Stochastic Filtering for Quorum Sensing in Robot Swarms under 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.