Input-to-Output Stability for a Coverage Controller

The coverage control problem involves spatially disseminating a network of mobile agents using distributed control laws, or coverage controllers, over a desired region to locally minimize an associated cost function. Mobile robots using coverage controllers will be subject to various disturbances, such as uncertainty, errors, and delays. Asymptotic stability of [Cortés et al.’s 2004] coverage controller and its variations have been studied; however, rates of convergence are omitted. Recent work has provided convergence rates for a coverage controller under certain assumptions, including regions where the network locally converges exponentially. The main contribution of this work is to show that a variation of [Cortés et al.’s 2004] coverage controller also features robust stability properties, specifically input-to-output stability, under the same set of assumptions. Conservative bounds are used to provide theoretical guarantees on stability, and simulations are used to verify the results and highlight practical performance of the controller.