Flocking for multi-agent dynamic systems: algorithms and theory
Olfati-Saber, R.
Thayer Sch. of Eng., Dartmouth Coll., Hanover, NH, USA;
This paper appears in: Automatic Control, IEEE Transactions on
Publication Date: March 2006
Volume: 51,
Issue: 3
On page(s): 401- 420
ISSN: 0018-9286
INSPEC Accession Number: 8942874
Digital Object Identifier: 10.1109/TAC.2005.864190
Current Version Published: 2006-03-13
Abstract
In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in free-space and presence of multiple obstacles are considered. We present three flocking algorithms: two for free-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 approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of lattice-shape objects called α-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or α-agents, and virtual agents associated with α-agents called β- and γ-agents. We show that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need 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.
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