月球软着陆自主导航、制导与控制问题研究
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摘要
2007年10月24日,随着”嫦娥一号”的发射升空,中国迈出了月球探索的第一步。中国的探月计划将分为三步走:绕、落、回。后续,我国要在月球上(正面或背面)建立基地,开发月球各种矿物资源,用于补充地球的能源。这就要求着陆器具有自主、定点软着陆的能力。本论文结合国家自然科学基金重点项目“月球探测器的建模、传感、导航与控制基础理论与关键技术研究”,对未来实现定点着陆的着陆器从环月轨道到月面这一过程中的制导、导航与控制所涉及的关键技术进行研究。
首先,介绍了从环月轨道上下降到月面的过程中的制导、导航与控制系统所涉及的基础知识,给出了时间计量系统的定义、不同参考坐标系的定义和日月星历的计算。建立了从环月轨道到月面过程中的不同阶段的轨道动力学、姿态动力学、姿态运动学模型及质量流方程。
然后,为了给软着陆动力下降段提供高精度的导航起始点,本文研究了环月轨道上基于日地月方位信息的高精度自主导航算法。环月轨道上的导航系统采用日地月集成敏感器来确定日地月方位。研究了紫外月球敏感器的测量原理,给出了测量数据的模拟方法。研究了敏感器成像时满足的代数约束,给出了考虑月球扁率的月心矢量的精确确定方法。结合日地敏感器的输出信息,利用双矢量定姿原理和考虑常值系统偏差修正的最小二乘滤波算法得到了一套考虑月球扁率的自主定轨和定姿算法。数值仿真验证了这种导航算法的有效性,此方法能够修正月球扁率对月心矢量确定的误差,达到很高的导航精度。
为了实施软着陆,探测器需要从初始的圆轨道上机动到近月点高度为15km的椭圆轨道上,基于此背景,本文研究了两种任意环月轨道之间的时间自由的最优两脉冲转移,以主矢量理论和正则Mathieu变换为工具,将变边界的两点边值问题转换成一组带有27个未知常数的27个代数方程。利用非线性最小二乘方法求解这些未知常数,确定两脉冲的转移轨迹。数值仿真也验证了这种方法的有效性。这种方法还可以进一步推广到多脉冲转移的情况。
接下来研究了基于嵌入自主性的动力下降段的制导、导航与控制问题。基于合理的假设,利用量纲分析、级数展开和待定系数法求解了动力下降段的近似解析次优解,设计了鲁棒的自适应控制器去跟踪解析轨道。该控制器能很好的应付燃料消耗、惯量矩阵、推进器安装误差及部分推进器失效带来的参数或者模型不确定性。此外,本文设计了动力下降段的辅助惯性导航系统,利用惯导系统来估计探测器的位置、速度、角速度和四元素,并利用外部的高度计和速度计来修正IMU的累积误差和初始导航误差。解析式轨道和鲁棒的自适应控制器以及自主导航系统实现了系统的嵌入自主性。仿真结果也验证了动力下降段的制导、导航与控制系统的设计的合理性。
最后,进行了终端着陆段的制导、导航与控制系统设计。得出了最优姿态角公式,以及特殊情形下的最优解析轨迹。针对一般情形,最优轨迹数值解的计算复杂性,由二次型最优指标,导出了时间自由和时间固定的多项式显式制导律,以实现定点着陆。设计了带终端姿态约束的多项式制导律,保证探测器以垂直的姿态在月面上实现定点着陆。另一方面,动力下降段中的姿态控制器部分可以直接应用于终端着陆段。终端着陆段同样采用辅助惯性导航的方式,惯导系统用来估计探测器的轨道和姿态信息,外部的图像成像敏感器通过对月面上的特征点成像,修正惯导系统的估计误差,精确估计着陆器的轨道和姿态。仿真结果表明终端着陆段的制导、导航和控制的设计能够保证实现垂直姿态的定点软着陆。
On October 24, 2007, the successful launching of Chang’E-1 satellite became a mile-stone of Chinese Lunar Exploration Programme (CLEP) which takes three steps: orbiting,soft-landing and return. In the future, China will establish bases on the near side or farside of moon to supply plentiful resource for the earth. Therefore, it is required that thelunar probe can achieve pin-point soft-landing and autonomous navigation without rely-ing on the ground stations. With the support of the Chinese Science Nature Foundation -the Fundamental Research of the Key Technology for Lunar Probe’s Modeling, Sensing,Navigation and Control, this dissertation studies the key technologies on guidance, nav-igation and control (GNC) system of lunar probe from lunar orbit to the moon’s surfacefor future lunar exploration missions.
Firstly, this dissertation introduces preliminary knowledge of the GNC system of thelunar probe from lunar orbit to lunar surface. As essential elements of dynamical sys-tems, the definitions of time system and reference coordinates are given. The calculationmethod of sun and moon ephemeris is given. The orbit dynamics, rotational kinematics,attitude dynamics and mass ?ow equation for different phases from lunar orbit to lunarsurface are established.
