Multivehicle coverage control for a nonstationary spatiotemporal field

Abstract

This paper presents a multivehicle sampling algorithm to generate trajectories for nonuniform coverage of a nonstationary spatiotemporal field characterized by spatial and temporal decorrelation scales that vary in space and time, respectively. The sampling algorithm described in this paper uses a nonlinear coordinate transformation that renders the field locally stationary so that existing multivehicle control algorithms can be used to provide uniform coverage. When transformed back to the original coordinates, the sampling trajectories are concentrated in regions of short spatial and temporal decorrelation scales. For fields with coupled spatial statistics, i.e., the spatial decorrelation scales are functions of both spatial dimensions, the coordinate transformation is implemented numerically, whereas for decoupled spatial statistics, the transformation is expressed analytically. We show that the analytical transformation results in vehicle motion that preserves the vehicle sampling speed (which is a measure of vehicle speed scaled by the ratio of the spatial and temporal decorrelation scales), in the original domain; the sampling speed determines the minimum number of vehicles needed to cover a spatiotemporal domain. Theoretical results are illustrated by numerical simulations.