Planar flow model identification for improved navigation of small AUVs

Abstract

Motivated by the desire to improve the navigation performance of small autonomous underwater vehicles, we seek simple methods for modeling the local flow that affects the vehicle's trajectory. We propose a low-complexity, planar flow field model that consists of a uniform flow component and a singular flow component. Assuming this simplified flow field model, we develop identification algorithms that can be performed quickly using small, sparse data sets collected by a platoon of vehicles. The basic approach involves estimating the uniform flow component, localizing an assumed flow singularity, and identifying the parameters which characterize the singular flow. In order to identify the singular flow component, we propose a least squares and a constrained least squares approach. In the latter case, the minimization is constrained to preserve the average divergence and circulation of the measured flow. Preserving divergence and circulation predictably results in a larger overall error because it eliminates two free model parameters, but it produces a flow model which more realistically captures the flow in the larger region of the measurement points. Numerical simulations and an initial experiment illustrate the parameter identification process as well as the benefits of incorporating a flow field model for vehicle navigation.