Using Abstraction For Swarm Control Of A Parent System

Swarms of robots have many uses, from exploring an area in a parallel manner to manipulating objects, both on the ground and in the air. In this paper, we consider a class of swarms in which robots within the swarm work together to manipulate a parent system with its own dynamics. Using the process of abstraction, we find a set of variables that represent key elements of the swarm such as its mean position, the variance of the swarm's distribution, etc. Using these variables, we can generate a simplified model of how the swarm interacts with the parent system and design a controller to control the parent system through this abstract state. We show that we are able to use a swarm to regulate the parent system, track a step input, and reject step disturbances in an example problem involving a swarm of robots balancing a plane that is allowed to rotate about an axis through its center.