Distributed Formation Control of Multi-Agent Systems Using Complex Laplacian

作者:Lin, Zhiyun; Wang, Lili; Han, Zhimin; Fu, Minyue 刊名:IEEE Transactions on Automatic Control 上传者:郑开敏


IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 59, NO. 7, JULY 2014 1765 Distributed Formation Control of Multi-Agent Systems Using Complex Laplacian Zhiyun Lin, Senior Member, IEEE, Lili Wang, Zhimin Han, and Minyue Fu, Fellow, IEEE Abstract—The paper concentrates on the fundamental coordi-nation problem that requires a network of agents to achieve a specific but arbitrary formation shape. A new technique based on complex Laplacian is introduced to address the problems of which formation shapes specified by inter-agent relative positions can be formed and how they can be achieved with distributed control ensuring global stability. Concerning the first question, we show that all similar formations subject to only shape constraints are those that lie in the null space of a complex Laplacian satisfying certain rank condition and that a formation shape can be realized almost surely if and only if the graph modeling the inter-agent specification of the formation shape is 2-rooted. Concerning the second question, a distributed and linear control law is developed based on the complex Laplacian specifying the target formation shape, and provable existence conditions of stabilizing gains to as-sign the eigenvalues of the closed-loop system at desired locations are given. Moreover, we show how the formation shape control law is extended to achieve a rigid formation if a subset of knowledgable agents knowing the desired formation size scales the formation while the rest agents do not need to