A Family of Objective Functions for Time-Varying Coverage Control

A typical coverage control objective function, known as the locational cost, is ill-suited for theoretical analysis of time-varying coverage control. This paper proposes a family of objective functions that unify and generalise several objective functions from the literature. Coverage control laws that enforce a decrease condition on an objective function from this family render the multi-agent system locally stable and optimal with respect to the locational cost in the time-varying coverage control setting. Two distinct classes of time-varying coverage controller are proposed: one that tracks centroids via inversion of local position-centroid kinematics, and another that directly descends the objective function, obviating computationally expensive matrix inversions. Local stability of both coverage controllers with time-varying density functions and coverage regions is established using the proposed objective functions via a Lyapunov-style argument. Simulation results demonstrate improved centroid-tracking performance when compared to existing coverage controllers in the literature.