Viable Algorithmic Options for Designing Reactive Robot Swarms

A central problem in swarm robotics is to design a controller that will allow the member robots of the swarm to collectively perform a given task. Of particular interest in massively distributed applications are reactive controllers with severely limited computational and sensory abilities. In this article, we give the results of the first computational complexity analysis of the reactive swarm design problem. Our core results are derived relative to a generalization of what is arguably the simplest possible type of reactive controller, the so-called computation-free controller proposed by Gauci et al., which operates in grid-based environments in a noncontinuous manner. We show that the design of a generalized computation-free swarm for an arbitrary given task in an arbitrary given environment is not polynomial-time solvable either in general or by the most desirable types of approximation algorithms (including evolutionary algorithms with high probabilities of producing correct solutions) but is solvable in effectively polynomial time relative to several types of restrictions on swarms, environments, and tasks. All of our results hold for the design of several more complex types of generalized computation-free swarms. Moreover, all of our intractability and inapproximability results hold for the design of any type of reactive swarm (including those based on the popular feed-forward neural network and Brooks-style subsumption controllers) operating in grid-based environments in a noncontinuous manner whose member robots satisfy two simple conditions. As such, our results give the first theoretical survey of the types of efficient exact and approximate solution algorithms that are and are not possible for designing several types of reactive swarms.