Can a Simple Control Scheme Work for a Formation Control of Multiple Autonomous Underwater Vehicles?

Abstract—The proportional and derivative (PD) and propor-tional, integral, and derivative (PID) controllers have been used extensively in industry due to their simplicity and effectiveness. This paper aims to investigate whether simple PD and adaptive PD-based controllers work for a complex system consisting of a group of multiple autonomous underwater vehicles (AUVs). Simple control laws with exact and uncertain gravity compen-sation are proposed for shape control of multiple AUVs. The proposed adaptive PD-based controller, in the presence of gravity uncertainty, requires only the model of gravity and buoyancy re-gressor matrix and does not require any knowledge of the inertia matrix, Coriolis and centripetal force, hydrodynamic damping and the parameters of the gravity, and buoyancy forces of the AUVs. Hence, the proposed controllers have the advantages of simplicity and ease of implementation. A novel collision and ob-stacle avoidance strategy using multi-layer region control concept, which limit the unnecessary use of high control efforts that lead to oscillatory movements of AUVs, is discussed. Lyapunov-like func-tions are proposed for the stability analysis. Simulation studies on AUVs with 6 degrees-of-freedom are presented to demonstrate the effectiveness of the proposed controllers. Index Terms—Adaptive control, coordination control, multiple autonomous underwater vehicles (AUVs) systems, proportional and derivative (PD) control, shape control. I