Nextly, autonomous navigation methods of lunar orbit, which play important rolesfor pin-point landing, based on the orientation information of sun-earth-moon are studied.Nadir vector determination is an important element in autonomous navigation algorithm.Therefore, according to the principle of imaging, algebraical constraints of the images ofthe lunar edge are established and the nadir vector is determined from these algebraicalconstraints, of which the in?uence of lunar oblateness is considered. Combined with theinformation from sun and earth sensors, a high accuracy autonomous navigation with theconsideration of the lunar oblateness is proposed. Numerical simulations show that theproposed navigation algorithms can correct lunar oblateness effectively and achieve highaccuracy navigation.
Subsequently, the optimal impulse maneuvers between two lunar orbits are studiedsince the probe is required to transfer from initial lunar orbit to another orbit which is moresuitable for landing sometimes. General time-free two-impulse optimal transfers between two orbits are studied. Using the powerful tools of primer vector theory and Mathieutransformation, the two-point boundary problem with variable boundary is converted to27 algebraical equations with 27 unknown constants. The 27 unknown constants can besolved by a nonlinear Least-Squares method which implies that the two impulse trajectoryis determined. The method is testified by numerical simulations. It should be notedthat the method can be also expanded to multiple-impulse trajectories. However, thecomputation time would increase for multiple-impulse trajectories.
Thereafter, the GNC system with embedded autonomy in the powered descent phaseis studied. Based on reasonable assumptions, a sub-optimal analytical trajectory is found.A robust adaptive controller is designed to track the reference trajectory. Such a controllercan cope with uncertainty of mass consumption, inertia matrix, thrust misalignment andthrust failures. In additional, An aid-Inertial Navigation System (A-INS) is designed.Inertial Navigation System (INS) is adopted to estimate the probe’s orbit and attitudeinformation, and external altimeter and velocimeter are used to estimate the inertial er-rors. The analytical solution, robust controller and autonomous navigation method enablesystem’s embedded autonomy. The design is also verified by numerical simulations.
Finally, the GNC system for the terminal descent phase is proposed. A polynomialquadratic optimal guidance law is derived for time-free and time-fixed descent problemwhich can ensure the pin-point landing. A polynomial guidance law with attitude con-straint is also designed which can ensure pin-landing with vertical attitude. The proposedattitude controller in power descent phase can be also used for terminal descent. AnA-INS system is designed. INS system is used to estimate probe’s orbit and attitude in-formation, and external lunar imaging sensor is used correct the inertial errors. Numericalsimulations show that the GNC system for terminal descent phase can ensure pin-pointsoft landing with almost vertical attitude.
首先,介绍了从环月轨道上下降到月面的过程中的制导、导航与控制系统所涉及的基础知识,给出了时间计量系统的定义、不同参考坐标系的定义和日月星历的计算。建立了从环月轨道到月面过程中的不同阶段的轨道动力学、姿态动力学、姿态运动学模型及质量流方程。
然后,为了给软着陆动力下降段提供高精度的导航起始点,本文研究了环月轨道上基于日地月方位信息的高精度自主导航算法。环月轨道上的导航系统采用日地月集成敏感器来确定日地月方位。研究了紫外月球敏感器的测量原理,给出了测量数据的模拟方法。研究了敏感器成像时满足的代数约束,给出了考虑月球扁率的月心矢量的精确确定方法。结合日地敏感器的输出信息,利用双矢量定姿原理和考虑常值系统偏差修正的最小二乘滤波算法得到了一套考虑月球扁率的自主定轨和定姿算法。数值仿真验证了这种导航算法的有效性,此方法能够修正月球扁率对月心矢量确定的误差,达到很高的导航精度。
为了实施软着陆,探测器需要从初始的圆轨道上机动到近月点高度为15km的椭圆轨道上,基于此背景,本文研究了两种任意环月轨道之间的时间自由的最优两脉冲转移,以主矢量理论和正则Mathieu变换为工具,将变边界的两点边值问题转换成一组带有27个未知常数的27个代数方程。利用非线性最小二乘方法求解这些未知常数,确定两脉冲的转移轨迹。数值仿真也验证了这种方法的有效性。这种方法还可以进一步推广到多脉冲转移的情况。
接下来研究了基于嵌入自主性的动力下降段的制导、导航与控制问题。基于合理的假设,利用量纲分析、级数展开和待定系数法求解了动力下降段的近似解析次优解,设计了鲁棒的自适应控制器去跟踪解析轨道。该控制器能很好的应付燃料消耗、惯量矩阵、推进器安装误差及部分推进器失效带来的参数或者模型不确定性。此外,本文设计了动力下降段的辅助惯性导航系统,利用惯导系统来估计探测器的位置、速度、角速度和四元素,并利用外部的高度计和速度计来修正IMU的累积误差和初始导航误差。解析式轨道和鲁棒的自适应控制器以及自主导航系统实现了系统的嵌入自主性。仿真结果也验证了动力下降段的制导、导航与控制系统的设计的合理性。
最后,进行了终端着陆段的制导、导航与控制系统设计。得出了最优姿态角公式,以及特殊情形下的最优解析轨迹。针对一般情形,最优轨迹数值解的计算复杂性,由二次型最优指标,导出了时间自由和时间固定的多项式显式制导律,以实现定点着陆。设计了带终端姿态约束的多项式制导律,保证探测器以垂直的姿态在月面上实现定点着陆。另一方面,动力下降段中的姿态控制器部分可以直接应用于终端着陆段。终端着陆段同样采用辅助惯性导航的方式,惯导系统用来估计探测器的轨道和姿态信息,外部的图像成像敏感器通过对月面上的特征点成像,修正惯导系统的估计误差,精确估计着陆器的轨道和姿态。仿真结果表明终端着陆段的制导、导航和控制的设计能够保证实现垂直姿态的定点软着陆。
