## Energy-Optimal Path Planning in the Coastal Ocean

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 re-analysis, 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 vehiclespeed
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 a particle backtracking equation. Theoretically, the present
methodology is PDE-based and provides fundamental energy-optimal predictions without
heuristics. Computationally, it is three- to four-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.