Nonlinear control protocols are proposed for consensus control of a multi-agent system of N heterogeneous rigid bodies in the framework of the tangent bundles TSO(3) and TSE(3) associated with Lie groups SO(3) and SE(3), respectively. The control objective is to stabilise the relative pose configurations with velocity synchronisation of the rigid bodies which share their states according to a static undirected communication topology. The feedback control design is conducted on the dynamic level, and uses the rotation matrix as opposed to various attitude parameterisations. Almost global asymptotic stability of the consensus subspace is demonstrated both analytically using an extension of the Morse–Lyapunov (M–L) approach, and through numerical simulations. Also, the presence of unstable non-consensus equilibria in the closed-loop dynamics is discussed and shown in illustrative examples.

提出了非线性控制协议用于N的多智能体系统的一致性控制切线束 TSO(3) 和 TSE(3) 框架中的异质刚体分别与李群 SO(3) 和 SE(3) 相关联。控制目标是通过静态无向通信拓扑共享其状态的刚体的速度同步来稳定相对位姿配置。反馈控制设计在动态水平上进行，并使用旋转矩阵而不是各种姿态参数化。使用 Morse-Lyapunov (M-L) 方法的扩展分析和数值模拟都证明了共识子空间的几乎全局渐近稳定性。此外，在说明性示例中讨论并显示了闭环动力学中不稳定的非共识平衡的存在。