Motion Guidance for Ocean Sampling by Underwater Vehicles using Autonomous Control and Oceanographic Models with Forecast Uncertainty

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This project addresses fundamental questions on how to select the optimal locations to collect observations and how to ensure that the sensor platforms travel to these locations along informative paths in an expansive, dynamic process such as the ocean. The significance of the proposed research lies in the observation that climate processes occur on long time scales. Understanding these processes requires a combination of ocean models and observations, which can be collected over large space-time volumes by fleets of high-endurance autonomous submarines that steer intelligently to maximize the utility of their measurements. Underwater vehicles that sample the ocean interior are important for understanding ocean processes in general, because -- unlike weather prediction in the atmosphere -- the subsurface ocean environment is difficult to sample remotely. Thus, the long-term goal of this project is create new path-planning strategies for unmanned, mobile sensor platforms to measure information-rich but undersampled dynamic processes in the ocean. Indeed the methods developed in this project will be readily transferrable to operational data assimilation systems.The specific objective of the research is to apply tools from data assimilation, nonlinear control, and dynamical systems theory to design sampling trajectories for accurate estimation and prediction of circulating ocean currents represented by a system of vortices. The technical approach is to (1) synthesize Lagrangian analysis based on deterministic, dynamical systems theory with data assimilation techniques that properly account for uncertainty via a Monte Carlo approach; (2) construct a theoretically justified framework for multi-vehicle control using a fluids-inspired strategy based on the nonlinear feedback control of active singularities; and (3) formulate an optimal sampling framework to generate long-endurance vehicle trajectories using Lagrangian descriptors of the flow geometry while maximizing flowfield observability. The intellectual significance lies in the anticipated contributions to the practice of Lagrangian data assimilation and nonlinear feedback control for the guidance of autonomous sampling platforms by incorporating uncertainty. Lagrangian analysis methods are well suited for sampling deterministic dynamical systems with autonomous sensor platforms because they use platform motion as a sensor measurement and do not require onboard flow sensors. By relaxing the deterministic assumptions of the observing system, an ensemble-based, probabilistic approach to planning with Lagrangian analysis promises to improve the accuracy of the forecast of the estimated processes. A principled design of path-planning algorithms based on artificial flow potentials will allow sampling platforms to exploit whenever possible the underlying motion of ocean currents to maximize endurance.