Human-Swarm Interactions via Coverage of Time-Varying Densities

One of the main challenges in human-swarm interactions is the construction of suitable abstractions that make an entire robot team amenable to human control. For such abstractions to be useful, they need to scale gracefully as the number of robots increases. In this work, we consider the use of time-varying density functions to externally influence a robot swarm. Density functions abstract away the size of the robot team and describe instead the concentration of agents over the domain of interest. This allows a human operator to design densities so as to manipulate the robot swarm as a whole, instead of at the individual robot level. We discuss coverage of time-varying density functions as a mechanism to translate densities into robotic movement, and provide a series of control laws that guarantee optimal coverage by the robot team. Distributed approximations allow the solutions to scale with the size of the robot team. This renders coverage a viable choice of method for influencing a robot swarm. Lastly, we provide a framework for the design of density functions that shape the swarm to achieve specified geometric configurations within the domain of interest. We show through robotic implementation in two different platforms the viability of human-swarm interactions with the proposed schemes.