Consensus Stability of a Large-Scale Robotic Network Under Input and Transmission Delays

Abstract

A large-scale network of differential-wheeled robots seeking consensus is considered in the presence of input and transmission delays. Consensus stability of this nonlinear network dynamics holds if its linear part can be shown to achieve consensus stability despite the delays. We present theoretical and computational results on this linear “large-scale” system. From a theoretical point of view, conditions on the amount of input delays are revealed such that stability is guaranteed independent of any transmission delay, and in the case this is not possible, a computationally efficient algorithm is proposed to reveal the largest transmission delay that the network can accommodate without losing stability.