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500米口径球面射电望远镜（Five-hundred-meter Aperture Spherical radio Telescope，简称FAST）是世界最大单口径球面射电望远镜。FAST馈源支撑系统是调节馈源接收机位姿的机构，它是由轻型索牵引并联机构、AB转轴机构和连接馈源接收机的Stewart机构组成的大跨度刚柔耦合系统。因地球的自转，地球与射电源存在着相对运动，要实现望远镜对天体准时、准确观测，离不开对目标轨迹进行带有时间对齐约束的合理规划。另外，馈源支撑系统各运动机构间存在运动耦合，为解决馈源支撑耦合机构的协调控制问题，须设计有效的耦合机构位姿分配算法。为此，本文围绕FAST馈源支撑系统天文轨迹规划、系统刚度及馈源支撑系统位姿分配展开研究。主要内容如下：

1.  建立了用于天文观测轨迹生成的时角坐标系、赤道坐标系和东北天坐标系，从天体的周日视运动出发，推导出了馈源接收机在FAST焦曲面上轨迹的数学表达式。分析了望远镜静态扫描、换源、天文跟踪、编织式扫描、运动中扫描和自定义扫描模式的特征，在此基础上，为减小急速变速、变向、急起、急停的复杂目标轨迹对机构的冲击，并保障规划前后轨迹时间对齐，提出了一种将三维空间轨迹规划转换到天球坐标系进行规划的算法，减小了轨迹直接在三维空间规划的复杂度。最后，数值仿真验证了所提轨迹规划算法的有效性。

2.  据FAST观测需求，推导出了馈源舱回照策略的数学表达式，建立了带有馈源舱时变重心模型和馈源舱回照策略的馈源支撑悬索力学模型。针对索牵引并联机构和AB轴机构对馈源接收机目标位姿的冗余分配问题，提出了考虑馈源舱回照的索力均衡位姿分配算法和馈源终端零自旋位姿分配算法。通过数值仿真，分析了馈源舱回照角度在焦曲面的分布情况，验证了所提出的两种馈源支撑位姿分配算法的有效性；仿真结果表明索力均衡位姿分配算法的索力分配更加均衡，但引入馈源终端最大1.2°的理论自旋角，适合对馈源接收机自旋角没有要求的单波束观测；馈源终端零自旋位姿分配算法没有产生馈源接收机自旋角，索力相对不均衡，但索力没有出现虚牵和超限情况，可直接应用于对馈源接收机自旋角有要求的多波束观测。

3.  从系统刚度定义出发，导出了馈源支撑系统刚度矩阵的解析表达式。为同时保障馈源支撑系统在运行过程中的稳定性和抗扰动性，以六索索力方差最小和馈源支撑系统刚度最大为目标函数，提出了一种基于遗传算法的馈源支撑位姿优化分配算法。最后，数值仿真表明，该算法不仅没有产生馈源终端自旋角，而且综合提高了馈源支撑系统刚度、优化了索力分布，从而，提高了系统的抗扰动性，验证了该算法的优越性。

4.  为协调控制馈源支撑各机构，并解决馈源支撑各系统间实时大数据量通信问题，设计了基于POWERLINK的馈源支撑系统网络控制结构，开发了馈源支撑整体控制系统的通信、轨迹规划和协调控制等核心模块。并在FAST现场，对本文提出的天文轨迹规划算法、馈源支撑位姿分配算法以及基于遗传算法的馈源支撑位姿优化分配算法的性能进行测验。实验验证了本文提出的天文轨迹规划算法和馈源支撑位姿分配算法的有效性；结果表明馈源支撑位姿优化分配算法能明显提高馈源支撑系统的控制精度，验证了馈源支撑位姿优化分配算法的优越性。

另外，设计并开发的馈源支撑整体控制系统参与中国首次对脉冲星的搜寻任务，并搜寻到数颗得到国际认证的脉冲星，实现了中国对脉冲星搜寻从无到有的历史性突破。进一步验证了本文提出方法的有效性。

 

