Gathering Multiple Robots in a Ring and an Infinite Grid

Abstract

Gathering can be coined as one of the primary interaction parameters in systems of autonomous mobile agents or sensors, known as robots. These robots are identical and placed in the nodes of an unlabeled graph. They operate in wait-look-compute-move cycles. In one cycle, first the sensors of the robots are activated independent of each other (wait). Then a robot takes a snapshot of the current configuration (look), makes a decision to stay idle or to move to one of its adjacent nodes (compute), and in the latter case makes an instantaneous move to this neighbor (move). Then the robot again goes back to its initial phase (wait). Cycles are performed asynchronously for each robot. The robots are oblivious, i.e., they do not use any computed data from the previous cycle. The robots do not agree on a common coordinate system. They cannot differentiate between a node having single robot and a node having multiple robots, i.e., multiplicity of a node. The robots are not able to see all the nodes of the graph. They do not know the total number of robots in the system. In this paper, we have developed two algorithms to gather these robots at a single node (not known beforehand) of a Ring Graph and an infinite Grid, in finite time. To the best of our knowledge, this is one of the first reported results on gathering multiple robots under limited visibility in an infinite grid and a ring.