This paper is concerned with the decentralized formation control of multi-agent systems moving in the plane. Using a single-integrator agent model, we propose a new distributed control law to asymptotically stabilize the inter-agent distance error dynamics. Our approach exploits the infinitesimal and minimal rigidity of the undirected graph that models the formation. A Lyapunov-based analysis shows that these two properties are necessary conditions for asymtptotic stability. The control, which is explicitly dependent on the graph rigidity matrix, is derived for a class of potential functions.
- Dynamic Systems and Control Division
On the Stabilization of Planar Multi-Agent Formations
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Cai, X, & de Queiroz, M. "On the Stabilization of Planar Multi-Agent Formations." Proceedings of the ASME 2012 5th Annual Dynamic Systems and Control Conference joint with the JSME 2012 11th Motion and Vibration Conference. Volume 2: Legged Locomotion; Mechatronic Systems; Mechatronics; Mechatronics for Aquatic Environments; MEMS Control; Model Predictive Control; Modeling and Model-Based Control of Advanced IC Engines; Modeling and Simulation; Multi-Agent and Cooperative Systems; Musculoskeletal Dynamic Systems; Nano Systems; Nonlinear Systems; Nonlinear Systems and Control; Optimal Control; Pattern Recognition and Intelligent Systems; Power and Renewable Energy Systems; Powertrain Systems. Fort Lauderdale, Florida, USA. October 17–19, 2012. pp. 423-429. ASME. https://doi.org/10.1115/DSCC2012-MOVIC2012-8534
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