A Stochastic Optimization Method for Energy-Based Path Planning

Deepak N. Subramani, Tapovan Lolla, Patrick J. Haley Jr., Pierre F. J. Lermusiaux

Abstract: 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.