A general stability condition for multi-agent coordination by coupled estimation and control

Many multi-agent coordinated behaviors can be achieved using decentralized estimation-and-control, where each agent uses limited communication with neighbors in a network to estimate global properties of the performance of the group. This global information is used in each agent's local motion controller, creating a feedback connection between the estimators and controllers. To ensure the stability of the coupled system, we derive a small-gain condition that can be roughly expressed as a bound on motion control gains as a function of the estimator gains and a lower bound on the algebraic connectivity of the communication network. The condition is derived for systems of agents with first-order dynamics implementing gradient controllers based on averages of the group sensor inputs. The condition is applied to two very different tasks: formation control and cooperative target localization.