Consensus in Multi-Agent Systems with Uniform and Nonuniform Communication Delays

TL;DR

This paper studies how communication delays affect consensus in multi-agent systems, providing theoretical convergence conditions, explicit delay-dependent consensus values, and validating results through simulations and robotic experiments.

Contribution

It introduces new convergence analysis for consensus algorithms under both uniform and nonuniform delays, with explicit delay-dependent steady-state values and practical robotic implementations.

Findings

Consensus is achievable despite communication delays.

Explicit formulas for delay-dependent consensus values.

Robustness of the algorithm demonstrated on ground robots.

Abstract

This paper analyzes consensus in multi-agent systems under uniform and nonuniform communication delays, a key challenge in distributed coordination with applications to robotic swarms. It investigates the convergence of a consensus algorithm accounting for delays across communication links in a connected, undirected graph. Novel convergence results are derived using Rouch\'e's theorem and Lyapunov-based stability analysis. The system is shown to reach consensus at a steady-state value given by a weighted average determined by the delay distribution, with stability ensured under explicit parameter bounds. Both uniform and nonuniform delay scenarios are analyzed, and the corresponding convergence values are explicitly derived. The theoretical results are validated through simulations, which explore the impact of delay heterogeneity on consensus outcomes. Furthermore, the algorithm is implemented and experimentally tested on a swarm of QBOT3 ground robots to solve the rendezvous problem, demonstrating the agents' ability to converge to a common location despite realistic communication constraints, thus confirming the algorithm's robustness and practical applicability. The results provide guidelines for designing consensus protocols that tolerate communication delays, offer insights into the relationship between network delays and coordination performance, and demonstrate their applicability to distributed robotic systems.