Abstract
In this letter, we develop a distributed consensus-based online monitoring framework for a robot swarm with a fixed graph structure. Each agent can monitor whether the swarm satisfies specifications given in the form of Swarm Signal Temporal Logic (SwarmSTL) formulas. SwarmSTL formulas describe temporal properties of swarm-level features represented by generalized moments (GMs), e.g., centroid and variance. To deal with measurement noise, we propose a generalized moment consensus algorithm (GMCA) with Kalman filter (KF), allowing each agent to estimate the GMs. Besides, we prove the convergence properties of the GMCA and derive an upper bound for the error between an agent's estimate of the GMs and the actual GMs. This upper bound is derived to be dependent on the maximal allowed velocity but independent of the agents' exact motion. A set of distributed monitoring rules for SwarmSTL formulas are proposed based on the estimation error bound. As a result, the agents can monitor the satisfaction of SwarmSTL formulas over swarm features during execution. The distributed monitoring framework is applied to a supply transportation example, where the efficacy of KF in the GMCA is also shown.
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