Autonomous Path Planning to Optimally Harvest Dynamic Fields

The challenge of navigating from one point to another in a time optimal fashion is an age-old problem with applications ranging from security and surveillance to the minimization of delays in the transportation of goods. In this work, we extend our exact differential equations for time-optimal paths in complex dynamic flow fields to the prediction of paths that maximize the collection of a dynamic field of interest. This include the collection of environmental energy along the way as well as the harvesting of any other additional dynamic fields. Some of the practical questions that motivated our work and that are answered by our results include: 'How does an UUV/USV travel from point A to point B in fastest time while also collecting sufficient energy (tidal, solar, or wind) to reach point B?', 'What path should a vehicle choose to collect the maximum amount of a certain dynamic field as it progresses from a start to an end point?' and 'Where should one deploy and collect an AUV so as to collect a required amount of a dynamic field in fastest time?'. Our proposed methodology answers such questions and related ones by using a Hamilton-Jacobi-Bellman formulation with an augmented state which includes the additional state variables of interest. Our work, specifically the ability to harvest time and space varying fields can be used for many practical applications including efficient offshore macroalgae farming as well as the cleanup of plastics, debris, and other pollutants in the ocean.