Localization of Upstream Obstacles by Learning From Spectra of the Koopman Operator

Abstract

Abstract Objects moving in water or stationary objects in streams create a vortex wake. An underwater robot encountering the wake created by another body experiences disturbance forces and moments. These disturbances can be associated with the disturbance velocity field and the bodies creating them. Essentially, the vortex wakes encode information about the objects and the flow conditions. Underwater robots that often function with constrained sensing capabilities can benefit from extracting this information from vortex wakes. Many species of fish do exactly this, by sensing flow features using their lateral lines as part of their multimodal sensing capabilities. Besides the necessary sensing hardware, a more important aspect of sensing is related to the algorithms needed to extract the relevant information about the flow. This paper advances a framework for such an algorithm using the setting of a pitching hydrofoil in the wake of a thin plate (obstacle). Using time series pressure measurements on the surface of the hydrofoil and the angular velocity of the hydrofoil, a Koopman operator is constructed that propagates the time series forward in time. Multiple approaches are used to extract dynamic information from the Koopman operator to estimate the plate position and are bench marked against a state-of-the-art convolutional neural network (CNN) applied directly to the time series. We find that using the Koopman operator for feature extraction improves the estimation accuracy compared to the CNN for the same purpose, enabling “blind” sensing using the lateral line.