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The Impact of Diversity on Optimal Control Policies for Heterogeneous Robot Swarms

We consider the problem of distributing a large group of heterogeneous 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, in which each species (robot type) is defined by the traits (capabilities) that it owns. In order to solve the distribution problem, we develop centralized as well as decentralized methods to efficiently control the heterogeneous swarm of robots. Our methods assume knowledge of the underlying task topology and are based on a continuous model of the system that defines transition rates to and from tasks, for each robot species. Our optimization of the transition rates is fully scalable with respect to the number of robots, number of species, and number of traits. Building on this result, we propose a real-time optimization method that enables an online adaptation of transition rates as a function of the state of the current robot distribution. We also show how the robot distribution can be approximated based on local information only, consequently enabling the development of a decentralized controller. We evaluate our methods by means of microscopic simulations and show how the performance of the latter is well predicted by the macroscopic equations. Importantly, our framework also includes a diversity metric that enables an evaluation of the impact of swarm heterogeneity on performance. The metric defines the notion of minspecies, i.e., the minimum set of species that are required to achieve a given goal. We show that two distinct goal functions lead to two specializations of minspecies, which we term as eigenspecies and coverspecies. Quantitative results show the relation between diversity and performance.