On October 24, 2007, the successful launching of Chang’E-1 satellite became a mile-stone of Chinese Lunar Exploration Programme (CLEP) which takes three steps: orbiting,soft-landing and return. In the future, China will establish bases on the near side or farside of moon to supply plentiful resource for the earth. Therefore, it is required that thelunar probe can achieve pin-point soft-landing and autonomous navigation without rely-ing on the ground stations. With the support of the Chinese Science Nature Foundation -the Fundamental Research of the Key Technology for Lunar Probe’s Modeling, Sensing,Navigation and Control, this dissertation studies the key technologies on guidance, nav-igation and control (GNC) system of lunar probe from lunar orbit to the moon’s surfacefor future lunar exploration missions.
Firstly, this dissertation introduces preliminary knowledge of the GNC system of thelunar probe from lunar orbit to lunar surface. As essential elements of dynamical sys-tems, the definitions of time system and reference coordinates are given. The calculationmethod of sun and moon ephemeris is given. The orbit dynamics, rotational kinematics,attitude dynamics and mass ?ow equation for different phases from lunar orbit to lunarsurface are established.
Nextly, autonomous navigation methods of lunar orbit, which play important rolesfor pin-point landing, based on the orientation information of sun-earth-moon are studied.Nadir vector determination is an important element in autonomous navigation algorithm.Therefore, according to the principle of imaging, algebraical constraints of the images ofthe lunar edge are established and the nadir vector is determined from these algebraicalconstraints, of which the in?uence of lunar oblateness is considered. Combined with theinformation from sun and earth sensors, a high accuracy autonomous navigation with theconsideration of the lunar oblateness is proposed. Numerical simulations show that theproposed navigation algorithms can correct lunar oblateness effectively and achieve highaccuracy navigation.
Subsequently, the optimal impulse maneuvers between two lunar orbits are studiedsince the probe is required to transfer from initial lunar orbit to another orbit which is moresuitable for landing sometimes. General time-free two-impulse optimal transfers between two orbits are studied. Using the powerful tools of primer vector theory and Mathieutransformation, the two-point boundary problem with variable boundary is converted to27 algebraical equations with 27 unknown constants. The 27 unknown constants can besolved by a nonlinear Least-Squares method which implies that the two impulse trajectoryis determined. The method is testified by numerical simulations. It should be notedthat the method can be also expanded to multiple-impulse trajectories. However, thecomputation time would increase for multiple-impulse trajectories.
Thereafter, the GNC system with embedded autonomy in the powered descent phaseis studied. Based on reasonable assumptions, a sub-optimal analytical trajectory is found.A robust adaptive controller is designed to track the reference trajectory. Such a controllercan cope with uncertainty of mass consumption, inertia matrix, thrust misalignment andthrust failures. In additional, An aid-Inertial Navigation System (A-INS) is designed.Inertial Navigation System (INS) is adopted to estimate the probe’s orbit and attitudeinformation, and external altimeter and velocimeter are used to estimate the inertial er-rors. The analytical solution, robust controller and autonomous navigation method enablesystem’s embedded autonomy. The design is also verified by numerical simulations.
Finally, the GNC system for the terminal descent phase is proposed. A polynomialquadratic optimal guidance law is derived for time-free and time-fixed descent problemwhich can ensure the pin-point landing. A polynomial guidance law with attitude con-straint is also designed which can ensure pin-landing with vertical attitude. The proposedattitude controller in power descent phase can be also used for terminal descent. AnA-INS system is designed. INS system is used to estimate probe’s orbit and attitude in-formation, and external lunar imaging sensor is used correct the inertial errors. Numericalsimulations show that the GNC system for terminal descent phase can ensure pin-pointsoft landing with almost vertical attitude.
引文
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