Multi-Agent Algorithms for Collective Behavior: A structural and application-focused atlas

The goal of this paper is to provide a survey and application-focused atlas of collective behavior coordination algorithms for multi-agent systems. We survey the general family of collective behavior algorithms for multi-agent systems and classify them according to their underlying mathematical structure. In doing so, we aim to capture fundamental mathematical properties of algorithms (e.g., scalability with respect to the number of agents and bandwidth use) and to show how the same algorithm or family of algorithms can be used for multiple tasks and applications. Collectively, this paper provides an application-focused atlas of algorithms for collective behavior of multi-agent systems, with three objectives:

1. to act as a tutorial guide to practitioners in the selection of coordination algorithms for a given application;
2. to highlight how mathematically similar algorithms can be used for a variety of tasks, ranging from low-level control to high-level coordination;
3. to explore the state-of-the-art in the field of control of multi-agent systems and identify areas for future research.