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The problem of synchronization and balancing around simple closed polarcurves is addressed for unicycle-type multi-agent systems. Leveraging theconcept of barrier Lyapunov function in conjunction with bounded Lyapunov-likecurve-phase potential functions, we propose distributed feedback control lawsand show that the agents asymptotically stabilize to the desired closed curve,their trajectories remain bounded within a compact set, and their turn-ratesadhere to the saturation limits. We also characterize the explicit nature ofthe boundary of this trajectory-constraining set based on the magnitude of thesafe distance of the exterior boundary from the desired curve. We furtherestablish a connection between the perimeters and areas of thetrajectory-constraining set with that of the desired curve. We obtain bounds ondifferent quantities of interest in the post-design analysis and providesimulation results to illustrate the theoretical findings.

Synchronization and Balancing around Simple Closed Polar Curves with Bounded Trajectories and Control Saturation