地月空间拟周期轨道上航天器自主导航与轨道保持研究
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摘要
地月共线平动点附近轨道上的飞行器适合于科学数据采集、中继通讯以及深空导航组网等任务。研究该轨道上的飞行器具有显著的理论和现实意义。与日地系统相比，地月系统平动点轨道的周期更短、第二主天体的轨道偏心率更大、太阳作为第三引力体对地月系统的引力影响更强烈，圆形限制性三体问题中的周期轨道并不存在于地月平动点附近，取而代之的是一种“拟”周期轨道的形态。因此，地月系统共线平动点轨道上飞行器的任务轨道设计、自主导航以及轨道保持任务将面临更大挑战。论文结合国家自然科学基金群体项目“航天飞行器鲁棒控制理论与应用”中“弱稳定轨道上航天器动力学、导航与鲁棒制导问题研究”，致力于研究地月平动点拟周期轨道上航天器动力学建模、轨道设计、自主导航和轨道保持问题，为我国早日实现地月平动点探测提供技术支持。
首先，研究了地月平动点拟周期轨道上飞行器的建模问题。由于，圆形限制性三体问题是研究地月平动点拟周期轨道上飞行器的理论基础，因此，本文建立了地月系统的圆形限制性三体模型，给出了地月系统中圆形限制性三体条件下，与共线平动点相关的轨道解析解。然而，仅仅研究圆形限制性三体模型无法真实反映飞行器在地月平动点附近的运动特征，而传统高阶模型存在形式复杂和计算繁琐等不足。因此，本文提出了一种结构简单的高精度地月平动点动力学模型，该模型使用标准星历来表示太阳和月球的运动状态，从而实现了在动力学中考虑太阳的直接引力、间接引力以及月球的偏心率等因素的目的。仿真验证表明，相比圆形限制性三体模型、椭圆形限制性三体模型以及双圆四体模型，本文提出的模型具有更高的精度。
其次，本文研究了地月平动点拟周期轨道上飞行器任务轨道的设计问题。由于使用限制性三体模型设计任务轨道时会缺乏对摄动因素的考虑，因此，本文沿用了使用高精度星历模型和多步打靶法来设计地月平动点拟周期轨道的思路。更进一步地，针对传统方法的不足提出了两点改进措施：第一，采用了地月平动点拟周期轨道飞行器在地月旋转系下的高精度动力学模型，从而避免了传统设计方法中大量的会合坐标系与惯性坐标系之间的转换以及转换中对于角速度做出的二体假设；第二，根据地月平动点拟周期轨道在瞬时平动点会合坐标系中的轨道特征以及瞬时L2点在地心会合坐标系中的状态来计算拼接点信息，由此，简化了其他文献中所记载的拼接点求取方法。
再次，本文研究了地月平动点拟周期轨道飞行器的自主导航和轨道保持问题。这是两个相互耦合的问题，由于平动点拟周期轨道处于动力学混沌系统中，其对于轨道初值具有强烈的敏感性。初始入轨偏差会导致飞行器状态很快发散并大范围地偏离设计轨道，因此，轨道保持系统在探测器入轨后不久就必须启动工作，导航系统必须在短弧段测量的条件下提供精确的估计结果以满足弱稳定轨道的需要。
因此，在自主导航方案的选择中必须考虑来自轨道保持的约束。针对地月L2点探测器所处的弱稳定拟周期轨道，本文论证了基于日地月信息的自主导航方法的可行性。在此基础上，考虑到弱稳定轨道不同于近地强稳定轨道的特性，提出了三种敏感器组合方案，并给出各方案的导航观测方程。借鉴Genesis、ARTEMIS等平动点探测器实际轨道保持过程中对于自主导航的要求，结合非线性可观测性理论，对本文提出的三种敏感器组合的可观测性进行了分析。
此外，在轨道保持策略设计中必须考虑来自自主导航的约束。因此，本文列出了地月平动点飞行器在实际飞行过程中由动力学环境以及控制执行机构本身对轨道保持算法带来的约束条件，特别的在约束中加入了来自自主导航的约束要求。然后，对常见的几种轨道保持算法进行了约束分析。在满足自主导航约束的基础上，针对存在初始入轨偏差条件下，传统基准轨道靶点法无法保证控制效果的情况，提出了改进的基准轨迹靶点法，并对其进行了仿真验证。
最后，通过闭环仿真对本文提出的自主导航方案和轨道保持策略的可行性进行了验证。
The probes about the Earth-Moon collinear libration points are suitable forscientific data collection, relay communication and navigation network for deepspace tasks. The study of those orbits has significant theoretical and practicalsignificance. For Earth-Moon system, however, the applications are morechallenging than those in the Sun-Earth system, in part because of the shorter timescales, the larger orbital eccentricity of the secondary, and the fact that the Sun actsas a significant perturbing body in terms of the gravitational force as well as solarradiation pressure. Instead of the periodic orbits in the circular restricted three bodyproblem, the orbits in real Earth-Moon system present the quasi-periodicity.Therefore, the system modeling, orbit design, autonomous navigation and orbitmaintance for the orbits about the Earth-Moon collinear libration points are morechallenging. With the support of the Chinese Science National Foundation-theFundamental Research of Spacecraft Robust Control and Application, thisdissertation focuses on modeling, orbit design, autonomous navigation and orbitmaintance for the probes about the Earth-Moon collinear libration points.
