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Transporting Robotic Swarms via Mean-Field Feedback Control

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Document pages: 8 pages

Abstract: With the rapid development of AI and robotics, transporting a large swarm ofnetworked robots has foreseeable applications in the near future. Existingresearch in swarm robotics has mainly followed a bottom-up philosophy withpredefined local coordination and control rules. However, it is arduous toverify the global requirements and analyze their performance. This motivates usto pursue a top-down approach, and develop a provable control strategy fordeploying a robotic swarm to achieve a desired global configuration.Specifically, we use mean-field partial differential equations (PDEs) to modelthe swarm and control its mean-field density (i.e., probability density) over abounded spatial domain using mean-field feedback. The presented control lawuses density estimates as feedback signals and generates corresponding velocityfields that, by acting locally on individual robots, guide their globaldistribution to a target profile. The design of the velocity field is thereforecentralized, but the implementation of the controller can be fully distributed-- individual robots sense the velocity field and derive their own velocitycontrol signals accordingly. The key contribution lies in applying the conceptof input-to-state stability (ISS) to show that the perturbed closed-loop system(a nonlinear and time-varying PDE) is locally ISS with respect to densityestimation errors. The effectiveness of the proposed control laws is verifiedusing agent-based simulations.

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