Swarm control for distributed construction: A computational complexity perspective

Over the last 20 years, human interaction with robot swarms has been investigated as a means to mitigate problems associated with the control and coordination of such swarms by either human teleoperation or completely autonomous swarms. Ongoing research seeks to characterize those situations in which such interaction is both viable and preferable. In this paper, we contribute to this effort by giving the first computational complexity analyses of problems associated with algorithm, environmental influence, and leader selection methods for the control of swarms performing distributed construction tasks. These analyses are done relative to a simple model in which swarms of deterministic finite-state robots operate in a synchronous error-free manner in 2D grid-based environments. We show that all three of our problems are polynomial-time intractable in general and remain intractable under a number of plausible restrictions (both individually and in many combinations) on robot controllers, environments, target structures, and sequences of swarm control commands. We also give the first restrictions relative to which these problems are tractable, as well as discussions of the implications of our results for both the design and deployment of swarm control assistance software tools and the human control of swarms