First of all, since the Circular Restricted Three-body Problem (i.e CR3BP) isthe basic model for the Earth-Moon libration missions, the Earth-Moon system isdecribed in the CR3BP condition as well as the analytical solutions for Earth-Moonlibration orbits. However, the CR3BP cannot precisely reflect the motions of theprobes around the Earth-Moon libration points and the traditional high-order modelis too complex. Therefore, this dissertation proposes an accurate model for theprobes around the Earth-Moon libration points with simple structure, which usesthe standard ephemeris to represent the motions of the Sun and the Moon in order totake the direct and indirect influence of the Sun into account as well as theeccentricity of the Moon. Simulation shows that, compared with the CR3BP, theelliptic restricted three-body model and restricted four-body model, the proposedmodel is more accurate.
Secondly, this dissertation studies orbit design problem for the Earth-Moonlibration quasi-periodic orbit. Designing orbit with multiple shooting method andhigh-accuracy ephemeris model is the latest method which can overcome sometraditional defects in the restricted three-body problem, such as the disregard for theSun’s perturbation. Due to complex calculations for patch points and lots ofcoordinate transformations involved in this method, two improvements areproposed in this dissertation to ameliorate the condition. Firstly, the traditionalephemeris model is reformed and established in the Earth-Moon rotating frame,which can avoid large amounts of coordinate transformations during the multipleshooting. Secondly, based on the characteristics of quasi-periodic orbits about thetranslunar libration point, instead of massive calculations, simple coordinatetransformations can provide necessary information for patch points of multipleshooting. Simulation results show that the proposed method can be used effectivelyto design quasi-periodic orbits about the translunar libration point.
Subsequently, this dissertation studies the autonomous navigation andstationkeeping problem, which are mutual coupling problems. An initial error couldtrigger a fast divergence of the unstable state and drift a probe far away from thenominal orbit. The station-keeping system must be started soon after the probe isinjected, while the navigation system should provide convergent results within ashort period and the results need to be accurate enough for the station-keepingsystem.
Therefore, the constraints from the stationkeeping system must be consideredduring the design of autonomous navigation. Sun-Earth-Moon (i.e., SEM)autonomous navigation problem is investigated for the quasi-lissajous orbit and theQuasi-periodic Halo orbit about the translunar libration point. Generally, SEMnavigation method can offer a convergent estimation by using orientationinformation. However, due to the unstable nature of the translunar libration orbit, itis still indispensable to further prove that only orientation information canguarantee the convergence. Therefore, three sensor configurations are studied tofind an appropriate sensor configuration for translunar libration probe. The observability analysis and experiences from Genesis probe, ARTEMIS probe areused to evaluate the feasibility of each sensor configuration. Autonomousnavigation is obtained by extended Kalman Filtering.
