新方法让编队在3D空间任意旋转缩放，无需复杂配置
Formation Maneuver Control Based on the Augmented Laplacian Method
- 用矩阵权重替代标量，实现3D空间任意轴旋转
- 支持动态加入新成员，编队可自由调整形状与方向
- 理论证明保持编队原结构，实施更简单高效
本文提出一种新型编队机动控制方法，适用于二维和三维空间，使编队能够实现任意方向的平移、缩放和旋转。核心创新在于改进了增广拉普拉斯矩阵的权重设计：不再使用标量，而是采用基于指定旋转轴设计的矩阵权重，从而实现三维空间中的任意轴旋转。为进一步提升灵活性与可扩展性，提出了旋转轴调节方法和动态节点重配置策略，支持编队在三维空间中绕任意轴旋转，并允许新智能体动态加入。理论分析表明，该方法能保持编队原始构型。相比基于复数拉普拉斯的方法，本方法仍具备邻域需求低、不依赖通用或凸形初始构型的优势，同时通过更简化的实现方式实现了任意方向旋转。二维与三维空间的仿真验证了方法的有效性。
原文摘要 · Abstract (English)
This paper proposes a novel formation maneuver control method for both 2-D and 3-D space, which enables the formation to translate, scale, and rotate with arbitrary orientation. The core innovation is the novel design of weights in the proposed augmented Laplacian matrix. Instead of using scalars, we represent weights as matrices, which are designed based on a specified rotation axis and allow the formation to perform rotation in 3-D space. To further improve the flexibility and scalability of the formation, the rotational axis adjustment approach and dynamic agent reconfiguration method are developed, allowing formations to rotate around arbitrary axes in 3-D space and new agents to join the formation. Theoretical analysis is provided to show that the proposed approach preserves the original configuration of the formation. The proposed method maintains the advantages of the complex Laplacian-based method, including reduced neighbor requirements and no reliance on generic or convex nominal configurations, while achieving arbitrary orientation rotations via a more simplified implementation. Simulations in both 2-D and 3-D space validate the effectiveness of the proposed method.
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