# Transporting Robotic Swarms via Mean-Field Feedback Control

arXiv: https://arxiv.org/abs/2006.11462 · HTML: https://mlsanity.com/paper/2006.11462/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2020.

## Built on by (most cited first, 6 of 6)

- [A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.03859/) (2022)
- [SwarmDiff: Swarm Robotic Trajectory Planning in Cluttered Environments via Diffusion Transformer](https://mlsanity.com/paper/2505.15679/) (2025)
- [Scalable Task-Driven Robotic Swarm Control via Collision Avoidance and Learning Mean-Field Control](https://mlsanity.com/paper/2209.07420/) (2022)
- [Nonlocal Mean Field Schr"odinger Bridge with Learned Interactions](https://mlsanity.com/paper/2606.04265/) (2026)
- [Learning distributed channel access policies for networked estimation: data-driven optimization in the mean-field regime](https://mlsanity.com/paper/2112.05837/) (2021)
- [Multi-Robot Motion Planning from Vision and Language using Heat-Inspired Diffusion](https://mlsanity.com/paper/2512.13090/) (2025)

## Abstract (arXiv)

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.