In addition, the constraints from the autonomous navigation system must beconsidered during the design of stationkeeping. Several stationkeeping strategiesare analysed based on the constraints from dynamical environment, actuator andautonomous navigation system. Then, an impoved control-point strategy isproposed which can provide converged results when initial injection error,navigation error and execution error are considered.
Finally, a closed-loop simulation of autonomous navigation and stationkeepingstrategy is performed to verify the feasibility.
首先，研究了地月平动点拟周期轨道上飞行器的建模问题。由于，圆形限制性三体问题是研究地月平动点拟周期轨道上飞行器的理论基础，因此，本文建立了地月系统的圆形限制性三体模型，给出了地月系统中圆形限制性三体条件下，与共线平动点相关的轨道解析解。然而，仅仅研究圆形限制性三体模型无法真实反映飞行器在地月平动点附近的运动特征，而传统高阶模型存在形式复杂和计算繁琐等不足。因此，本文提出了一种结构简单的高精度地月平动点动力学模型，该模型使用标准星历来表示太阳和月球的运动状态，从而实现了在动力学中考虑太阳的直接引力、间接引力以及月球的偏心率等因素的目的。仿真验证表明，相比圆形限制性三体模型、椭圆形限制性三体模型以及双圆四体模型，本文提出的模型具有更高的精度。
其次，本文研究了地月平动点拟周期轨道上飞行器任务轨道的设计问题。由于使用限制性三体模型设计任务轨道时会缺乏对摄动因素的考虑，因此，本文沿用了使用高精度星历模型和多步打靶法来设计地月平动点拟周期轨道的思路。更进一步地，针对传统方法的不足提出了两点改进措施：第一，采用了地月平动点拟周期轨道飞行器在地月旋转系下的高精度动力学模型，从而避免了传统设计方法中大量的会合坐标系与惯性坐标系之间的转换以及转换中对于角速度做出的二体假设；第二，根据地月平动点拟周期轨道在瞬时平动点会合坐标系中的轨道特征以及瞬时L2点在地心会合坐标系中的状态来计算拼接点信息，由此，简化了其他文献中所记载的拼接点求取方法。
再次，本文研究了地月平动点拟周期轨道飞行器的自主导航和轨道保持问题。这是两个相互耦合的问题，由于平动点拟周期轨道处于动力学混沌系统中，其对于轨道初值具有强烈的敏感性。初始入轨偏差会导致飞行器状态很快发散并大范围地偏离设计轨道，因此，轨道保持系统在探测器入轨后不久就必须启动工作，导航系统必须在短弧段测量的条件下提供精确的估计结果以满足弱稳定轨道的需要。
因此，在自主导航方案的选择中必须考虑来自轨道保持的约束。针对地月L2点探测器所处的弱稳定拟周期轨道，本文论证了基于日地月信息的自主导航方法的可行性。在此基础上，考虑到弱稳定轨道不同于近地强稳定轨道的特性，提出了三种敏感器组合方案，并给出各方案的导航观测方程。借鉴Genesis、ARTEMIS等平动点探测器实际轨道保持过程中对于自主导航的要求，结合非线性可观测性理论，对本文提出的三种敏感器组合的可观测性进行了分析。
此外，在轨道保持策略设计中必须考虑来自自主导航的约束。因此，本文列出了地月平动点飞行器在实际飞行过程中由动力学环境以及控制执行机构本身对轨道保持算法带来的约束条件，特别的在约束中加入了来自自主导航的约束要求。然后，对常见的几种轨道保持算法进行了约束分析。在满足自主导航约束的基础上，针对存在初始入轨偏差条件下，传统基准轨道靶点法无法保证控制效果的情况，提出了改进的基准轨迹靶点法，并对其进行了仿真验证。
最后，通过闭环仿真对本文提出的自主导航方案和轨道保持策略的可行性进行了验证。
The probes about the Earth-Moon collinear libration points are suitable forscientific data collection, relay communication and navigation network for deepspace tasks. The study of those orbits has significant theoretical and practicalsignificance. For Earth-Moon system, however, the applications are morechallenging than those in the Sun-Earth system, in part because of the shorter timescales, the larger orbital eccentricity of the secondary, and the fact that the Sun actsas a significant perturbing body in terms of the gravitational force as well as solarradiation pressure. Instead of the periodic orbits in the circular restricted three bodyproblem, the orbits in real Earth-Moon system present the quasi-periodicity.Therefore, the system modeling, orbit design, autonomous navigation and orbitmaintance for the orbits about the Earth-Moon collinear libration points are morechallenging. With the support of the Chinese Science National Foundation-theFundamental Research of Spacecraft Robust Control and Application, thisdissertation focuses on modeling, orbit design, autonomous navigation and orbitmaintance for the probes about the Earth-Moon collinear libration points.
