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In this paper, we present a novel algorithm for deterministically mapping an undirected graph-like world with multiple synchronized agents. The application of this algorithm is the collective mapping of an indoor environment with multiple mobile robots while leveraging an embedded topological decomposition of the environment. Our algorithm relies on a group of agents that all depart from the same initial vertex in the graph and spread out to explore the graph. A centralized tree of graph hypotheses is maintained to consider loop-closure, which is deterministically verified when agents observe each other at a common vertex. To achieve efficient mapping, we introduce an active exploration method in which agents dynamically request rendezvous tasks from other available agents to validate graph hypotheses.

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