Hierarchical abstractions for robotic swarms

Abstract We develop a hierarchical framework for planning and control of arbitrarily large groups of fully actuated robots with polyhedral velocity bounds (swarm) moving in polygonal environments with polygonal obstacles. At the rst level of hierarchy, we aggregate the high dimensional control system of the swarm into a small dimensional control system capturing its essential features. These features describe the position of the swarm in the world and its size. At the second level, we reduce the problem of controlling the essential features of the swarm to a model checking problem. In the obtained hierarchical framework, high level specications given in natural language such as Linear Temporal Logic formulas over linear predicates in the essential features are automatically mapped to provably correct robot control laws. I