Randomized Pattern Formation Algorithm for Autonomous Mobile Robots

We present a randomized pattern formation algorithm for asynchronous oblivious (i.e., memoryless) mobile robots that enables formation of any target pattern. As for deterministic pattern formation algorithms, the class of patterns formable from an initial configuration I is characterized by the symmetricity (i.e., the order of rotational symmetry) of I, and in particular, every pattern is formable from I if its symmetricity is 1. The randomized pattern formation algorithm ψPF we present in this paper consists of two phases: The first phase transforms a given initial configuration I into a configuration I ′ such that its symmetricity is 1, and the second phase invokes a deterministic pattern formation algorithm ψCWM by Fujinaga et al. (DISC 2012) for asynchronous oblivious mobile robots to finally form the target pattern.