Tutorial 1-3: Leader Election and Pattern Formation in Swarms of Deterministic Robots

Abstract

In a given environment, the ability for the swarm of robots to succeed in the accomplishment of the assigned task greatly depends on global properties assigned to the swarm, and individual capabilities each robot has. Examples of such global properties are the ability to distinguish among themselves at least one (or, more) robots (leader), to agree on a common global direction (sense of direction), or to agree on a common handedness (chirality). The individual capacities of each robot are its moving capabilities and its sensory organs. To deal with cost, flexibility, resilience to dysfunction, and autonomy, many problems arise for handling the distributed coordination of swarms of robots in a deterministic manner. This issue is motivated by the minimal level of ability that the robots are required to have in the accomplishment of basic cooperative tasks. In other words, the feasibility of some given tasks is addressed assuming swarm of autonomous robots either devoid or not of capabilities like (observable) identifiers, direct means of communication, means of storing previous observations, sense of direction, chirality, etc. Leader election and arbitrary pattern formation are fundamental tasks for a set of autonomous mobile robots. The former consists in moving the system from an initial configuration were all entities are in the same state into a final configuration were all entities are in the same state, except one, the leader. The latter consists in the design of protocols allowing autonomous mobile robots to form any (arbitrary) geometric pattern. The solvability of both these tasks turns out to be necessary in order to achieve more complex tasks. During this tutorial, we address both problems. We first consider the deterministic solvability of the pattern formation problem assuming swarms of anonymous robots. Next, under the same assumptions, we provide a complete characterization (necessary and sufficient conditions) on the robots positions to deterministically elect a leader. Finally, we show that Leader Election and Pattern Formation are two equivalent problems in the precise sense that, the former is solvable if and only if the latter problem is solvable.