Time snapshots of three communicating robots (black) tracing the coherent structures in time dependent double gyre flow. The bright red signatures shown are ridges that contain the coherent structures of the flow. The coherent structures are unstable; i.e., if one starts a single tracer near the red structures, it is quickly swept away into some basin of attraction. Even though the coherent structures are unstable, the trio of autonomous robots shown track the most unstable regions throughout the phase spac
Time snapshots of three communicating robots (black) tracing the coherent structures in time dependent double gyre flow. The bright red signatures shown are ridges that contain the coherent structures of the flow. The coherent structures are unstable; i.e., if one starts a single tracer near the red structures, it is quickly swept away into some basin of attraction. Even though the coherent structures are unstable, the trio of autonomous robots shown track the most unstable regions throughout the phase space shown.

Dr. Ira B. Schwartz and colleagues have derived and implemented a novel autonomous communicating robot architecture to track coherent structures in ocean flows, such as those structures which separate large eddy flows in the Gulf of Mexico. Coherent structures are time evolving unstable objects in the ocean that play a large role in the determination of transport. These structures, therefore, play an important role in temperature distribution, algae bloom development, and climate and weather prediction. The multi-robot design uses communication and local velocity measurement information to control the robot positions along the coherent structures. The technique has been applied to time dependent flows modeling double gyres, and has been verified in experiments.

Background: Coherent structures (CS) in dynamical systems are similar to separatrices, or manifolds, that divide the flow into dynamically distinct regions. CS are extensions of stable and unstable manifolds to general time-dependent flows, and they carry a great deal of information about the dynamics of the flows. For two-dimensional (2D) flows, CS are analogous to ridges defined by local maximum instability. To improve weather and climate forecasting, and to better understand contaminant transport, one would like to use autonomous sensors to measure a variety of quantities of interest. One drawback to operating sensors in time-dependent and stochastic environments like the ocean is that the sensors will tend to escape from their monitoring region of interest. Since the CS are inherently unstable and denote regions of the flow where more escape events may occur, knowledge of the CS are of paramount importance in maintaining a sensor in a particular monitoring region.

Accomplishment: We have derived and designed a collaborative robotic control strategy designed to track stable and unstable manifolds, such as CS, in general two dimensional 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 on a team of robots to track coherent structures on static flows as well as time-dependent models of wind-driven double-gyre often seen in the ocean. The theory has been tested in simulation and experiments, and theoretical guarantees of the collaborative tracking strategy have been derived.

Significance: Tracking coherent structures in dynamical systems is important for many applications such as oceanography and weather prediction. Different from previous work, we devise a boundary tracking strategy that relies solely on local measurements of the velocity field. Our technique is quite general, and may be applied to any conservative flow. Our work is novel in that the robots are determining the location of a global structure based solely on local information, and as far as we know, the sensing of CS in the ocean has never been performed using autonomous vehicles. Moreover, only initial state knowledge of the CS is required locally to get an accurate prediction of the global structure.

Application: The main application of our technique will be to ocean and climate prediction. CS play a major role in determining the boundaries of large invariant structures as well as transport across boundaries. The long-term transition envisioned will be to use unmanned ocean gliders to predict regions of coherent structure along major transport occurs in the ocean, thus predicting temperature gradients and coupling of ocean dynamics to [FINISH THIS SENTENCE?]