A Formal Framework for Reasoning Emergent Behaviors in Swarm Robotic Systems

Swarm robotic system is a complex system comprising a large number of distributed robots. Although a single robot has limited ability of computation and communication, their microscopic behaviors can finally lead to a macroscopic system behavior. Such phenomenon is called emergent behavior which is significantly useful but difficult to engineering due to its indecompositionality over time and scale. In this paper, we propose a formal framework to specify and verify the causality between the macroscopic emergent property and microscopic behaviors of robots. The framework supports hybrid specification of both continuous dynamics of robots and their discrete control programs. A refinement notion is defined in this framework which provides a formal development and verification approach to guide the design of a swarm robotic system satisfying expected emergent properties. We demonstrate the framework on a simple robot swarm consensus scenario.