Distributed Average Consensus and Abstract Control

There are multiple challenges to swarm control, including controller complexity, scalability, and the need for shared information in a coordinated fashion. One key solution to moving swarms of robots is abstract control, where an abstract state is chosen to represent the swarm and determine how it interacts with its objectives. Knowledge of the current abstract state of the swarm is necessary to control said state. In previous work, this has largely been calculated using an external global observer, however this presents a severe limitation in scalability and practicality. This paper proposes a method for calculating the swarm's abstract state utilizing a simple distributed average consensus algorithm that allows for time varying communication graphs with limited connectivity. We discuss our consensus driven abstract control framework and discuss how it works per several metrics including convergence speed, and stability. We present simulated results demonstrating this framework on a toy problem with a time-varying, stochastic communications graph.