Constrained Attitude Control of the 3D Pendulum

摘要本文研究具有控制约束的三维摆的全局姿态控制问题。考虑到姿态控制问题的科学意义和工程意义，缺乏具有控制约束的全局姿态控制研究，以及主要研究人员在姿态动力学和控制方面的理论和实验研究。与所有姿态控制系统一样，三维摆的关键特征是所有可能姿态构型的集合是一个紧致的非交换李群。所研究的控制问题分为两类：开环最优和近最优姿态控制机动的算法和计算方法，以及基于liapunov的闭环反馈姿态稳定方法。在每一类姿态控制问题中，新的结果将在全球范围内有效，而不需要使用局部姿态图或坐标。三维摆的物理实现，称为三轴姿态控制试验台（TACT），是实验部分研究的基础。TACT由几乎无摩擦的空气轴承支点支撑的刚性基座组成，是研究姿态动力学和控制实际方面的优秀实验室研究工具。研究的动机是在不同的科学和工程领域出现的重要的姿态动力学和控制问题。约束姿态动力学和控制的重要应用包括机器人设备，如龙门吊和运输刚体载荷的建筑设备；先进的地面指向和跟踪系统；以及许多空间应用，包括惯性平台和航天器姿态稳定和机动。该研究还与天体力学中的全身问题有重要联系，如双星小行星的相互动力学和小行星的近地通过。具有控制约束的三维摆的全局姿态控制的研究是由这些应用驱动的，它将寻求在这些领域中开发衍生结果。

AbstractThis novel research program investigates the global attitude control of a 3D pendulum with control constraints. The research program is motivated by the scientific and engineering significance of attitude control problems, the lack of prior research on global attitude control with control constraints, and by prior theoretical and experimental research of the principal investigator on attitude dynamics and control. The key feature of the 3D pendulum, as for all attitude control systems, is that the set of all possible attitude configurations is a compact, noncommutative Lie group. The control problems to be investigated fall into two categories: algorithms and computational methods for open loop optimal and near-optimal attitude control maneuvers and Liapunov-based methods for closed loop attitude stabilization using feedback. In each category of attitude control problems, new results will be globally valid without requiring use of local attitude charts or coordinates. A physical implementation of a 3D pendulum, referred to as the triaxial attitude control testbed (TACT), is the basis for the experimental part of the research. The TACT, consisting of a rigid base body supported by a near-frictionless air-bearing pivot, is an excellent laboratory-based research tool for studying the practical aspects of attitude dynamics and control. The research is motivated by important attitude dynamics and control problems that arise in diverse scientific and engineering fields. Important applications of constrained attitude dynamics and control include robotic devices such as gantry cranes and construction equipment for transporting rigid bodies loads; advanced ground-based pointing and tracking systems; and numerous space applications including inertial platforms and spacecraft attitude stabilization and maneuvers. The research also has important connections with full body problems in celestial mechanics, such as the mutual dynamics of binary asteroids and the near Earth passage of asteroids. The research on global attitude control of the 3D pendulum, with control constraints, is motivated by these applications and it will seek to develop spin-off results in several of these areas.