Time-Varying Density Control for Large-Scale Multi-Agent Systems Using Heat and Continuity Equation

This is the webpage for our project in the course Advanced Topics in Control at ETH spring 2023.

Abstract—The presented work examines the feasibility of coordinating a large-scale multi-agent system according to a time-varying probability density function using nature-inspired control techniques. The proposed method works in a decentralized manner where only information about neighboring agents positions are required. The information is then used to estimate the local density which further is used to generate a velocity command. Building upon previous work, a feedback law based on heat equation is extended by a feed-forward term based on the continuity equation. This accommodates a velocity field driving the agents towards the desired time-varying spatial density. We show how the proposed technique can be used to track both simple and complex time-varying densities. The proposed control law is tested in a simulation to verify its performance.