基于能观能控理论的航天器自主导航与控制方法研究
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摘要
自主导航与控制是航天技术领域的重要研究课题。随着航天科技的发展,航天器需要完成的任务更加复杂,对导航方式与控制器的选择提出了更高的要求,加之航天器系统本身具有较强的非线性,对导航与控制系统的设计和分析带来了诸多挑战。为此,本学位论文基于非线性系统的能观性与能控性理论,对航天器自主导航系统的量测方案选择与性能分析以及小推力控制方法进行深入的研究,以期为未来相关技术的发展提供理论依据。论文的主要内容包括以下几个方面:
研究了自主导航系统的能观性分析方法。首先基于线性系统能观性鲁棒性的研究,建立了基于线性化的非线性系统局部能观性判据,利用该判据分析了基于视线矢量测量的自主导航系统能观性,并以飞越小天体自主导航为例进行仿真验证。其次通过系统微分方程本身的处理和推导,建立系统输出与初始状态之间的映射关系,借助于反函数定理给出一个利用矩阵的秩描述的局部能观性判据。进一步考虑中心引力场下运行的航天器与参考星,将所得能观性结论应用于自主导航系统的量测方案选择问题,并结合仿真算例进行分析和验证。
研究了能观性度量与自主导航性能评价方法。首先针对确定性非线性系统,给出了基于条件数的能观性度量方法,将其用于圆型限制性三体系统,按参考轨迹给出航天器各位置分量对系统状态的能观度。其次针对随机非线性系统,论证了FIM(Fisher Information Matrix)与能观性之间的关系,进而利用FIM的迹定义系统的能观度,并将其用于视线测量自主导航系统的能观度分析。然后利用FIM与状态估计精度之间的关系严格推导了最优状态估计误差方差阵的传播规律,将其作为衡量自主导航算法性能的指标,为实际导航系统的设计与分析提供理论依据。
以椭圆轨道转移问题为背景,研究了基于能控性分析的小推力控制方法。鉴于在笛卡尔坐标系下和利用轨道根数描述的小推力控制系统均为仿射非线性系统,本文基于微分几何理论研究了仿射非线性系统的能控性,发展了基于漂移向量场弱Poisson稳定的能控性判据,并利用相关结果论证了小推力控制系统的能控性,进而提出了基于阻尼反馈的小推力椭圆轨道转移控制方法,将其应用于环绕地球椭圆轨道之间的转移,利用仿真分析验证方法的有效性。
设计了半物理仿真系统对自主导航与小推力控制方法的可行性进行分析。针对环月探测器,建立了基于光学导航相机、月球图像模拟器和Matlab/Simulink/dSPACE的自主导航与控制半物理仿真系统,利用光学导航相机和激光高度计构建探测器到月心的矢量,并利用扩展卡尔曼滤波估计探测器的位置和速度,进一步将自主导航模块的输出用于小推力轨道转移的反馈控制,从而实现了环月探测器从高轨道到低轨道的转移,验证了基于矢量测量的自主导航和基于阻尼反馈的小推力控制方法的可行性。
The development of techniques for autonomous navigation and control has become an important topic in the domain of aerospace science. Because the spacecraft system and its mission are more and more complex, it raises higher demand for advanced navigation and control technology. On the other hand, the nonlinearity of the spacecraft system challenges the design and analysis of the navigation and control system. The present thesis studies the observable selction and performance analysis of spacecraft autonomous navigation, as well as the method of low-thrust orbit transfer from the control point of view by using nonlinear observability and controllability theory. The main contents of this dissertation are as follows:
Firstly, the observability problem of autonomous navigation systems is studied. The robustness of observability is studied for linear systems under nonlinear perturbations in the state dynamics and the output channel, which demonstrates the validity of linearization for observability analysis of nonlinear systems, corresponding method is used to autonomous navigation system based on line-of-sight (LOS) vector measurement, and simulation of flyby autonomous navigation is given. Then, by using the theory of ordinary differential equation, the functional relationship between the output and the initial state is derived for nonlinear dynamic systems, and a observability criteria is formulated in the form of rank conditions based on inverse function theorem, which is used to analyse the observability of various combinations of measurements for spacecraft and reference point in a central gravitation field.
Secondly, the measure of observability and performance analysis of autonomous navigation algorithm is studied. An analytical expression of observability index by using condition number for nonlinear determinant systems is presented, by using which the effects of selection of observables on analysis of dynamics for spacecraft in the restricted three body system are given. Then, the observability degree for stochastic nonlinear systems is defined by using the trace of FIM (Fisher Information Matrix), and autonomous navigation system based on LOS measurement is analysed. Further, according to the relationship between FIM and the accuracy of navigation filter, a methodology of performance analysis of autonomous navigation algorithm is presented, which can be used as a standard in design and analysis of practical navigation system.
Thirdly, the method of low-thrust control for orbit transfer is studied based on controllability analysis. To give a practical controllability criterion for low-thrust spacecraft system, controllability of affine nonlinear systems is studied by using differential geometric theory, the controllability criterion based on weakly positively Poisson stability of drift vector field is developed, by using which the controllalbiltiy property of the low-thrust transfer between elliptic orbits is analysed. A damping feedback stabilizer is then designed to steer a spacecraft from initial elliptic orbit to a given elliptic orbit, and the performance of the proposed cotroller is lillustrated by simulating an orbital transfer between two elliptic orbits around the Earth.
Lastly, semi-physical simulation system of autonomous navigation and control is built up based on optical navigation camera, lunar picture simulator and Matlab/Simulink/dSPACE integration simulation flatform. The line-of-sight vector from spacecraft to Moon’s center is constructed by using optical navigation camera and laser altimeter, and the expanded Kalman filter is adopted to estimate the inertial position and velocity of the spacecraft.The output of autonomous navigation module is used as the feedback information of spacecraft for Lunar orbital transfer from higher orbit to lower orbit, simulation results demonstrate the feasibility of autonomous navigation based on LOS vector measurement and low-thrust control based on damping feedback.
