Multi-Robot Symmetric Rendezvous Search on the Line

We study the Symmetric Rendezvous Search Problem for a multi-robot system. There are
$n>2$
robots arbitrarily located on a line. Their goal is to meet somewhere on the line as quickly as possible. The robots do not know the initial location of any of the other robots or their own positions on the line. The symmetric version of the problem requires the robots to execute the same search strategy to achieve rendezvous. Therefore, we solve the problem in an online fashion with a randomized strategy. In this letter, we present a symmetric rendezvous algorithm which achieves a constant competitive ratio for the total distance traveled by the robots. We validate our theoretical results through simulations.