Five-hundred-meter Aperture Spherical radio Telescope (denoted as FAST for short), is the largest single-aperture spherical radio telescope in the world. The Feed Support System (FSS) of FAST, a highly coupled system with large-span workspace which is used to adjust the pose of the feed receiver, is comprised of a cable-driven parallel robot (CDPR), an A-B rotator and a rigid Stewart manipulator. Because the relative motion between the target radio source and the earth caused by the rotation of the earth, it necessary to properly plan the trajectory with constraint of time alignment in order to achieve accurate observation. In addition, in consideration of the kinematic coupling among the motion mechanisms of the FSS, designing an effective pose distribution algorithm is also crucial to cope with the coordinate control problem of the coupled mechanisms. So, this dissertation focuses on astronomical trajectory planning, system stiffness analysis and pose distribution of the FSS. The main contributions are summarized as follows:

1. The hour angle coordinate system, equatorial coordinate system and Cartesian coordinate system located on the earth, which are commonly used for trajectory generation of astronomical observation, are established. Then, the mathematical expression of the trajectory of the feed receiver on the FAST focal surface is deduced from the perspective of the apparent motion of celestial bodies. Subsequently, the characteristics of different operation modes, including drift-scan, slew, tracking, basket-weaving, On-The-Fly observing and user-defined mapping, are analyzed in detail. On these bases, a trajectory planning algorithm depending on the celestial coordinate system is proposed to decrease the impact on mechanisms caused by the complicated trajectories such as rapid speed changes, sudden start, sudden stop, and to ensure the time alignment of the trajectory. Compared with the planning algorithm depending on the original 3-dimensional space, the proposed trajectory planning algorithm greatly reduces the complexity of planning process. In the end, simulation is conducted to validate the effectiveness.

2. From the point of observation demands, mathematical expression of the back-illuminated strategy of the feed cabin is presented and the mechanical model of the FSS is established, in which the time-varying barycenter model and the back-illuminated strategy are taken into consideration. Besides, two pose distribution algorithms considering the back-illuminated strategy called cable forces equilibrium pose distribution algorithm (FEPDA) and zero spin pose distribution algorithm (ZSPDA) are designed to deal with the redundancy pose allocation problem of the feed receiver between the CDPR and the A-B rotator. In the end, Numerical simulations are conducted to analyze the distribution of the back-illuminated angle on the focal surface and the validity of the proposed algorithms. Numerical simulation demonstrates that: 1) the force equilibrium condition among six ropes achieved by FEPDA arises a maximum of 1.2° theoretical spin angle in the feed receiver, which means it is suitable for the single-beam feed observation with no constraint in the spin angle of the feed receiver. 2) The opposite case achieved by ZSPDA shows a relative unequilibrium of force allocation but with zero spin angle of the feed receiver and no occurrence of beyond the cable force limitation or virtual pull, this case can be used in multi-beam feed observation with constraint on spin angle of the feed receiver directly. 

3. According to the definition of the system stiffness, analytical expression of the stiffness matrix of FSS is deduced. In order to guarantee the stability and disturbance-resistant ability of FSS, a pose optimal distribution method based on genetic algorithm is proposed, the corresponding objective functions contains two parts: the minimization of the variance of cable forces and the maximization of FSS stiffness. Finally, simulation concludes that the proposed algorithm not only ensure the zero spin angle of the feed receiver but also retains a lower variance of cable tensions and higher stiffness of the FSS, which are crucial to the stability and disturbance-resistant ability of the FSS. The simulation demonstrates the superiorities of the proposed algorithm.

4. To control the mechanisms of FSS coordinately and implement the real-time communication with big data volume among the individual subsystems in FSS, the POWERLINK-based network topology is designed for FSS, and the whole control system of FSS, covering the FSS communication module, FSS trajectory planning and coordinate control module, is developed. After that, the experiments of applying the proposed algorithms in this dissertation have been conducted at the FAST site, and the results validate that 1) both the astronomical trajectory planning algorithm and the pose distribution algorithms of the FSS can work effectively; 2) the genetic algorithm based pose optimal distribution algorithm can realize higher accuracy than the normal pose distribution algorithm.

In addition, it is worth mentioning that the developed whole control system of FSS has served in the mission of searching pulsars for the first time and discovered several pulsars with international certification, which was a historical breakthrough for China. Meaningfully, it is a further verification of the research work in this thesis.