Robust coordinated rendezvous of depth-actuated drifters in ocean internal waves

Abstract

This paper considers a team of spatially distributed drifters that move underwater under the influence of an ocean internal wave. The overall objective is for the drifters to use the known depth-dependent ocean flowfield to rendezvous underwater and then return to the surface as a cluster for easy retrieval. From the structure of the internal wave, the ocean 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 linear model, where the drag force caused by the water accelerates the drifter. We design 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. Under the proposed algorithms, the drifters converge asymptotically to the same depth and position along the wave propagation direction. We also investigate the algorithms’ robustness against errors in actuation, estimation of the wave parameters, or state measurements. Various simulations illustrate our results.