Multi-robot Symmetric Rendezvous Search on the Line with an Unknown Initial Distance

TL;DR

This paper introduces and analyzes multi-robot symmetric rendezvous algorithms on a line with unknown initial distances, providing theoretical bounds and simulation validation for both synchronous and asynchronous scenarios.

Contribution

It extends previous symmetric rendezvous algorithms to multiple robots, analyzing their competitive ratios and addressing asynchronous start times.

Findings

MSR algorithm has a competitive ratio of O(n^{0.67})

MASR algorithm has a competitive ratio of O(n^{1.5})

Theoretical results are validated through simulations.

Abstract

In this paper, we study the symmetric rendezvous search problem on the line with n > 2 robots that are unaware of their locations and the initial distances between them. In the symmetric version of this problem, the robots execute the same strategy. The multi-robot symmetric rendezvous algorithm, MSR presented in this paper is an extension our symmetric rendezvous algorithm, SR presented in [23]. We study both the synchronous and asynchronous cases of the problem. The asynchronous version of MSR algorithm is called MASR algorithm. We consider that robots start executing MASR at different times. We perform the theoretical analysis of MSR and MASR, and show that their competitive ratios are $O(n^{0.67})$ and $O(n^{1.5})$, respectively. Finally, we confirm our theoretical results through simulations.