Analytical Swarm Chemistry: Characterization and Analysis of Emergent Swarm Behaviors

Swarm robotics has potential for a wide variety of applications, but real-world deployments remain rare due to the difficulty of predicting emergent behaviors arising from simple local interactions. Traditional engineering approaches design controllers to achieve desired macroscopic outcomes under idealized conditions, while agent-based and artificial life studies explore emergent phenomena in a bottom-up, exploratory manner. In this work, we introduce Analytical Swarm Chemistry, a framework that integrates concepts from engineering, agent-based and artificial life research, and chemistry. This framework combines macrostate definitions with phase diagram analysis to systematically explore how swarm parameters influence emergent behavior. Inspired by concepts from chemistry, the framework treats parameters like thermodynamic variables, enabling visualization of regions in parameter space that give rise to specific behaviors. Applying this framework to agents with minimally viable capabilities, we identify sufficient conditions for behaviors such as milling and diffusion and uncover regions of the parameter space that reliably produce these behaviors. Preliminary validation on real robots demonstrates that these regions correspond to observable behaviors in practice. By providing a principled, interpretable approach, this framework lays the groundwork for predictable and reliable emergent behavior in real-world swarm systems.