Olfati-Saber, Reza (2004) Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory. California Institute of Technology , Pasadena, CA. (Submitted) http://resolver.caltech.edu/CaltechCDSTR:2004.005
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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 alpha-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or alpha-agents, and virtual agents associated with alpha-agents called beta- and gamma-agents. We show that the tracking/migration problem for flocks can be solved using an algorithm with a peer-to-peer architecture. Each node (or macro-agent) of this peer-to-peer network is the aggregation of all three species of agents. The implication of this fact is that ``flocks need no leaders''. We discuss what constitutes flocking and provide a universal definition of ``flocking'' for particle systems that has the same role as ``Lyapunov stability'' for nonlinear dynamical systems. By ``universal'', we mean independent of the method of trajectory generation for particles. Various simulation results are provided that demonstrate the effectiveness of our novel algorithms and analytical tools. This includes performing 2-D and 3-D flocking, split/rejoin maneuver, and squeezing maneuver for 40 to 150 agents (e.g. particles and UAVs).
|Item Type:||Report or Paper (Technical Report)|
|Group:||Control and Dynamical Systems Technical Reports|
|Official Citation:||R. Olfati-Saber. "Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory." Technical Report 2004-005, California Institute of Technology, Control and Dynamical Systems, Pasadena, CA, June 2004.|
|Usage Policy:||You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.|
|Deposited By:||Imported from CaltechCDSTR|
|Deposited On:||28 Jun 2004|
|Last Modified:||26 Dec 2012 14:29|
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