For many applications of mobile sensor networks, it is useful to design their dynamics so that their trajectories are as uniformly distributed as possible in the domain of interest. In this work, we propose centralized feedback control laws so that the mobile sensors achieve uniform coverage.

There are many scenarios where it is useful to design dynamics of mobile sensor networks so that their trajectories are uniformly spaced. One such scenario is where fleets of gliders in the ocean are taking various measurements and it is desirable that their trajectories are uniformly spaced so that spatial averages of various oceanographic fields like temperature, salinity and flow can be estimated accurately and efficiently. Another such scenario is for military and search-and-rescue operations, where it is beneficial to have little space between the trajectories of the mobile sensors so that it becomes difficult for a target to evade detection by the sensors. To achieve this goal of uniform coverage, we propose an algorithm referred to as Spectral Multiscale Coverage. We propose centralized feedback control laws for sensor dynamics so that their trajectories cover a given domain as uniformly as possible. The design of the feedback law is based on a measure for uniformity of the trajectories given as a distance between a certain delta-like distribution on the trajectories and a desired probability distribution. The design of control is Lyapunov-based and we develop control laws so that the agents move with constant speed or constant forcing in the case of second-order dynamics.