发表机构
Indian Institute of Technology Bombay（印度理工学院孟买分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对SO(3)上带多个姿态指向约束和匹配外部扰动的航天器姿态跟踪问题，构造固有姿态势函数，提出非奇异固定时间几何滑模控制律，通过理论分析和数值仿真验证了控制方法的有效性。
AI 中文摘要
本文研究了在存在多个姿态指向约束和匹配外部扰动的情况下，黎曼构型流形SO(3)上带约束的航天器姿态跟踪问题。为解决该问题，本文在SO(3)上固有地构造了一个姿态势函数，并通过固有几何分析确立了其关键性质。在温和条件下，该势函数在SO(3)的容许子集上（该子集排除了禁止姿态区域以及测度为零的集合）于期望姿态处存在唯一非退化极小值，从而确保带约束的姿态跟踪问题适定。黎曼海森分析表明，该势函数的海森在期望姿态的开邻域内局部一致正定，由此确立了局部强凸性。利用该势函数的黎曼梯度，本文提出了一种非奇异固定时间几何滑模流形，进而得到了基于几何固定时间滑模的带约束姿态控制律。研究表明，对于容许子集内的每一个初始姿态，闭环状态轨迹在SO(3)×ℝ³上演化，姿态在整个机动过程中始终保持在容许子集内，同时状态在规定的固定时间内收敛到期望平衡点的足够小的紧邻域。数值仿真验证了所提出的控制方法，并说明了理论结果的正确性。
英文摘要
This paper studies constrained spacecraft attitude tracking on the Riemannian configuration manifold $\mathrm{SO}(3)$ in the presence of multiple attitude pointing constraints and matched external disturbances. To address this, an attitude potential function is proposed intrinsically on $\mathrm{SO}(3)$, and its key properties are established using intrinsic geometric analysis. Under mild conditions, the potential function is shown to admit a unique nondegenerate minimum at the desired attitude over the admissible subset of $\mathrm{SO}(3)$, defined by excluding the forbidden attitude regions as well as a measure-zero set, thereby ensuring a well-posed constrained attitude tracking problem. A Riemannian Hessian analysis shows that the Hessian of the potential function is locally uniform positive definite in an open neighborhood of the desired attitude, thereby establishing local strong convexity. A nonsingular fixed-time geometric sliding manifold is proposed using the Riemannian gradient of the potential function, leading to a geometric fixed-time sliding-mode-based constrained attitude control law. It is shown that, for every initial attitude in the admissible subset, the closed-loop state trajectory evolves on $\mathrm{SO}(3)\times\mathbb{R}^3$, with the attitude remaining in the admissible subset throughout the maneuver, while the state converges to a sufficiently small compact neighborhood of the desired equilibrium in a prescribed fixed time. Numerical simulations validate the proposed control approach and illustrate the theoretical results.
