Modeling and Energy–Optimal Neuro–Fuzzy Control of Cylindrical Autonomous Underwater Vehicles

This paper presents a reduced–order mathematical model and an energy–optimal neuro–fuzzy control method for a cylindrical autonomous underwater vehicle (AUV). The standard six DOFs formulation is simplified to translational motions under the assumption that rotational motions are stabilized near a nominal operating point. To address the concern that a diagonal reduction may become three independent single DOF systems, cross–axis coupling terms are retained in the reduced inertia and damping matrices. The vehicle is represented with four thrusters acting on three translational degrees of freedom; therefore, the control–effectiveness matrix is rectangular and the actuator–force vector is not unique for a given virtual control force. The proposed controller combines adaptive neuro–fuzzy uncertainty compensation with a quadratic actuator–allocation layer that penalizes force mismatch, propulsion effort and command variation. Illustrative MATLAB/Simulink–style simulations compare the method with PID, fuzzy–PID and sliding mode control using tracking error, energy index and actuator–saturation metrics