Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory
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 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).
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 22, 2004
- Accession Number
- ADA462317
Entities
People
- Reza Olfati-saber
Organizations
- California Institute of Technology