Using Expected Improvement of Gradients for Robotic Exploration of Ocean Salinity Fronts

We develop, test, and deploy a sampling design strategy that enables an autonomous underwater vehicle (AUV) to explore and detect large gradients in spatio‐temporal random fields. Our approach models the field using a Gaussian random field, which means that the directional derivatives of the field are Gaussian distributed. Leveraging fast matrix factorization and data thinning techniques, we obtain real‐time data assimilation and design evaluation onboard the AUV. At each stage in the dynamic framework, possible design transects are formed based on a spider‐leg search space pattern, and the agent chooses the optimal design for the next stage. The design criterion used is based on expected improvement (EI) in directional derivatives. This means that we compute the expected value of observing a larger derivative than what has been seen already. EI is among the most popular acquisition functions in Bayesian optimization. To evaluate the effectiveness of this approach, we conduct a simulation study comparing EI with alternative selection criteria. Our algorithm was embedded on an AUV which was deployed for characterizing a river plume frontal system in a Norwegian fjord. Using EI in the salinity field derivatives, the vehicle successfully sampled the fjord for approximately 2 h without human intervention in two separate field experiments.