Distributed formation control for collaborative tracking of manifolds in flows

We address the development of a distributed control strategy for tracking Lagrangian coherent structures (LCS) in a geophysical fluid environment like the ocean. LCS are time-dependent structures that divide the flow into dynamically distinct regions and are important because they enable the estimation of the underlying geophysical fluid dynamics. In this work, we present a distributed formation control strategy designed to track stable and unstable manifolds. We build on our existing work and present an N-robot leader-follower tracking strategy that relies solely on local sensing, prediction, and correction. Our approach treats the N-robot team as a deformable body where distributed formation control for tracking coherent structures and manifolds is achieved using a sequence of homogeneous maps. We discuss the theoretical guarantees of the proposed strategy and validate it in simulation on static flows as well as the time-dependent model of a wind-driven double-gyre often seen in the ocean.