Continuous Rendezvous Algorithm for Memoryless Agents with Limited Visibility in the Euclidean Space

Abstract

A continuous-in-time rendezvous algorithm for memoryless agents with limited visibility on the Euclidean plane was proposed in [N. Gordon, I. A. Wagner, and A. M. Bruckstein in Ant Colony Optimization and Swarm Intelligence, Springer, Berlin, 2004, pp. 142--153] and was formulated as a system of differential equations in [L. I. Bellaiche and A. Bruckstein, Swarm Intell., 11 (2017), pp. 271--293]. We generalize this algorithm by letting the agents move in the Euclidean space of arbitrary dimension. And we provide a rigorous existence theory for this algorithm, which was not done before this work, even for the original algorithm for agents on a plane. Finally, for dimension not greater than three, we show that rendezvous is achieved in finite time, which is robust with respect to the number of the agents.