On the computational power of oblivious robots: forming a series of geometric patterns

We study the computational power of a distributed system consisting of simple autonomous robots moving on the plane. The robots are endowed with visual perception but do not have any means of explicit communication with each other, and have no memory of the past. In the extensive literature it has been shown how such simple robots can form a single geometric pattern (e.g., a line, a circle, etc), however arbitrary, in spite of their obliviousness. This brings to the front the natural research question: what are the real computational limits imposed by the robots being oblivious? In particular, since obliviousness limits what can be remembered, under what conditions can oblivious robots form a series of geometric patterns? Notice that a series of patterns would create some form of memory in an otherwise memory-less system. In this paper we examine and answer this question showing that, under particular conditions, oblivious robot systems can indeed form series of geometric patterns starting from any arbitrary configuration. More precisely, we study the series of patterns that can be formed by robot systems under various restrictions such as anonymity, asynchrony and lack of common orientation. These results are the first strong indication that oblivious solutions may be obtained also for tasks that intuitively seem to require memory.