Coordinated rendezvous of underwater drifters in ocean internal waves

This paper considers a team of spatially distributed drifters that move underwater under the influence of an ocean internal wave. The team´s objective is to estimate the physical parameters that determine the internal wave, use the then-known ocean dynamics to rendezvous underwater, and finally return to the surface as a cluster for easy retrieval. From the structure of the internal wave, the ocean´s flowfield is time-varying and spatially dependent on depth and position along the wave propagation direction. The drifters can control their depth by changing their buoyancy and are otherwise subject to the horizontal flowfield at their given depth. We consider two different drifter dynamical models: a first-order Lagrangian model, useful when the drifter´s mass is sufficiently small, and a second-order model, where the drag force caused by the water accelerates the drifter. We propose provably correct distributed algorithms that rely on the drifters opportunistically changing their depth so that the ocean flowfield takes them in a desirable direction to perform coordinated motion. The drifters converge to the same depth and position along the wave propagation direction asymptotically. Simulations illustrate our results.