Fault-tolerant gathering of asynchronous oblivious mobile robots under one-axis agreement

This paper addresses gathering, a fundamental coordination problem for multi-robot systems, for n≥2 asynchronous, oblivious mobile robots in the presence of f faulty robots. Earlier work has reported that the asynchronous robots cannot gather at a point without having some assumptions on multiplicity detection or total agreement in coordinate axis or constant amount of persistent memory bits. This paper shows that gathering is possible by agreeing only on one axis. Traditionally the robots have been assumed to be transparent. This work proves that gathering is achievable under one axis agreement even if the robots have obstructed visibility. In both the cases, deterministic fault-tolerant algorithms have been presented, for any initial static configuration of the robots. This paper is the first attempt at studying the gathering problem under the combination of three realistic model specifications (i) agreement in one axis (ii) obstructed visibility (iii) arbitrary number of faulty robots.