Congratulations to Ajay Jain and Chuang Tang for successfully completing their RSI 2015 summer research with our MSEAS group at MIT. They completed a report and presentation on “Time-Optimal Robotic Path Planning in Dynamic Ocean Flows: Efficiency and Sensitivity Studies” and “Time-Optimal Path Planning in Dynamic Flow Fields with Ship Wakes”, respectively. Ajay Jain was a visiting junior high-school student from Cupertino, CA, and Chuang Tang from Little Rock, AR.

Mostafa Momen and Prof. Elie Bou-Zeid
Princeton University, Princeton, N.J., US

Abstract Unsteady geostrophic forcing in the atmosphere or ocean not only influences the mean wind, but also affects the turbulent statistics. In these geophysical wall-bounded flows, it is important to understand when and if turbulence is in quasi-equilibrium with the mean flow. To that end, one needs to understand how the turbulence decays or develops, and how do the turbulent production, transport and dissipation respond to changes in the imposed forcing. The knowledge obtained from studying these questions help us understand the underlying physical dynamics of the unsteady boundary layers and develop better turbulence closures for weather/climate models and engineering applications. The present study focuses on the unsteady Ekman boundary layer where pressure gradient forces, Coriolis forces, and turbulent friction forces interact but are not in equilibrium. We perform a suite of large-eddy simulations with variable forcing and acquire the corresponding resolved turbulent kinetic energy budget terms for each simulation. Many cases with unsteady geostrophic forcing are simulated to examine how the turbulence is modulated by the variability of the mean pressure gradient. We also examined the influence of the forcing variability time scale on the turbulence equilibrium and TKE budget, and assessed the implications for mean-turbulence nonlinear interactions and turbulence modeling in such flows.

We present a novel stochastic optimization method to compute energy-optimal paths, among all time-optimal paths, for vehicles traveling in dynamic unsteady currents. The method defines a stochastic class of instantaneous nominal vehicle speeds and then obtains the energy-optimal paths within the class by minimizing the total time-integrated energy usage while still satisfying the strong-constraint time-optimal level set equation. This resulting stochastic level set equation is solved using a dynamically orthogonal decomposition and the energy-optimal paths are then selected for each arrival time, among all stochastic time-optimal paths. The first application computes energy-optimal paths for crossing a steady front. Results are validated using a semi-analytical solution obtained by solving a dual nonlinear energy-time optimization problem. The second application computes energy-optimal paths for a realistic mission in the Middle Atlantic Bight and New Jersey Shelf/Hudson Canyon region, using dynamic data-driven ocean field estimates.

As the concurrent use of multiple autonomous vehicles in ocean missions grows, systematic control for their coordinated operation is becoming a necessity. Many ocean vehicles, especially those used in longer–range missions, possess limited operating speeds and are thus sensitive to ocean currents. Yet, the effect of currents on their trajectories is ignored by many coordination techniques. To address this issue, we first derive a rigorous level-set methodology for distance–based coordination of vehicles operating in minimum time within strong and dynamic ocean currents. The new methodology integrates ocean modeling, time-optimal level-sets and optimization schemes to predict the ocean currents, the short-term reachability sets, and the optimal headings for the desired coordination. Schemes are developed for dynamic formation control, where multiple vehicles achieve and maintain a given geometric pattern as they carry out their missions. Secondly, we obtain an efficient, non–intrusive technique for level-set-based time–optimal path planning in the presence of moving obstacles. The results are time-optimal path forecasts that rigorously avoid moving obstacles and sustain the desired coordination. They are exemplified and investigated for a variety of simulated ocean flows. A wind–driven double–gyre flow is used to study time-optimal dynamic formation control. Currents exiting an idealized strait or estuary are employed to explore dynamic obstacle avoidance. Finally, results are analyzed for the complex geometry and multi–scale ocean flows of the Philippine Archipelago.