Autonomous Robots manuscript No. (will be inserted by the editor) Tracking Attracting Manifolds in Flows Dhanushka Kularatne · M. Ani Hsieh Received: 3/21/2016 / Accepted: date Abstract This paper presents a collaborative control strat- egy designed to enable a team of robots to track attracting Lagrangian coherent structures (LCS) and unstable mani- folds in two-dimensional flows. Tracking LCS in flows is important for many applications such as planning energy op- timal paths in the ocean and for predicting the evolution of various physical and biological processes in the ocean. The proposed strategy which tracks attracting LCS and unsta- ble manifolds in real-time through direct computation of the local finite time Lyapunov exponent field, does not require global information about the dynamics of the surrounding flow, and is based on local sensing, prediction, and correc- tion. The collaborative control strategy is implemented on a team of robots and theoretical guarantees for the tracking and formation keeping strategies are presented. We demon- strate the performance of the tracking strategy in simulation using actual ocean flow data and experimental flow data gen- erated in a tank. The strategy is validated experimentally us- ing a team of micro autonomous surface vehicles (mASVs) in an actual fluid environment. Keywords Marine Robotics · Manifold Tracking · LCS · Distributed Robot Systems This work was supported by the Office of Naval Research (ONR) Awards No. N000141211019 and No. N000141310731 and the Na- tional Science Foundation (NSF) grant IIS-1253917. Dhanushka Kularatne Scalable Autonomous Systems Lab, Drexel University, Philadelphia Tel.: +1-469-200-9338 E-mail: dnk32@drexel.edu M. Ani Hsieh Scalable Autonomous Systems Lab, Drexel University, Philadelphia Tel.: +1-215-895-5803 E-mail: mah349@drexel.edu 1 Introduction We are interested in the development of collaborative con- trol strategies for distributed sensing and tracking of coher- ent structures and manifolds in flows using teams of au- tonomous underwater and surface vehicles (AUVs and ASVs). Specifically, we are interested in deploying teams of robots to track a class of coherent structures that are important for quantifying transport phenomena in flows. Inanc et al. showed that time and fuel optimal paths in the ocean can coincide with a specific class of coher- ent structures called Lagrangian coherent structures (LCS) (Inanc et al., 2005; Senatore and Ross, 2008). LCS are the extensions of stable and unstable manifolds to general time dependent flows (Haller and Yuan, 2000; Haller, 2011) and are similar to separatrices that divide the flow into dynami- cally distinct regions. This is supported by Forgoston et al.’s work where they showed that LCS coincide with regions in the flow field where more escape events occur (Forgoston et al., 2011). Furthermore, it has been shown that biologi- cal phenomena in the ocean, such as the dispersion of algea blooms, can be predicted using knowledge about propaga- tion of LCS boundaries (Olascoaga et al., 2008). More im- portantly, Olascoaga et al. have shown that, the class of LCS that we are interested in i.e., attracting LCS, was responsi- ble for pushing spilled oil from the Deepwater Horizon spill in 2010, towards the coast of Florida (Olascoaga and Haller, 2012). As such, knowledge of LCS is important for plan- ning energy efficient trajectories in the ocean, maintaining sensors in their desired monitoring regions (Mallory et al., 2013; Hsieh et al., 2014; Heckman et al., 2014), predict- ing pollutant dispersion and for enabling efficient, computa- tionally tractable estimation and prediction of the underlying geophysical fluid dynamics. Existing methods require complete knowledge of the un- derlying flow field to numerically compute and track the lo- cation of an LCS in a flow. However, accessibility to and the overall quality of ocean current hindcasts, nowcasts, and forecasts provided by Navy Coastal Ocean Model (NCOM) databases (SCRIPPS, 2014), regional ocean model systems (ROMS) (Smith et al., 2010), and/or other numerical models are generally low. This is because most existing ocean mod- els are derived from assimilated satellite and field data with predictions from numerical PDE models (Shchepetkin and McWilliams, 1998, 2005). As such, existing data sets that describe ocean flows are mostly finite time, of low spatio- temporal resolution and are limited to specific regions. Due to this sparseness of available ocean data, locating and track- ing LCS in real time is problematic. In this paper we seek to establish a methodology that will enable a team of ASV’s to track an attracting LCS in real time, using on board flow velocity measurements. To the best of our knowledge this is