Stability analysis of swarms in a noisy environment

Bacteria, bees and birds often work together. A group of robots can be designed to coordinate their activities to collect objects. Networked cooperative uninhabited autonomous vehicles (UAVs) are being developed for various applications. We refer to all such groups of entities as "social foraging swarms." In order for such multi-agent systems to succeed it is often critical that they can both maintain cohesive behaviors and appropriately respond to environmental stimuli. In this paper we characterize swarm cohesiveness as a stability property and use a Lyapunov approach to develop conditions under which local agent actions will lead to cohesive foraging even in the presence of "noise," characterized by uncertainty on sensing other agent\´s position and velocity, and in sensing nutrients that each agent is foraging for. The results quantify earlier claims that social foraging is in a certain sense superior to individual foraging when noise is present, and provide clear connections between local agent-agent interactions and emergent group behavior.