accuracy（2）The optimal design problem of safe rendezvous trajectory for satellites is studied.Considering the influence of navigation and control deviations,a quantitative safety evaluation index is proposed,and the calculation method is given.From three aspects of objective function,optimization variables and constraints,a safe rendezvous trajectory optimization model that takes into account the optimal fuel and safety is constructed.An algebraic criterion is introduced to determine the passive safety constraints,which avoids the huge computation of numerical iterations.Through numerical simulation,the relationship between fuel consumption and the safety index is analyzed and summarized,and a proposed scheme that can be used for actual rendezvous missions is given.The simulation of the thrustless free flight phase shows that the rendezvous scheme only considering the fuel optimization has potential collision risk,and the optimization scheme considering the safety index can ensure the safety of the rendezvous trajectory.（3）The angles-only relative navigation problem is studied.The camera offset installation method is adopted to improve the observability of the system,and an observability analysis method of‘quasi linear’transformation is used to give the camera offset installation conditions with relative distance observable.In order to solve the problem of sample dilution inherent in the particle filter algorithm,an improved firefly algorithm is proposed to optimize its resampling process,and the convergence of the optimization algorithm is proved.On this basis,an improved particle filter algorithm is proposed,which effectively improves the estimation performance of the algorithm and provides a reference scheme for solving the problem of angles-only relative navigation.（4）The relative navigation of GEO hybrid maneuvering targets is studied.Considering the common thrust configuration of GEO satellites,the typical maneuver characteristics are analyzed.Aiming at the problem that IMM algorithm is difficult to match the model of hybrid maneuvering targets,an interactive model set considering three cases of no maneuver,impulse maneuver and limited thrust maneuver is established,which covers the typical maneuvering characteristics of GEO satellites.Furthermore,aiming at the problem of model transition probability approximation of IMM algorithm,an adaptive modified model transition probability calculation method based on acceleration estimation is proposed,which enhances the role of matching model.The performance of the proposed improved algorithm is greatly improved compared with the traditional IMM algorithm,which can effectively realize the relative navigation of GEO hybrid thrust maneuvering targets.（5）The ground simulation verification problem of the proposed theoretical method is studied.Based on the existing experimental conditions,a set of ground semi-physical simulation verification system for space rendezvous is designed and built.The system functions and requirements are discussed in detail,the specific composition and working principle of the system are given,and the corresponding relationship between the scale of the system and the simulation ability is given according to the principle of system scale simulation.Based on the built simulation platform,the simulation schemes of the safe rendezvous trajectory optimization method,the angles-only relative navigation method and the hybrid thrust maneuvering target relative navigation method are designed respectively,and the angles-only relative navigation method proposed in this thesis is tested to verify the correctness of the theoretical method and the platform design.This thesis systematically analyses and studies the trajectory optimization and relative navigation problems in the GEO satellites rendezvous mission.The proposed methods and the obtained results presented in this thesis are of great practical significance for future missions for GEO satellites,such as on-orbit maintenance,space debris removal and space attack and defense,et al.更多还原