Gaussian Process Adaptive Sampling using the Cross-Entropy Method for Environmental Sensing and Monitoring

In this paper, we focus on adaptive sampling on a Gaussian Processes (GP) using the receding-horizon Cross-Entropy (CE) trajectory optimization. Specifically, we employ the GP upper confidence bound (GP-UCB) as the optimization criteria to adaptively plan sampling paths that balance the exploitation-exploration trade-off. Path planning at the initial stage focuses on exploring and learning a model of the environment, and later, on exploiting the learned model to focus sampling around regions that exhibit extreme sensory measurements and much higher spatial variability, denoted as the Region of Interest (ROI). The integration of the CE trajectory optimization allows the sampling density to be dynamically adjusted based on the latest sensory measurements, thus providing an efficient sampling strategy for sensing and localizing the ROI. We demonstrate the effectiveness of the proposed method in exploring simulated scalar fields with single or multiple ROIs. Field experiments with an Unmanned Surface Vehicle (USV) in a coastal bathymetry mapping mission validate the approach's capability in quickly exploring and mapping the given area, and then focusing and increasing the sampling density around the deepest region, as a surrogate for e.g. the extremal concentration of a pollutant in the environment.