This paper proposes a computationally-efficient controller for an AUV which could be implemented using a single-purpose microcontroller. The AUV under study has a complex eight-thruster mechanical configuration. Such system imposes concerns like non-linear behavior, coupled dynamics and parameter uncertainty. An extensive study on vehicle kinematics/dynamics is proposed, followed by formulating a non-linear model for the test vehicle. Dynamic decoupling is applied to break the system into two sub-systems controlled using two independent simple controllers. An LQR controller is used for stabilizing vehicle depth and roll/pitch attitude. A self-tuning PID controller is used for trajectory tracking of surge velocity and yaw attitude. The combined LQR/Adaptive PID control architecture deals very well with noise and uncertainty with minimal computational effort. The controller is verified experimentally using multiple motion scenarios for a test AUV.