Asynchronous Pattern Formation without Chirality

We propose a new probabilistic pattern formation algorithm for oblivious mobile robots that operate in the ASYNC model. Unlike previous work, our algorithm makes no assumptions about the local coordinate systems of robots (the robots do not share a common “North” nor a common “Right”), yet it preserves the ability to form any general pattern (and not just patterns that satisfy symmetricity predicates). Our proposal also gets rid of the previous assumption (in the same model) that robots do not pause while moving (so, our robots really are fully asynchronous), and the amount of randomness is kept low – a single random bit per robot per Look-Compute-Move cycle is used. Our protocol consists in the combination of two phases, a probabilistic leader election phase, and a deterministic pattern formation one. As the deterministic phase does not use chirality, it may be of independent interest in the deterministic context. A straightforward extension of our algorithm permits to form patterns with multiplicity points (provided robots are endowed with multiplicity detection), a new feature in the context of pattern formation that we believe is an important feature of our approach.