Physics-Guided Active Learning of Environmental Flow Fields

We propose a physics-based method to learn environmental fields (EFs) using a mobile robot. Common data-driven methods require prohibitively many measurements to accurately learn such complex EFs. On the other hand, while physics-based models provide global knowledge of EFs, they require experimental validation, depend on uncertain parameters, and are intractable to solve onboard mobile robots. To address these challenges, we propose a Bayesian framework to select and improve upon the most likely physics-based models of EFs in real-time, from a pool of numerical solutions generated offline as a function of the uncertain parameters. Specifically, we use Gaussian Processes (GPs) to construct statistical models of EFs, and rely on the pool of numerical solutions to inform their prior mean. To incorporate flow measurements into these GPs, we control a custom-built mobile robot through a sequence of waypoints that maximize the information content of the measurements. We experimentally demonstrate that our proposed framework constructs a posterior distribution of the flow field that better approximates the real flow compared to the prior numerical solutions and purely data-driven methods.