Mutual Visibility by Robots with Persistent Memory

Abstract: This paper addresses the mutual visibility problem for a set of semi-synchronous, opaque robots occupying distinct positions in the Euclidean plane. Since robots are opaque, if three robots lie on a line, the middle robot obstructs the visions of the two other robots. The mutual visibility problem asks the robots to coordinate their movements to form a configuration, within finite time and without collision, in which no three robots are collinear. Robots are endowed with a constant bits of persistent memory. In this work, we consider the FSTATE computational model in which the persistent memory is used by the robots only to remember their previous internal states. Except from this persistent memory, robots are oblivious i.e., they do not carry forward any other information from their previous computational cycles. The paper presents a distributed algorithm to solve the mutual visibility problem for a set of semi-synchronous robots using only 1 bit of persistent memory. The proposed algorithm does not impose any other restriction on the capability of the robots and guarantees collision-free movements for the robots.