A Degree of Flowability for Virtual Flow Fields

This letter proposes a new notion of virtual flow field and a measure of its quality. Unlike velocity fields for robotic swarm control, the virtual flow field here is described by several functions of space and time. It represents the variation of the properties of the robotic swarm, such as velocity and density. With the development of swarm control technology, there is an emerging demand to evaluate the quality of the virtual flow field and support the path planning of the robotic swarm accordingly. For such a purpose, this letter adopts a notion of the degree of flowability (DOF) for the virtual flow fields, which is relevant to the density of the swarm and the external energy input for the robots to pass through the field. Then, one method for calculating the DOF for the virtual flow field is proposed with simple examples for feasibility analysis. Calculations and simulations of three different virtual flow fields are performed to demonstrate the feasibility of the method.