Studying direct and indirect human influence on consensus in swarms

Many cooperative control problems ranging from formation following, to rendezvous to flocking can be expressed as consensus problems. The ability of an operator to influence the development of consensus within a swarm therefore provides a basic test of the quality of human-swarm interaction (HSI). Two plausible approaches are : Direct- dictate a desired value to swarm members or Indirect- control or influence one or more swarm members relying on existing control laws to propagate that influence. Both approaches have been followed by HSI researchers. The Indirect case uses standard consensus methods where the operator exerts influence over a few robots and then the swarm reaches a consensus based on its intrinsic rules. The Direct method corresponds to flooding in which the operator directly sends the intention to a subset of the swarm and the command then propagates through the remainder of the swarm as a privileged message. In this paper we compare these two methods regarding their convergence time and properties in noisy and noiseless conditions with static and dynamic graphs. We have found that average consensus method (indirect control) converges much slower than flooding (direct) method but it has more noise tolerance in comparison with simple flooding algorithms. Also, we have found that the convergence time of the consensus method behaves erratically when the graph's connectivity (Fiedler value) is high.