Back-stepping Technique-based Distributed Formation Control of Multiple Under-actuated Autonomous Underwater Vehicles

This paper focuses on a distributed formation control for multiple under-actuated autonomous underwater vehicles (AUVs) with prescribed performance subject to external disturbance. First, distributed formation tracking errors are calculated using graph theory and state transformation. The errors are dexterously transformed into new error variables to satisfy the predefined performance. Based on the back-stepping procedure, the distributed formation controller is then developed and combined with a nonlinear disturbance observer (NDO) to enhance the robustness against external disturbances. It is mathematically proven that the proposed formation controller guarantees that all signals in the whole control system are uniformly ultimately bounded (UUB) and the distributed formation tracking errors always remain within the predefined regions. Finally, numerical simulations verify the proposed controller's effectiveness and feasibility.