航天器姿轨一体化动力学建模、控制与导航方法研究
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摘要
航天器轨道和姿态的动力学建模、控制与导航是完成航天任务的重要保障，因此世界各国的研究学者都投入了大量精力进行相关问题的研究，并取得了丰硕的研究成果。传统的方式是将航天器的在轨运动分解为轨道运动和姿态运动并对其分别进行研究。然而随着航天器新型任务的出现，这种分而治之的研究方式体现了一定的局限性。针对上述问题，本学位论文深入研究了航天器轨道与姿态一体化动力学建模方法、一体化控制方法与一体化相对导航方法，主要包括以下几个方面的工作：
针对航天器轨道与姿态的一体化动力学建模问题，选择对偶四元数这一数学工具，以一体化的方式描述航天器在轨运行的轨道运动与姿态运动，并重新导出由其描述的航天器一般运动的运动学模型；在对偶数代数框架内，利用力学基本原理，建立单航天器一般运动的动力学模型；在单航天器相关研究基础上，对两个航天器间的相对轨道与相对姿态进行动力学建模与分析；考虑到由于非质心点引起的姿轨耦合影响，建立航天器非质心点相对运动的动力学模型。针对航天器轨道与姿态运动的跟踪控制问题，在考虑外界干扰和模型不确定性的情况下，设计线性滑模变结构控制器和类PD鲁棒控制器，并分别采用Lyapunov方法和Barbalat引理证明闭环系统的渐近稳定性。最后，结合航天器悬停的任务背景，对上述控制算法进行数学仿真验证。
针对航天器相对轨道与相对姿态的一体化控制问题，以对偶四元数的对数作为控制变量，设计终端滑模控制器，该控制器可以实现对期望状态的有限时间跟踪，并具有对外界干扰以及航天器模型不确定部分的鲁棒性；考虑到由于空间环境的复杂性而不能获知干扰及模型不确定性的信息，提出不需要广义干扰上界的自适应终端滑模控制器；进一步的，为了提高控制器的快速性，基于航天器相对运动的类拉格朗日模型设计快速滑模控制器，并对线性滑模面、终端滑模面和快速滑模面的收敛速度进行比较分析。最后，结合航天器交会对接的应用背景，对上述控制算法进行数学仿真验证。
针对航天器的相对位置与相对姿态的一体化确定问题，提出基于多种几何特征的单目视觉导航方法。在对偶代数的框架内，统一描述特征点、特征线和特征圆，特别的，特征圆的对偶数描述是基于一种动态定义实现的。利用单目视觉原理，分别建立基于特征点、特征线和特征圆的测量模型。基于上述测量模型，分别采用龙贝格-马尔塔算法、扩展卡尔曼滤波算法和无迹卡尔曼滤波算法实现对航天器间的相对位置和相对姿态的估计。最后，通过数学仿真验证上述算法的可行性，并比较分析各种算法的精度，以及特征点数目和分散程度对估计精度的影响。
针对航天器相对导航的鲁棒滤波问题，提出基于改进强跟踪滤波和鲁棒无迹卡尔曼滤波的航天器相对导航方法。考虑系统模型的不确定性以及目标运动状态的机动性，提出航天器相对位姿估计的改进强跟踪滤波算法，该算法具有较强的关于模型不确定性的鲁棒性和关于突变状态的跟踪能力，并且适用于测量矩阵不是满秩矩阵的情况。考虑到特征信息失效的测量故障情况，为了抑制测量故障引起的滤波失效，分别设计单比例因子鲁棒无迹卡尔曼滤波算法和多比例因子鲁棒无迹卡尔曼滤波算法，其中多比例因子算法可以针对每个测量量做出不同的反应。最后，以故障或失效的航天器为目标航天器，通过数学仿真验证上述算法的有效性。
The modelling, control and navigation of spacecraft's orbit and attitude is importantissues in aerospace missions. Therefore, a huge number of studies and results have beenobtained during recent decades. However, there is a crucial problem which most missionsshould face: modelling the orbit and attitude dynamics seperately in most flying missionsis an inaccurate approximate method which should be checked all the time. As a result,this dissertation concentrates on integrated dynamics modelling mothed, integratedcontrol strategy, and integrated relative navigation approach. The major contents of thisdissertation consist of the following parts.
