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Eissa, Hazem and Htet, Thant Minn (2026) The Metastable Consensus Cliff Under Communication Delay in a Swarm of Robots. Swarm Intelligence. (Submitted)

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Abstract

Abstract

Decentralised robot swarms must reach agreement using only local, range-limited, delayed communication while moving through cluttered terrain. A widely reported observation is that increasing communication delay produces a sharp, cliff-like collapse of consensus. Through a controlled simulation study of a mobile binary weighted-voter swarm on obstacle terrain, we show that this collapse is largely an artefact of how consensus is measured, and that the phenomenon is better described as destabilisation than as slowing or fragmentation. Three controls drive the argument. First, extending the observation budget in a wall-free setting slides the cliff to larger delays and then saturates: below a threshold, consensus is reachable given time (a budget-relative, slow-approach regime); above it, consensus fails even at ten times the budget (a genuine-failure regime). Second, the collapse is not fragmentation: because agent motion is opinion-independent, the time-varying graph is delay-invariant, and the cliff persists at full strength on graphs that stay connected throughout. Third, consensus is metastable, roughly a quarter of runs that reach it subsequently leave, a fraction that grows with delay, so the swarm hovers near but cannot lock onto agreement. On well-connected graphs, the cliff is quantitatively predicted by a mixing-time law; on marginally connected graphs, it holds only approximately, as metastable wandering dominates. Throughout, survivability is decoupled from consensus. We relate these findings to metastable-consensus theory in noisy opinion dynamics, and draw a methodological lesson: binary thresholds and finite observation budgets can make smooth, metastable dynamics appear as a sharp non-linear collapse.

Item Type: Article
Depositing User: Hazem Eissa
URI: https://sure.sunderland.ac.uk/id/eprint/20836

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20836
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Date Deposited
10 Nov 2026 15:57
Last Modified
10 Nov 2026 16:00

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