Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory

—In this paper, we present a theoretical framework for designandanalysisofdistributedfl[login to view URL] flocking in free-space and presence of multiple obstacles are [login to view URL]flockingalgorithms:twoforfree-flocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approachtoextractionofinteractionrulesthatleadtotheemergence of collective behavior. We show that the first algorithm generically leadstoregularfragmentation,whereasthesecondandthirdalgorithms both lead to flocking. A systematic method is provided for constructionofcostfunctions(orcollectivepotentials)forflocking. These collective potentials penalize deviation from a class of lattice-shape objects called -lattices. We use a multi-species framework for construction of collective potentials that consist of flockmembers,or -agents,andvirtualagentsassociatedwith -agents called - and -agents. We show that migration of flocks can be performedusingapeer-to-peernetworkofagents,i.e.,“flocksneed no leaders.” A “universal” definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2-D and 3-D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms