Maximizing Seaweed Growth on Autonomous Farms: A Dynamic Programming Approach for Underactuated Systems Navigating on Uncertain Ocean Currents

Abstract: Seaweed biomass presents a substantial opportunity for climate mitigation, yet to realize its potential, farming must be expanded to the vast open oceans. However, in the open ocean neither anchored farming nor floating farms with powerful engines are economically viable. Thus, a potential solution are farms that operate by going with the flow, utilizing minimal propulsion to strategically leverage beneficial ocean currents. In this work, we focus on low-power autonomous seaweed farms and design controllers that maximize seaweed growth by taking advantage of ocean currents. We first introduce a Dynamic Programming (DP) formulation to solve for the growth-optimal value function when the true currents are known. However, in reality only short-term imperfect forecasts with increasing uncertainty are available. Hence, we present three additional extensions. Firstly, we use frequent replanning to mitigate forecast errors. Second, to optimize for long-term growth, we extend the value function beyond the forecast horizon by estimating the expected future growth based on seasonal average currents. Lastly, we introduce a discounted finite-time DP formulation to account for the increasing uncertainty in future ocean current estimates. We empirically evaluate our approach with 30-day simulations of farms in realistic ocean conditions. Our method achieves 95.8\% of the best possible growth using only 5-day forecasts.This demonstrates that low-power propulsion is a promising method to operate autonomous seaweed farms in real-world conditions.