Gossip-Based Estimation of Centroid and Common Reference Frame in Open Multi-Agent Systems

Decentralized estimation of centroid and common reference frame in multi-agent systems is a challenging problem, particularly when agents do not have access to global positioning data. This challenge intensifies in Open Multi-Agent Systems (OMAS), where the network composition dynamically changes due to agents joining or leaving, causing fluctuations in the number of participants. This paper presents a novel, decentralized gossip-based algorithm that enables agents in OMAS to collaboratively estimate both the centroid and a common reference frame in a 2-D environment where the number of agents may fluctuate over time. Notably, our approach remains robust despite noisy distance measurements and intermittent participation, as it relies on asynchronous, local pairwise interactions. Designed to accommodate the dynamic nature of network topologies, our algorithm can be employed for real-world applications where agents can join or leave the system due to failures, resource limitations or external environmental factors.