Tracking Attracting Lagrangian Coherent Structures in Flows

Abstract

This paper presents a collaborative control strategy designed to enable a team of robots to track attracting Lagrangian coherent structures (LCS) and unstable manifolds in two-dimensional flows. Tracking LCS in dynamical systems is important for many applications such as planning energy optimal paths in the ocean and predicting various physical and biological processes in the ocean. Similar to existing approaches, the proposed strategy does not require global information about the dynamics of the surrounding flow, and is based on local sensing, prediction, and correction. Different from existing approaches, the proposed strategy has the ability to track attracting LCS and unstable manifolds in real time through direct computation of the local finite time Lyapunov exponent field. The collaborative control strategy is implemented on a team of robots and the theoretical guarantees of the tracking strategy is briefly discussed. We demonstrate the tracking strategy in simulation using static and time dependent flows and experimentally validate the strategy using a team of micro autonomous surface vehicles (mASVs) in an actual fluid environment.