Mathematical Modeling of Large Multi-Agent Systems

Abstract

The biologically-inspired swarm paradigm is being used to design self-organizing systems of locally interacting agents. A major difficulty in designing swarms with desired characteristics is understanding the causal relation between individual agent and collective behaviors. Mathematical analysis of swarm dynamics can address this difficulty to gain insight into system design. This project developed a formal framework for mathematical modeling and analysis of multi-agent swarms. Though the behavior of an individual agent can be considered to be stochastic and unpredictable, collective behavior of a swarm can have a simple probabilistic description. We showed that a class of mathematical models that describe the dynamics of collective behavior of multi-agent systems can be written down from the details of the individual agent controller. We have successfully applied this formalism to study collective behavior of distributed robot systems for which a body of experimental and simulations data exists.