SO(3)上具有设计者指定进展行为的无奇异性引导向量场
Singularity-Free Guiding Vector Fields on SO(3) with Designer-Specified Progression Behavior
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中文总结 AI 辅助
本文提出SO(3)上无奇异性引导向量场，结合增广状态与李群几何实现姿态路径跟踪，并将进展行为作为设计自由度，仿真验证了其有效性。
中文摘要 AI 辅助
本文开发了一种用于特殊正交群SO(3)上路径跟踪的无奇异性引导向量场（SF-GVF）。首先，我们将欧几里得空间中的SF-GVF构造提升到SO(3)上，将增广状态方法与内在李群几何相结合，获得了一种闭式几何制导律，其积分曲线收敛到设计者指定的姿态路径。该场定义在SO(3)的一个稠密开子集上，仅排除测度为零的对映点集——这是SO(3)上连续全局镇定拓扑障碍的体现。该构造无需逐步优化，并直接在so(3)中产生作为机体角速度的控制输入。其次，我们将沿路径的进展行为形式化为设计者提供的函数\nu(\xi)，将参数速度从隐式求解的自由度提升为一等设计规范。与欧几里得条件v=0（该条件排除了具有最小速度约束的载体）相比，SO(3)上的相应条件\omega=0对于大多数具有主动姿态控制的平台在物理上是可接受的，这使得进展行为成为SO(3)上结构上可用但欧几里得设置中缺失的设计自由度。该框架的结构性结果在双不变黎曼度量下建立，并统一适用于路径、进展和李雅普诺夫增益的选择。该框架在自相交路径上进行了仿真验证，涵盖了恒定和点收敛两种进展行为。
英文摘要
This paper develops a singularity-free guiding vector field (SF-GVF) for path following on the special orthogonal group SO(3). First, we lift the Euclidean SF-GVF construction to SO(3), integrating the augmented-state approach with the intrinsic Lie-group geometry and obtaining a closed-form geometric guidance law whose integral curves converge to a designer-specified attitude path. The field is defined on a dense open subset of SO(3), excluding only the measure-zero antipodal set - a manifestation of the topological obstruction to continuous global stabilization on SO(3). The construction requires no per-step optimization and produces a control input intrinsically in so(3) as body angular rates. Second, we formalize the progression behavior along the path as a designer-supplied function ν(ξ), promoting the parametric speed from an implicitly resolved degree of freedom to a first-class design specification. In contrast to the Euclidean condition v = 0, which excludes vehicles with minimum-speed constraints, the corresponding condition ω= 0 on SO(3) is physically admissible for most platforms with active attitude control, making the progression behavior a design freedom structurally available on SO(3) but absent in the Euclidean setting. The framework's structural results are established under a bi-invariant Riemannian metric and hold uniformly across choices of path, progression, and Lyapunov gain. The framework is illustrated in simulation on self-intersecting paths under both constant and point-convergence progression behaviors.
发表机构
- University of Granada（格拉纳达大学）
机构由 AI 辅助整理，请以论文原文为准。
