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Study of Impossibility Results on Swarm Based Grid Exploration in Discrete Domain

Exploration of a graph by a swarm of autonomous mobile robots is a widely addressed problem in discrete domain. There exists a solution for a successful exploration of a grid graph which proves that the minimum number of robots required to explore a grid is three. In the existing solution, all three robots participate in orienting the grid as robots do not have a sense of direction. However, the actual exploration is performed by a single robot. This does not comply with the concept of a swarm that requires a task to be collectively achieved by a group of robots. In this paper, we study whether or not the existing algorithm, works successfully when the number of robots is greater than three.