研究了自主导航系统的能观性分析方法。首先基于线性系统能观性鲁棒性的研究,建立了基于线性化的非线性系统局部能观性判据,利用该判据分析了基于视线矢量测量的自主导航系统能观性,并以飞越小天体自主导航为例进行仿真验证。其次通过系统微分方程本身的处理和推导,建立系统输出与初始状态之间的映射关系,借助于反函数定理给出一个利用矩阵的秩描述的局部能观性判据。进一步考虑中心引力场下运行的航天器与参考星,将所得能观性结论应用于自主导航系统的量测方案选择问题,并结合仿真算例进行分析和验证。
研究了能观性度量与自主导航性能评价方法。首先针对确定性非线性系统,给出了基于条件数的能观性度量方法,将其用于圆型限制性三体系统,按参考轨迹给出航天器各位置分量对系统状态的能观度。其次针对随机非线性系统,论证了FIM(Fisher Information Matrix)与能观性之间的关系,进而利用FIM的迹定义系统的能观度,并将其用于视线测量自主导航系统的能观度分析。然后利用FIM与状态估计精度之间的关系严格推导了最优状态估计误差方差阵的传播规律,将其作为衡量自主导航算法性能的指标,为实际导航系统的设计与分析提供理论依据。
以椭圆轨道转移问题为背景,研究了基于能控性分析的小推力控制方法。鉴于在笛卡尔坐标系下和利用轨道根数描述的小推力控制系统均为仿射非线性系统,本文基于微分几何理论研究了仿射非线性系统的能控性,发展了基于漂移向量场弱Poisson稳定的能控性判据,并利用相关结果论证了小推力控制系统的能控性,进而提出了基于阻尼反馈的小推力椭圆轨道转移控制方法,将其应用于环绕地球椭圆轨道之间的转移,利用仿真分析验证方法的有效性。
设计了半物理仿真系统对自主导航与小推力控制方法的可行性进行分析。针对环月探测器,建立了基于光学导航相机、月球图像模拟器和Matlab/Simulink/dSPACE的自主导航与控制半物理仿真系统,利用光学导航相机和激光高度计构建探测器到月心的矢量,并利用扩展卡尔曼滤波估计探测器的位置和速度,进一步将自主导航模块的输出用于小推力轨道转移的反馈控制,从而实现了环月探测器从高轨道到低轨道的转移,验证了基于矢量测量的自主导航和基于阻尼反馈的小推力控制方法的可行性。
The development of techniques for autonomous navigation and control has become an important topic in the domain of aerospace science. Because the spacecraft system and its mission are more and more complex, it raises higher demand for advanced navigation and control technology. On the other hand, the nonlinearity of the spacecraft system challenges the design and analysis of the navigation and control system. The present thesis studies the observable selction and performance analysis of spacecraft autonomous navigation, as well as the method of low-thrust orbit transfer from the control point of view by using nonlinear observability and controllability theory. The main contents of this dissertation are as follows:
Firstly, the observability problem of autonomous navigation systems is studied. The robustness of observability is studied for linear systems under nonlinear perturbations in the state dynamics and the output channel, which demonstrates the validity of linearization for observability analysis of nonlinear systems, corresponding method is used to autonomous navigation system based on line-of-sight (LOS) vector measurement, and simulation of flyby autonomous navigation is given. Then, by using the theory of ordinary differential equation, the functional relationship between the output and the initial state is derived for nonlinear dynamic systems, and a observability criteria is formulated in the form of rank conditions based on inverse function theorem, which is used to analyse the observability of various combinations of measurements for spacecraft and reference point in a central gravitation field.
Secondly, the measure of observability and performance analysis of autonomous navigation algorithm is studied. An analytical expression of observability index by using condition number for nonlinear determinant systems is presented, by using which the effects of selection of observables on analysis of dynamics for spacecraft in the restricted three body system are given. Then, the observability degree for stochastic nonlinear systems is defined by using the trace of FIM (Fisher Information Matrix), and autonomous navigation system based on LOS measurement is analysed. Further, according to the relationship between FIM and the accuracy of navigation filter, a methodology of performance analysis of autonomous navigation algorithm is presented, which can be used as a standard in design and analysis of practical navigation system.
Thirdly, the method of low-thrust control for orbit transfer is studied based on controllability analysis. To give a practical controllability criterion for low-thrust spacecraft system, controllability of affine nonlinear systems is studied by using differential geometric theory, the controllability criterion based on weakly positively Poisson stability of drift vector field is developed, by using which the controllalbiltiy property of the low-thrust transfer between elliptic orbits is analysed. A damping feedback stabilizer is then designed to steer a spacecraft from initial elliptic orbit to a given elliptic orbit, and the performance of the proposed cotroller is lillustrated by simulating an orbital transfer between two elliptic orbits around the Earth.
Lastly, semi-physical simulation system of autonomous navigation and control is built up based on optical navigation camera, lunar picture simulator and Matlab/Simulink/dSPACE integration simulation flatform. The line-of-sight vector from spacecraft to Moon’s center is constructed by using optical navigation camera and laser altimeter, and the expanded Kalman filter is adopted to estimate the inertial position and velocity of the spacecraft.The output of autonomous navigation module is used as the feedback information of spacecraft for Lunar orbital transfer from higher orbit to lower orbit, simulation results demonstrate the feasibility of autonomous navigation based on LOS vector measurement and low-thrust control based on damping feedback.
引文
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