Transporting Robotic Swarms via Mean-Field Feedback Control

With the rapid development of AI and robotics, deploying a large swarm of networked robots has foreseeable applications in the near future. Existing research in swarm robotics has mainly followed a bottom-up philosophy with predefined local coordination and control rules. However, it is arduous to verify the global requirements and analyze their performance. This motivates us to pursue a top-down approach, and develop a provable control strategy for transporting a robotic swarm to achieve a desired global configuration. Specifically, we use mean-field partial differential equations (PDEs) to model the swarm and control its mean-field density (i.e., probability density) over a bounded spatial domain using mean-field feedback. The presented control law uses density estimates as feedback signals and generates corresponding velocity fields that, by acting locally on individual robots, guide their global distribution to a target profile. The design of the velocity field is therefore centralized, but the implementation of the controller can be fully distributed -- individual robots sense the velocity field and derive their own velocity control signals accordingly. The key contribution li