Robust Geometric Formation Control of Multiple Autonomous Underwater Vehicles With Time Delays

Abstract—This paper develops a robust controller for au-tonomous underwater vehicles with bounded time delays, so that the AUVs form and keep a desired formation shape and track a desired trajectory. We use a six-degree-of-freedom dynamic model for each AUV to describe its motions in the three-dimensional space. We design an orientation controller based on feedback linearization, so that the orientation of each AUV converges to its desired value. We derive formation dynamics of AUVs and decouple the dynamics into a formation shape and a formation center, using the Jacobi transform. We treat couplings in the formation dynamics as perturbations and design a robust formation-keeping controller to tolerate both the perturbations and the time delays. We demonstrate the effectiveness of our controller in simulations. I