In this paper, we develop a distributed monitoring framework for robot swarms
so that the agents can monitor whether the executions of robot swarms satisfy
Swarm Signal Temporal Logic (SwarmSTL) formulas. We define generalized moments
(GMs) to represent swarm features. A dynamic generalized moments consensus
algorithm (GMCA) with Kalman filter (KF) is proposed so that each agent can
estimate the GMs. Also, we obtain an upper bound for the error between an
agent's estimate and the actual GMs. This bound is independent of the motion of
the agents. We also propose rules for monitoring SwarmSTL temporal and logical
operators. As a result, the agents can monitor whether the swarm satisfies
SwarmSTL formulas with a certain confidence level using these rules and the
bound of the estimation error. The distributed monitoring framework is applied
to a swarm transporting supplies example, where we also show the efficacy of
the Kalman filter in the dynamic generalized moments consensus process