Convergence results for multi-agent rendezvous algorithm with rectilinear decision domain

This paper presents a proof of convergence of a computationally efficient decentralized rendezvous algorithm for a group of autonomous agents. The algorithm uses a rectilinear decision domain (RDD) as against the circular decision domain assumed in earlier work reducing its computational complexity considerably. Simulation results in earlier work has shown that, compared to the standard Ando's algorithm, the RDD algorithm shows very significant improvement in convergence time performance. In this paper analytical results to prove the convergence of the algorithm based on some relevant results on rendezvous problems are presented.