Problem
Research questions and friction points this paper is trying to address.
Consensus
Small Robot Teams
Disturbed Communication Environments
Phase Transition of the 3-Majority Dynamics with Uniform Communication Noise
🤖 AI Summary
This paper addresses the consensus problem in swarms of small robots subject to uniform communication noise. Method: We analyze the phase-transition behavior of the 3-majority dynamics system using stochastic process analysis, Markov chain coupling, and asymptotic expansions. Contribution/Results: We rigorously establish, for the first time, an exact analytical relationship between noise intensity and the consensus phase-transition threshold, proving a critical threshold θ_c = 1/3: below θ_c, global consensus is achieved with high probability; above it, the system exhibits persistent oscillation and fails to converge stably. Crucially, we uncover a non-monotonic phase-transition mechanism induced by noise—low-level noise can enhance local coordination, whereas exceeding θ_c triggers systemic disagreement. Our theoretical predictions align closely with numerical simulations, providing a new theoretical benchmark and design principle for robust distributed cooperative control.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Robotic Swarm Consensus
3-Majority Rule
Pending State Dynamics
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