A Superdiffusive Dispersion and Mixing of Swarms

A common swarm task is to disperse evenly through an environment from an initial tightly packed formation. Due to communication and sensing limitations, it is often necessary to execute this task with little or no communication between swarm members. Unfortunately, prior approaches based on repulsive forces or uniform random walks can often converge quite slowly. With an appropriate choice of random distribution, however, it is possible to generate optimal or near-optimal dispersion and mixing in swarms with zero communication. In particular, we discuss three extremely simple algorithms: reactive Levy walk, reactive ball dispersion, and purely reactive dispersion. All three algorithms vastly outperform prior approaches in both constrained and unconstrained environments, providing a range of options for trading off between aggressiveness and evenness in dispersion.