With the rapid development of robotics swarm technology, there are more tasks that require the swarm to pass through complicated environments safely and efficiently. Virtual tube technology is a novel way to achieve this goal. Virtual tubes are free spaces connecting two places that provide safety boundaries and direction of motion for swarm robotics. How to determine the design quality of a virtual tube is a fundamental problem. For such a purpose, this paper presents a degree of flowability (DOF) for two-dimensional virtual tubes according to a minimum energy principle. After that, methods to calculate DOF are proposed with a feasibility analysis. Simulations of swarm robotics in different kinds of two-dimensional virtual tubes are performed to demonstrate the effectiveness of the proposed method of calculating DOF.
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