Multi-modal Swarm Coordination via Hopf Bifurcations

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Journal of Intelligent and Robotic Systems
This paper outlines a methodology for the construction of vector fields that can enable a multi-robot system moving on the plane to generate multiple dynamical behaviors by adjusting a single scalar parameter. This parameter essentially triggers a Hopf bifurcation in an underlying time-varying dynamical system that steers a robotic swarm. This way, the swarm can exhibit a variety of behaviors that arise from the same set of continuous differential equations. Other approaches to bifurcation-based swarm coordination rely on agent interaction which cannot be realized if the swarm members cannot sense or communicate with one another. The contribution of this paper is to offer an alternative method for steering minimally instrumented multi-robot collectives with a control strategy that can realize a multitude of dynamical behaviors without switching their constituent equations. Through this approach, analytical solutions for the bifurcation parameter are provided, even for more complex cases that are described in the literature, along with the process to apply this theory in a multi-agent setup. The theoretical predictions are confirmed via simulation and experimental results with the latter also demonstrating real-world applicability.
This version of the article has been accepted for publication in Journal of Intelligent and Robotic Systems, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: © The Author(s), under exclusive licence to Springer Nature B.V. 2023. This article will be embargoed until 10/04/2024.
multi-agent systems, multi-behavioral systems, hopf bifurcation
Baxevani, K., Tanner, H.G. Multi-modal Swarm Coordination via Hopf Bifurcations. J Intell Robot Syst 109, 34 (2023).