Applied Math Seminar: Jeremy Brandman (DCS corporation)

Title

Control algorithms for unmanned underwater vehicles: new approaches based on Hamilton-Jacobi equations and reinforcement learning.

Abstract

Unmanned underwater vehicles (UUVs) are defined by their ability to operate without direct human intervention.  As a result, UUVs are valuable for surveillance tasks, especially in the presence of hazardous environmental conditions. Specific applications of UUVs include seafloor mapping, mine detection, and oil pipeline inspection.

In this talk, we propose new algorithms for two aspects of UUV control: path planning and vehicle guidance.  Path planning identifies a vehicle trajectory, based on anticipated environmental conditions, that achieves desired mission objectives (e.g. obstacle avoidance, minimization of energy consumption). Vehicle guidance responds to observed environmental conditions in order to maintain fidelity to the path selected by the path planner.

The first half of this talk considers a new approach to path planning based on solving Hamilton-Jacobi partial differential equations (PDE).  The starting point for this method is the observation that the vehicle’s minimum travel-time satisfies a time-independent Hamilton-Jacobi equation .  Numerical solutions to this PDE are efficiently computed using the fast sweeping method.  Our approach is validated through several examples for which optimal trajectories are derived using the calculus of variations.

The second half of this talk introduces a reinforcement learning framework for incorporating in situ ocean current measurements into the guidance system in an energetically optimal manner.  Scaling and symmetry considerations turn out to play an important role in the framework’s efficiency and robustness.  Numerical results demonstrate that the energetic cost of transits executed under the guidance of a trained agent approaches optimal performance.