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.

Without access to GPS and high-quality visual landmarks, many autonomous underwater vehicles (AUV) face a fundamental navigation vs. cost tradeoff: advanced navigation systems that might include an INS, Doppler velocity, or long-baseline acoustics are expensive. Supporting low-cost operations, this work focuses on collaborative positioning for a team of AUV's, given a bathymetric terrain map, and only an altimeter and acoustic modem on each vehicle. The joint localization is performed via decentralized particle filtering, where we extend the usual measurement model to allow received information to modulate the importance function. We investigate the impact on performance of sensor noise, communication interval and number of vehicles. Results are shown for bathymetry maps near St. John's Island, Singapore, and for the Charles River Basin, Boston. In the second case, we ran our algorithm with physical measurements from actual vehicles executing trajectories.