A consensus dynamics with delay-induced instability can self-regulate for stability via agent regrouping.

Abstract

Dynamics of many multi-agent systems is influenced by communication/activation delays τ. In the presence of delays, there exists a certain margin called the delay margin τ*, less than which system stability holds. This margin depends strongly on agents' dynamics and the agent network. In this article, three key elements, namely, the delay margin, network graph, and a distance threshold conditioning two agents' connectivity are considered in a multi-agent consensus dynamics under delay τ. We report that when the dynamics is unstable under this delay, its states can be naturally bounded, even for arbitrarily large threshold values, preventing agents to disperse indefinitely. This mechanism can also make the system recover stability in a self-regulating manner, mainly induced by network separation and enhanced delay margin. Under certain conditions, unstable consensus dynamics can keep separating into smaller stable subnetwork dynamics until all agents stabilize in their respective subnetworks. Results are then demonstrated on a previously validated robot coordination model, where specifically robustness of τ* is studied against the delay τinh inherently present in the orientation measurements of the robots. To this end, a mathematical framework to compute τ* with respect to τinh in quasi-state is developed, demonstrating that τ* can be sensitive to τinh, yet robot regrouping and stabilization of subnetworks is still possible.