Leader election and gathering for asynchronous fat robots without common chirality

This paper proposes a deterministic gathering   algorithm for n≥5n≥5 autonomous, homogeneous, asynchronous, oblivious unit disc robots (fat robots). The robots do not have common coordinate system and chirality. A robot can sense or observe its surroundings by collecting information about the positions of all the robots. Based on this information, they compute their destinations for moving and move there. Initially, the robots are stationary and separated. Robots are assumed to be transparent but solid. The algorithm for gathering is designed in such a way that the robots do not collide. In order to avoid collision we do not allow all the robots to move at a time. A unique robot, called leader is elected to move to its destination. No other robot moves till the leader reaches its destination. When the leader reaches its destination, another leader is selected from the remaining robots. However, leader election may not be possible in an arbitrary configuration. In this paper, we characterize all geometric configurations where leader election is possible and present an algorithm for leader election in such a case. An important property of our leader election algorithm is that it is possible to elect a leader from the remaining set of robots also.