Mean-field models in swarm robotics: a survey.

We present a survey on the application of fluid approximations, in the form of mean-field models, to the design of control strategies in swarm robotics. Mean-field models that consist of ordinary differential equations, partial differential equations, and difference equations have been used in the swarm robotics literature, depending on whether the state of each agent and the time variable take values from a discrete or continuous set. These macroscopic models are independent of the number of agents in the swarm, and hence can be used to synthesize robot control strategies in a scalable manner, in contrast to individual-based microscopic models of swarms that represent finite numbers of discrete agents. Moreover, mean-field models are amenable to rigorous investigation using tools from dynamical systems theory, control theory, stochastic processes, and analysis of partial differential equations, enabling new insights and provable guarantees on the dynamics of collective behaviors. In this paper, we survey the applications of these models to problems in swarm robotics that include coverage, task allocation, self-assembly, consensus, and environmental mapping.