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This study addresses the challenge of accurate quorum sensing in robot swarms using anonymous communication protocols, which often suffer from double-counting bias due to indistinguishable message sources. By introducing a stochastic filtering protocol inspired by $k$-priority sampling, the authors demonstrate that their method, \ANTk, effectively stabilizes quorum estimates while managing the trade-off between accuracy and recovery time. The results show that while traditional anonymous protocols are fast but inaccurate, \ANTk significantly reduces temporary errors, leading to more reliable collective decision-making in swarms.
Stochastic filtering can drastically enhance the accuracy of quorum sensing in robot swarms, mitigating the biases of anonymous communication.
Quorum Sensing (QS) is a key capability for robot swarms, useful for coordination of activities at the group level. Effective communication is instrumental for individuals to estimate the quorum level of the entire swarm. Anonymous communication protocols where individuals exchange local information without revealing unique identities are helpful to support quorum estimates by sampling information from neighbours and maintain scalability of the QS process. However, because anonymous protocols cannot distinguish message sources, repeated messages from the same sender may be double-counted, thereby biasing collective quorum estimates. In this study, we introduce a stochastic filtering protocol inspired by $k$-priority sampling to improve estimate stability (\ANTk), and we compare it with a baseline anonymous protocols (\AN) and a randomised variant designed to improve accuracy (\ANT). We find that the baseline protocol \AN provides a parsimonious and fast solution, but remains highly inaccurate due to double-counting bias. The \ANT variant improves accuracy but suffers from information inertia, resulting in slower convergence. Finally, actively filtering the message buffer via the \ANTk protocol successfully decreases temporary errors and stabilises the estimate, at the cost of an increased time of recovery from errors.