Algorithms for the Analysis and Synthesis of a Bio-inspired Swarm Robotic System

We present a methodology for characterizing, analyzing, and synthesizing swarm behaviors using both a macroscopic continuous model that represents a swarm as a continuum and a macroscopic discrete model that enumerates individual agents. Our methodology is applied to a dynamical model of ant house hunting, a decentralized process in which a colony attempts to emigrate to the best site among several alternatives. The model is hybrid because the colony switches between different sets of behaviors, or modes, during this process. Using the model in [1], we investigate the relation of site population growth to initial system state with an algorithm called Multi-Affine Reachability analysis using Conical Overapproximations (Marco) [2]. We then derive a microscopic hybrid dynamical model of an agent that respects the specifications of the global behavior at the continuous level. Our multi-level simulations demonstrate that we have produced a rigorously correct microscopic model from the macroscopic descriptions.