Formalizing the impact of diversity on performance in a heterogeneous swarm of robots

We are interested in a principled study of the impact of diversity in heterogeneous large-scale distributed robotic systems. In order to evaluate the implications of heterogeneity on performance, we consider the concrete problem of distributing a large group of robots among a set of tasks that require specialized capabilities in order to be completed. We model the system of heterogeneous robots as a community of species, where each species (robot type) is defined by the traits (capabilities) that it owns. We develop a continuous model of the system at a macroscopic level, and formulate an optimization problem that produces an optimal set of transition rates for each species, so that the desired trait distribution is reached as quickly as possible. In order to evaluate the effects of heterogeneity, we propose a diversity metric that defines the notion of eigenspecies. We show that our metric correlates with performance: the higher the cardinality of the eigenspecies, the harder it becomes to optimize the system. Our approach is validated over multiple levels of abstraction, and real robot results confirm its validity on physical platforms.