用SO(3)几何控制实现无人机群三维寻源，避免角度奇异问题。
Distributed 3D Source Seeking via SO(3) Geometric Control of Robot Swarms
- 在SO(3)群上直接设计控制器，避免欧拉角奇点和四元数歧义。
- 所有无人机指数收敛到源方向，对未知扰动有鲁棒性。
- 适合多智能体系统、三维环境搜索任务的科研与工程应用。
本文提出一种基于李群SO(3)的几何控制框架，用于具有一阶姿态动力学和恒定平移速度的机器人在三维空间中寻源。通过在SO(3)上直接工作，该方法避免了欧拉角奇点和四元数歧义，提供了一种唯一且内在的姿态表示。设计了一种比例前馈控制器，确保每个智能体指数级对齐至估计的向源上升方向。控制器可适应有界未知变化，并保持群体形态的合理性。数值仿真验证了方法的有效性，所有代码开源以保证可复现性。
原文摘要 · Abstract (English)
This paper presents a geometric control framework on the Lie group SO(3) for 3D source-seeking by robots with first-order attitude dynamics and constant translational speed. By working directly on SO(3), the approach avoids Euler-angle singularities and quaternion ambiguities, providing a unique, intrinsic representation of orientation. We design a proportional feed-forward controller that ensures exponential alignment of each agent to an estimated ascending direction toward a 3D scalar field source. The controller adapts to bounded unknown variations and preserves well-posed swarm formations. Numerical simulations demonstrate the effectiveness of the method, with all code provided open source for reproducibility.
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