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Multi-modal Swarm Coordination via Hopf Bifurcations

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Abstract

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.

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Acknowledgements

This work is supported by the National Science foundation’s Smart and Connected Health program via award # 2014264.

Funding

This work is supported by the National Science foundation’s Smart and Connected Health program via award # 2014264.

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Authors and Affiliations

  1. Center for Autonomous and Robotics Systems, University of Delaware, Newark, DE, USA

    Kleio Baxevani & Herbert G. Tanner

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  1. Kleio Baxevani
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  2. Herbert G. Tanner
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Kleio Baxevani and Herbert Tanner. The first draft of the manuscript was written by Kleio Baxevani and all authors commented and edited the manuscript. All authors read and approved the final manuscript.

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Correspondence to Kleio Baxevani.

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Baxevani, K., Tanner, H.G. Multi-modal Swarm Coordination via Hopf Bifurcations. J Intell Robot Syst 109, 34 (2023). https://doi.org/10.1007/s10846-023-01966-4

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