In this paper, we present a first attempt toward experimental validation of a multi-robot strategy for tracking manifolds and Lagrangian coherent structures (LCS) in flows. LCS exist in natural fluid flows at various scales, and they are time-varying extensions of stable and unstable manifolds of time invariant dynamical systems. In this work, we present the first steps toward experimentally validating our previously proposed real-time manifold and LCS tracking strategy that relies solely on local measurements. Although we have validated the strategy in simulations using analytical flow models, experimental flow data, and actual ocean data, the strategy has never been implemented on an actual robotic platform. We demonstrate the tracking strategy using a team of micro autonomous surface vehicles (mASVs) in our laboratory testbed and investigate the feasibility of the strategy with vehicles operating in an actual fluid environment. Our experimental results show that the team of mASVs can successfully track LCS using a simulated velocity field, and we present preliminary results showing the feasibility of a team of mASVs tracking manifolds in real flows using only local measurements obtained from their onboard flow sensors.

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.

Tracking Lagrangian coherent structures in dynamical systems is important for many applications such as oceanography and weather prediction. In this paper, we present a collaborative robotic control strategy designed to track stable and unstable manifolds. The technique does not require global information about the fluid dynamics, and is based on local sensing, prediction, and correction. The collaborative control strategy is implemented on a team of three robots to track coherent structures and manifolds on static flows as well as a noisy time-dependent model of a wind-driven double-gyre often seen in the ocean. We present simulation and experimental results and discuss theoretical guarantees of the collaborative tracking strategy.

We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work has shown that a communication time delay in the swarm induces a pattern bifurcation that depends on the size of the coupling amplitude. We extend these results by completely unfolding the bifurcation structure of the mean field approximation. Our analysis reveals a direct correspondence between the different dynamical behaviors found in different regions of the coupling-time delay plane with the different classes of simulated coherent swarm patterns. We derive the spatiotemporal scales of the swarm structures, as well as demonstrate how the complicated interplay of coupling strength, time delay, noise intensity, and choice of initial conditions can affect the swarm. In particular, our studies show that for sufficiently large values of the coupling strength and/or the time delay, there is a noise intensity threshold that forces a transition of the swarm from a misaligned state into an aligned state. We show that this alignment transition exhibits hysteresis when the noise intensity is taken to be time dependent.

We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a translating state and a rotating state with stationary center of mass. Time delayed communication creates a bifurcation pattern dependent on the coupling amplitude between particles. Using a mean field model in the large number limit, we show how the complete bifurcation unfolds in the presence of communication delay and coupling amplitude. Relative to the center of mass, the patterns can then be described as transitions between translation, rotation about a stationary point, or a rotating swarm, where the center of mass undergoes a Hopf bifurcation from steady state to a limit cycle. Examples of some of the stochastic patterns will be given for large numbers of particles.