Distributed Covariance Steering via Non-Convex ADMM for Large-Scale Multi-Agent Systems

TL;DR

This paper introduces distributed covariance steering methods for large-scale multi-agent systems, balancing safety, efficiency, and scalability through novel ADMM-based algorithms with convergence guarantees.

Contribution

It proposes three new distributed covariance steering algorithms with different trade-offs and provides convergence analysis for non-convex ADMM in multi-agent safety control.

Findings

FCC-DCS yields the least conservative solutions.

PCC-DCS reduces computational demands by partial covariance exchange.

Simulations demonstrate scalability to thousands of agents.

Abstract

This paper studies the problem of steering large-scale multi-agent stochastic linear systems between Gaussian distributions under probabilistic collision avoidance constraints. We introduce a family of \textit{distributed covariance steering (DCS)} methods based on the Alternating Direction Method of Multipliers (ADMM), each offering different trade-offs between conservatism and computational efficiency. The first method, Full-Covariance-Consensus (FCC)-DCS, enforces consensus over both the means and covariances of neighboring agents, yielding the least conservative safe solutions. The second approach, Partial-Covariance-Consensus (PCC)-DCS, leverages the insight that safety can be maintained by exchanging only partial covariance information, reducing computational demands. The third method, Mean-Consensus (MC)-DCS, provides the most scalable alternative by requiring consensus only on mean states. Furthermore, we establish novel convergence guarantees for distributed ADMM with iteratively linearized non-convex constraints, covering a broad class of consensus optimization problems. This analysis proves convergence to stationary points for PCC-DCS and MC-DCS, while the convergence of FCC-DCS follows from standard ADMM theory. Simulations in 2D and 3D multi-agent environments verify safety, illustrate the trade-offs between methods, and demonstrate scalability to thousands of agents.