First of all, since the Circular Restricted Three-body Problem (i.e CR3BP) isthe basic model for the Earth-Moon libration missions, the Earth-Moon system isdecribed in the CR3BP condition as well as the analytical solutions for Earth-Moonlibration orbits. However, the CR3BP cannot precisely reflect the motions of theprobes around the Earth-Moon libration points and the traditional high-order modelis too complex. Therefore, this dissertation proposes an accurate model for theprobes around the Earth-Moon libration points with simple structure, which usesthe standard ephemeris to represent the motions of the Sun and the Moon in order totake the direct and indirect influence of the Sun into account as well as theeccentricity of the Moon. Simulation shows that, compared with the CR3BP, theelliptic restricted three-body model and restricted four-body model, the proposedmodel is more accurate.
Secondly, this dissertation studies orbit design problem for the Earth-Moonlibration quasi-periodic orbit. Designing orbit with multiple shooting method andhigh-accuracy ephemeris model is the latest method which can overcome sometraditional defects in the restricted three-body problem, such as the disregard for theSun’s perturbation. Due to complex calculations for patch points and lots ofcoordinate transformations involved in this method, two improvements areproposed in this dissertation to ameliorate the condition. Firstly, the traditionalephemeris model is reformed and established in the Earth-Moon rotating frame,which can avoid large amounts of coordinate transformations during the multipleshooting. Secondly, based on the characteristics of quasi-periodic orbits about thetranslunar libration point, instead of massive calculations, simple coordinatetransformations can provide necessary information for patch points of multipleshooting. Simulation results show that the proposed method can be used effectivelyto design quasi-periodic orbits about the translunar libration point.
Subsequently, this dissertation studies the autonomous navigation andstationkeeping problem, which are mutual coupling problems. An initial error couldtrigger a fast divergence of the unstable state and drift a probe far away from thenominal orbit. The station-keeping system must be started soon after the probe isinjected, while the navigation system should provide convergent results within ashort period and the results need to be accurate enough for the station-keepingsystem.
Therefore, the constraints from the stationkeeping system must be consideredduring the design of autonomous navigation. Sun-Earth-Moon (i.e., SEM)autonomous navigation problem is investigated for the quasi-lissajous orbit and theQuasi-periodic Halo orbit about the translunar libration point. Generally, SEMnavigation method can offer a convergent estimation by using orientationinformation. However, due to the unstable nature of the translunar libration orbit, itis still indispensable to further prove that only orientation information canguarantee the convergence. Therefore, three sensor configurations are studied tofind an appropriate sensor configuration for translunar libration probe. The observability analysis and experiences from Genesis probe, ARTEMIS probe areused to evaluate the feasibility of each sensor configuration. Autonomousnavigation is obtained by extended Kalman Filtering.
In addition, the constraints from the autonomous navigation system must beconsidered during the design of stationkeeping. Several stationkeeping strategiesare analysed based on the constraints from dynamical environment, actuator andautonomous navigation system. Then, an impoved control-point strategy isproposed which can provide converged results when initial injection error,navigation error and execution error are considered.
Finally, a closed-loop simulation of autonomous navigation and stationkeepingstrategy is performed to verify the feasibility.
引文
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