On the Stability of Swarm Consensus Under Noisy Control

TL;DR

This paper analyzes how a swarm of robots reaches consensus when their connectivity is probabilistic, demonstrating that a random walk control guarantees stability through Lyapunov methods, supported by simulations.

Contribution

It introduces a probabilistic connectivity model for swarm consensus and proves Lyapunov stability with a random walk control, supported by simulations.

Findings

Probabilistic connectivity affects swarm consensus behavior.

Random walk control ensures Lyapunov stability.

Simulation results validate the theoretical analysis.

Abstract

Representation of a swarm of independent robotic agents under graph-theoretic constructs allows for more formal analysis of convergence properties. We consider the local and global convergence behavior of an N-member swarm of agents in a modified consensus problem wherein the connectivity of agents is governed by probabilistic functions. The addition of a random walk control ensures Lyapunov stability of the swarm consensus. Simulation results are given and planned experiments are described.