Transporting Robotic Swarms via Mean-Field Feedback Control

TL;DR

This paper develops a top-down mean-field PDE control strategy for robotic swarms, enabling global distribution shaping through density feedback, with proven stability and verified via simulations.

Contribution

It introduces a provable, centralized velocity field control law for swarm deployment based on mean-field PDEs, ensuring stability despite density estimation errors.

Findings

Control law guides swarm to target distribution

System is locally input-to-state stable

Simulations confirm effectiveness

Abstract

With the rapid development of AI and robotics, transporting 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 deploying 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 lies in applying the concept of input-to-state stability (ISS) to show that the perturbed closed-loop system (a nonlinear and time-varying PDE) is locally ISS with respect to density estimation errors. The effectiveness of the proposed control laws is verified using agent-based simulations.