Kulkarni, C.S. and P.F.J. Lermusiaux, 2019. *Three-Dimensional Time-Optimal Path Planning in the Ocean*, Ocean Modelling, sub-judice.

Autonomous underwater vehicles (AUVs) operate in the three-dimensional and time-dependent marine environment with strong and dynamic currents. Our goal is to predict the time history of the optimal three-dimensional headings of these vehicles such that they reach the given destination location in the least amount of time, starting from a known initial position. We employ the exact differential equations for time-optimal path planning and develop theory and numerical schemes to accurately predict three-dimensional optimal paths for several classes of marine vehicles (e.g. floats, gliders, etc.), respecting their specific propulsion constraints. We further show that the three-dimensional path planning problem can be reduced to a two-dimensional one if the motion of the vehicle is partially known, e.g. if the vertical component of the motion is forced. This drastically reduces the computational cost. We then apply the developed theory in two three-dimensional analytically known flow fields to verify the schemes, benchmark the accuracy, and demonstrate capabilities. Finally, we showcase optimal path planning in data-assimilative realistic ocean simulations for three typical marine vehicles, namely propelled AUVs (with unrestricted motion), floats (that only move vertically), and gliders (that often perform sinusoidal yo-yo motions in vertical planes). These results highlight the effects of three-dimensional multiscale ocean currents on the optimal paths as well as the need to utilize ocean forecasts for planning of efficient autonomous missions.