Leader Election and Gathering for Asynchronous Transparent Fat Robots without Chirality

Gathering of autonomous mobile robots is a well known and challenging research problem for a system of multiple mobile robots. Most of the existing works consider the robots to be dimensionless or points. Algorithm for gathering fat robots (a robot represented as a unit disc) has been reported for three and four robots. This paper proposes a distributed algorithm which deterministically gathers n (n ≥ 5) asynchronous, fat robots. The robots are assumed to be transparent and they have full visibility. Since the robots are unit discs, they can not overlap; we define a gathering pattern for them. The robots are initially considered to be stationary. A robot is visible in its motion. The robots do not store past actions. They are anonymous and can not be distinguished by their appearances and do not have common coordinate system or chirality. The robots do not communicate through message passing. In the proposed gathering algorithm one robot moves at a time towards its destination. The robot which moves, is selected in such a way that, it will be the only robot eligible to move, until it reaches its destination. In case of a tie, this paper proposes a leader election algorithm which produces an ordering of the robots and the first robot in the ordering becomes the leader. The ordering is unique in the sense that, each robot, characterized by its location, agrees on the same ordering. We show that if a set of robots can be ordered then they can gather deterministically. The paper also characterizes the cases, where ordering is not possible. This paper also presents an important fact that, if leader election is possible then gathering pattern formation is possible even with no chirality. It is known that, pattern formation and leader election are equivalent, for n ≥ 4 robots when the robots agree on chirality. This paper proposes an algorithm for formation of the gathering pattern for transparent fat robots without chirality.