In this paper, a reachability-based approach is adopted to deal with the pursuit–evasion differential game between one evader and multiple pursuers in the presence of dynamic environmental disturba...

Ocean scientists have dreamed of and recently started to realize an ocean observing revolution with autonomous observing platforms and sensors. Critical questions to be answered by such autonomous systems are where, when, and what to sample for optimal information, and how to optimally reach the sampling locations. Definitions, concepts, and progress towards answering these questions using quantitative predictions and fundamental principles are presented. Results in reachability and path planning, adaptive sampling, machine learning, and teaming machines with scientists are overviewed. The integrated use of differential equations and theory from varied disciplines is emphasized. The results provide an inference engine and knowledge base for expert autonomous observing systems. They are showcased using a set of recent at-sea campaigns and realistic simulations. Real-time experiments with identical autonomous underwater vehicles (AUVs) in the Buzzards Bay and Vineyard Sound region first show that our predicted time-optimal paths were faster than shortest distance paths. Deterministic and probabilistic reachability and path forecasts issued and validated for gliders and floats in the northern Arabian Sea are then presented. Novel Bayesian adaptive sampling for hypothesis testing and optimal learning are finally shown to forecast the observations most informative to estimate the accuracy of model formulations, the values of ecosystem parameters and dynamic fields, and the presence of Lagrangian Coherent Structures.

We integrate data‐driven ocean modeling with the stochastic Dynamically Orthogonal (DO) level‐set optimization methodology to compute and study energy‐optimal paths, speeds, and headings for ocean vehicles in the Middle‐Atlantic Bight (MAB) region. We hindcast the energy‐optimal paths from among exact time‐optimal paths for the period 28 August 2006 to 9 September 2006. To do so, we first obtain a data‐assimilative multiscale reanalysis, combining ocean observations with implicit two‐way nested multiresolution primitive‐equation simulations of the tidal‐to‐mesoscale dynamics in the region. Second, we solve the reduced‐order stochastic DO level‐set partial differential equations (PDEs) to compute the joint probability of minimum arrival time, vehicle‐speed time series, and total energy utilized. Third, for each arrival time, we select the vehicle‐speed time series that minimize the total energy utilization from the marginal probability of vehicle‐speed and total energy. The corresponding energy‐optimal path and headings are obtained through the exact particle‐backtracking equation. Theoretically, the present methodology is PDE‐based and provides fundamental energy‐optimal predictions without heuristics. Computationally, it is 3–4 orders of magnitude faster than direct Monte Carlo methods. For the missions considered, we analyze the effects of the regional tidal currents, strong wind events, coastal jets, shelfbreak front, and other local circulations on the energy‐optimal paths. Results showcase the opportunities for vehicles that intelligently utilize the ocean environment to minimize energy usage, rigorously integrating ocean forecasting with optimal control of autonomous vehicles.