Title: Higher order mobile coverage control with application to localization,
Abstract: Most current results on coverage control using mobile sensors require that
one partitioned cell is associated with precisely one sensor. In this paper, we
consider a class of coverage control problems involving higher order Voronoi
partitions, motivated by applications where more than one sensor is required to
monitor and cover one cell. Such applications are frequent in scenarios
requiring the sensors to localize targets. We introduce a framework depending
on a coverage performance function incorporating higher order Voronoi cells and
then design a gradient-based controller which allows the multi-sensor system to
achieve a local equilibrium in a distributed manner. The convergence properties
are studied and related to Lloyd algorithm. We study also the extension to
coverage of a discrete set of points. In addition, we provide a number of real
world scenarios where our framework can be applied. Simulation results are also
provided to show the controller performance.