Abstract
We present a methodology for characterizing and synthesizing swarm behaviors using both a macroscopic model that represents a swarm as a continuum and a microscopic model that represents individual robots. We develop a systematic approach for synthesizing behaviors at the macroscopic level that can be realized on individual robots at the microscopic level. Our methodology is inspired by a dynamical model of ant house hunting [1], 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. At the macroscopic level, we are able to synthesize controllers that result in the deployment of a robotic swarm in a predefined ratio between distinct sites. We then derive hybrid controllers for individual robots using only local interactions and no communication that respect the specifications of the global continuous behavior. Our simulations demonstrate that our synthesis procedure yields a correct microscopic model from the macroscopic description with guarantees on performance at both levels
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