MeanFlow Meets Control: Scaling Sampled-Data Control for Swarms
This work addresses the problem of efficient swarm control for robotics or autonomous systems, but it appears incremental as it builds on MeanFlow and focuses on linear time-invariant dynamics.
The paper tackles the challenge of steering large-scale swarms with few control updates by introducing a control-space learning framework that respects sampled-data dynamics, resulting in a scalable approach for swarm steering.
Steering large-scale swarms in only a few control updates is challenging because real systems operate in sampled-data form: control inputs are updated intermittently and applied over finite intervals. In this regime, the natural object is not an instantaneous velocity field, but a finite-window control quantity that captures the system response over each sampling interval. Inspired by MeanFlow, we introduce a control-space learning framework for swarm steering under linear time-invariant dynamics. The learned object is the coefficient that parameterizes the finite-horizon minimum-energy control over each interval. We show that this coefficient admits both an integral representation and a local differential identity along bridge trajectories, which leads to a simple stop-gradient training objective. At implementation time, the learned coefficient is used directly in sampled-data updates, so the prescribed dynamics and actuation map are respected by construction. The resulting framework provides a scalable approach to few-step swarm steering that is consistent with the sampled-data structure of real control systems.