For the integrated modeling of spacecraft orbit and attitude motion, the mathematictool dual quaternion is firstly used to describe the orbit motion and attitude motionsimultaneously, and the integrated kinematics model is derived accordingly. Thedynamics of a single spacecraft is then proposed in the framework of dual number, whichcan describe the relationship between spacecraft and external forces and torques. Basedon the research of single spacecraft, modelling and analysis of relative orbit and attitudeare studied. In particular, the coupling effect due to the point deviating from the center ofmass is taken into account, and the dynamics model of relative motion between thepoints deviating from the center of mass is established. For the tracking control problemof spacecraft, a linear sliding mode controller and a PD-like robust controller areproposed. Lyapunov method and Barbalat lemma are used respectively to prove thestability of the system in the presence of disturbances and model uncertainties. Finally,simulations are done to demonstrate the effectiveness of the proposed controllers.
For the control problem of spacecraft relative orbit and attitude, a terminal slidingmode control strategy is designed based on the logarithm of dual quaternion. Thecontroller can realize finite-time tracking of desired attitude states while being robustagainst model uncertainties and disturbances. When the information of disturbances andmodel uncertainties are unavailable, an adaptive finite-time control approach is proposed.Furthermore, the Lagrange form of spacecraft's dynamics model is derived, and a fastfinite-time control law is developed. The convergence rate of linear sliding mode,terminal sliding mode and fast sliding mode is compared and analyzed. Finally, byconsidering spacecraft rendezvous and docking mission, numerical simulations are doneto illustrate the effectiveness of the proposed control methods.
For the estimation problem of relative position and attitude, single vision basednavigation approaches are proposed based on multiple geometric features. At first,feature point, line and circle are described in the frame of dual number. In particular, the description of feature circle is based on a kind of dynamic definition. By using the singlevision theory, the measurement models based on feature point, line and circle aredeveloped, respectively. Then, employing the measurement models, Levenberg-Marquardt algorithm, Extended Kalman Filter algorithm and Unscented Kalman Filteralgorithm are ultilized to estimate the relative position and attitude. Finally, by numericalsimulations of the aforementioned algorithms, the accuracies of all the algorithms arecompared, and the influence of number of feature points and their distribution onestimation accuracy is analized.
For model uncertainties and maneuverabilities of target spacecraft, an improvedstrong tracking filter is proposed to estimate relative position and attitude. This methodpossesses strong robustness against model uncertainties and competent tracking ability ofsuddenly-changed system states. In particular, this method is also effective if themeasurement matrix is not full-rank. Considering the measurement failures of featureinformation, a single coefficient robust Unscented Kalman Filter and a multiplecoefficient robust Unscented Kalman Filter algorithms are developed to avoid or alleviatethe failure of filters, where the multiple coefficient method can vary its coefficientsaccording to various measurement states. Finally, simulations of these approaches arepresented to validate their effectiveness.
针对航天器轨道与姿态的一体化动力学建模问题，选择对偶四元数这一数学工具，以一体化的方式描述航天器在轨运行的轨道运动与姿态运动，并重新导出由其描述的航天器一般运动的运动学模型；在对偶数代数框架内，利用力学基本原理，建立单航天器一般运动的动力学模型；在单航天器相关研究基础上，对两个航天器间的相对轨道与相对姿态进行动力学建模与分析；考虑到由于非质心点引起的姿轨耦合影响，建立航天器非质心点相对运动的动力学模型。针对航天器轨道与姿态运动的跟踪控制问题，在考虑外界干扰和模型不确定性的情况下，设计线性滑模变结构控制器和类PD鲁棒控制器，并分别采用Lyapunov方法和Barbalat引理证明闭环系统的渐近稳定性。最后，结合航天器悬停的任务背景，对上述控制算法进行数学仿真验证。
针对航天器相对轨道与相对姿态的一体化控制问题，以对偶四元数的对数作为控制变量，设计终端滑模控制器，该控制器可以实现对期望状态的有限时间跟踪，并具有对外界干扰以及航天器模型不确定部分的鲁棒性；考虑到由于空间环境的复杂性而不能获知干扰及模型不确定性的信息，提出不需要广义干扰上界的自适应终端滑模控制器；进一步的，为了提高控制器的快速性，基于航天器相对运动的类拉格朗日模型设计快速滑模控制器，并对线性滑模面、终端滑模面和快速滑模面的收敛速度进行比较分析。最后，结合航天器交会对接的应用背景，对上述控制算法进行数学仿真验证。
针对航天器的相对位置与相对姿态的一体化确定问题，提出基于多种几何特征的单目视觉导航方法。在对偶代数的框架内，统一描述特征点、特征线和特征圆，特别的，特征圆的对偶数描述是基于一种动态定义实现的。利用单目视觉原理，分别建立基于特征点、特征线和特征圆的测量模型。基于上述测量模型，分别采用龙贝格-马尔塔算法、扩展卡尔曼滤波算法和无迹卡尔曼滤波算法实现对航天器间的相对位置和相对姿态的估计。最后，通过数学仿真验证上述算法的可行性，并比较分析各种算法的精度，以及特征点数目和分散程度对估计精度的影响。
