Robotic Tracking of Coherent Structures in Flows

Lagrangian coherent structures (LCSs) are separatrices that delineate dynamically distinct regions in general dynamical systems and can be viewed as the extensions of stable and unstable manifolds to general time-dependent systems. Identifying LCS in dynamical systems is useful for many applications, including oceanography and weather prediction. In this paper, we present a collaborative robotic control strategy that is designed to track stable and unstable manifolds in dynamical systems, including ocean flows. The technique does not require global information about the dynamics, and is based on local sensing, prediction, and correction. The collaborative control strategy is implemented with a team of three robots to track coherent structures and manifolds on static flows, a time-dependent model of a wind-driven double-gyre flow often seen in the ocean, experimental data that are generated by a flow tank, and actual ocean data. We present simulation results and discuss theoretical guarantees of the collaborative tracking strategy.