A Unified Framework for Consensus and Synchronization on Lie Groups Admitting a Bi-Invariant Metric

• 成果类型: Article
• 署名作者: Chandrasekaran, Rama Seshan; Banavar, Ravi N.; Mahindrakar, Arun D.
• 署名单位: Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Madras; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Bombay
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3579202
• 发表日期: 2025
• 关键词: coordination

摘要

For a finite number of agents evolving in a Euclidean space and linked to each other by a connected graph, the Laplacian flow that is based on the interagent errors ensures consensus or synchronization for both first- and second-order dynamics. When such agents evolve on a circle (such as the Kuramoto oscillator), the flow that depends on the sinusoid of the interagent error angles generalizes the same result. In this work, it is shown that the Laplacian flow and the Kuramoto oscillator are special cases of a more general theory of consensus applicable on Lie groups that admit bi-invariant metrics. Such a theory enables generalization of these consensus and synchronization algorithms to Lie groups.