In this section we provide sufficient conditions that guarantee rendezvous for identical agents. Recall that agents are identical if all agents have the same speeds. Our results here are given for agents with unit speed (
), which generalizes easily to agents with arbitrary but identical speeds via scaling. After introducing the candidate Lyapunov function, we first study cyclic and intree assignment graph cases separately before arriving at the most general result that combines the two cases. In the main body of this paper, we only include proofs of theorems that are essential in delivering the ideas of our approach; the rest of the proofs can be found in Appendix B.