标题： 多三维刚体编队控制的双四元数控制律 显示英文标题

标题： A Dual Quaternion Control Law for Formation Control of Multiple 3-D Rigid Bodies

摘要： 本文研究了三维刚体多智能体系统的集成位置和姿态控制问题。 虽然[Olfati-Saber和Murray, 2004]中的最新方法为刚体编队控制建立了理论基础，但它要求所有智能体渐近收敛到相同的位置和姿态，这限制了其在必须保持不同期望相对配置的场景中的适用性。 在本文中，我们开发了一个基于双四元数的新框架，该框架推广了这一范式。 通过引入单位双四元数有向图（UDQDG）表示，我们通过相应的拉普拉斯矩阵推导出一种新的控制律，使得位置和姿态协调同时进行，并自然适应有向交互拓扑。 利用UDQDG谱理论的最新进展，我们证明了在右乘常数模下全局渐近收敛到期望的相对配置，并建立了由UDQDG拉普拉斯矩阵的次小特征值决定的R线性收敛速率。 提出了一种投影迭代方法来计算迭代状态。 最后，通过几个数值实验验证了所提出的方法。 显示英文摘要

摘要： This paper studies the integrated position and attitude control problem for multi-agent systems of 3D rigid bodies. While the state-of-the-art method in [Olfati-Saber and Murray, 2004] established the theoretical foundation for rigid-body formation control, it requires all agents to asymptotically converge to identical positions and attitudes, limiting its applicability in scenarios where distinct desired relative configurations must be maintained. In this paper, we develop a novel dual-quaternion-based framework that generalizes this paradigm. By introducing a unit dual quaternion directed graph (UDQDG) representation, we derive a new control law through the corresponding Laplacian matrix, enabling simultaneous position and attitude coordination while naturally accommodating directed interaction topologies. Leveraging the recent advances in UDQDG spectral theory, we prove global asymptotic convergence to desired relative configurations modulo a right-multiplicative constant and establish an R-linear convergence rate determined by the second smallest eigenvalue of the UDQDG Laplacian. A projected iteration method is proposed to compute the iterative states. Finally, the proposed solution is verified by several numerical experiments.