航天器姿轨控制研究综述:微分几何控制方法

作为空间任务顺利执行的关键技术,航天器姿态和轨道控制具有典型的非线性特征,其本质是对在矩阵李群SO (3)和SE (3)上演化的动态系统进行控制.与传统的参数化模型相比,航天器的矩阵李群模型对姿轨表征具有全局性、非奇异性和唯一性等固有优势,为控制设计提供了数学简洁、精度高、适用性好的模型基础.因此,近年来基于微分几何控制方法直接对其进行系统分析和控制设计的研究逐渐兴起,取得了一系列突破性成果.鉴于此,首先,系统地论述微分几何控制理论在航天器姿轨控制应用中的研究现状和进展;然后,面向空间任务的实际需要,分别对基于矩阵李群模型的单体航天器姿态控制、姿轨耦合控制、网络化航天器集群姿轨协同控制3个技术方向加以讨论;最后,对上述研究领域中存在的难题和挑战进行总结,并对未来发展方向进行展望.

A survey on spacecraft attitude and orbit control: Differential geometric control approaches

As a key technology for the success of space missions, spacecraft attitude and orbit control is typically nonlinear, and the essence is to control the dynamic system evolving on the matrix Lie groups SO(3) and SE(3). Compared with the traditional parameterized model, the matrix Lie group model of a spacecraft has some inherent advantages on the representation of attitude and orbit, such as globality, non-singularity, and uniqueness, which provides the model basis of mathematical simplicity, high precision and good applicability. In recent years, direct research on its system analysis and control design based on differential geometric control methods is gradually emerging, and a series of breakthrough achievements have been made. Thus, this paper summarizes the research results of the application of differential geometric control theory in spacecraft attitude and orbit control. Facing the requirements of actual space missions, the three technical directions of attitude control, orbit control and networked spacecraft cluster coordinated control based on the matrix Lie group model are discussed respectively. Finally, the challenges in the research field are summarized, while the future developments along the direction are prospected.