针对航天器相对导航的鲁棒滤波问题，提出基于改进强跟踪滤波和鲁棒无迹卡尔曼滤波的航天器相对导航方法。考虑系统模型的不确定性以及目标运动状态的机动性，提出航天器相对位姿估计的改进强跟踪滤波算法，该算法具有较强的关于模型不确定性的鲁棒性和关于突变状态的跟踪能力，并且适用于测量矩阵不是满秩矩阵的情况。考虑到特征信息失效的测量故障情况，为了抑制测量故障引起的滤波失效，分别设计单比例因子鲁棒无迹卡尔曼滤波算法和多比例因子鲁棒无迹卡尔曼滤波算法，其中多比例因子算法可以针对每个测量量做出不同的反应。最后，以故障或失效的航天器为目标航天器，通过数学仿真验证上述算法的有效性。
The modelling, control and navigation of spacecraft's orbit and attitude is importantissues in aerospace missions. Therefore, a huge number of studies and results have beenobtained during recent decades. However, there is a crucial problem which most missionsshould face: modelling the orbit and attitude dynamics seperately in most flying missionsis an inaccurate approximate method which should be checked all the time. As a result,this dissertation concentrates on integrated dynamics modelling mothed, integratedcontrol strategy, and integrated relative navigation approach. The major contents of thisdissertation consist of the following parts.
For the integrated modeling of spacecraft orbit and attitude motion, the mathematictool dual quaternion is firstly used to describe the orbit motion and attitude motionsimultaneously, and the integrated kinematics model is derived accordingly. Thedynamics of a single spacecraft is then proposed in the framework of dual number, whichcan describe the relationship between spacecraft and external forces and torques. Basedon the research of single spacecraft, modelling and analysis of relative orbit and attitudeare studied. In particular, the coupling effect due to the point deviating from the center ofmass is taken into account, and the dynamics model of relative motion between thepoints deviating from the center of mass is established. For the tracking control problemof spacecraft, a linear sliding mode controller and a PD-like robust controller areproposed. Lyapunov method and Barbalat lemma are used respectively to prove thestability of the system in the presence of disturbances and model uncertainties. Finally,simulations are done to demonstrate the effectiveness of the proposed controllers.
For the control problem of spacecraft relative orbit and attitude, a terminal slidingmode control strategy is designed based on the logarithm of dual quaternion. Thecontroller can realize finite-time tracking of desired attitude states while being robustagainst model uncertainties and disturbances. When the information of disturbances andmodel uncertainties are unavailable, an adaptive finite-time control approach is proposed.Furthermore, the Lagrange form of spacecraft's dynamics model is derived, and a fastfinite-time control law is developed. The convergence rate of linear sliding mode,terminal sliding mode and fast sliding mode is compared and analyzed. Finally, byconsidering spacecraft rendezvous and docking mission, numerical simulations are doneto illustrate the effectiveness of the proposed control methods.
For the estimation problem of relative position and attitude, single vision basednavigation approaches are proposed based on multiple geometric features. At first,feature point, line and circle are described in the frame of dual number. In particular, the description of feature circle is based on a kind of dynamic definition. By using the singlevision theory, the measurement models based on feature point, line and circle aredeveloped, respectively. Then, employing the measurement models, Levenberg-Marquardt algorithm, Extended Kalman Filter algorithm and Unscented Kalman Filteralgorithm are ultilized to estimate the relative position and attitude. Finally, by numericalsimulations of the aforementioned algorithms, the accuracies of all the algorithms arecompared, and the influence of number of feature points and their distribution onestimation accuracy is analized.
For model uncertainties and maneuverabilities of target spacecraft, an improvedstrong tracking filter is proposed to estimate relative position and attitude. This methodpossesses strong robustness against model uncertainties and competent tracking ability ofsuddenly-changed system states. In particular, this method is also effective if themeasurement matrix is not full-rank. Considering the measurement failures of featureinformation, a single coefficient robust Unscented Kalman Filter and a multiplecoefficient robust Unscented Kalman Filter algorithms are developed to avoid or alleviatethe failure of filters, where the multiple coefficient method can vary its coefficientsaccording to various measurement states. Finally, simulations of these approaches arepresented to validate their effectiveness.
引文
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