A novel adaptive control law for underwater vehicles

This paper proposes an approach to the design of control laws for underwater vehicles that takes into account the hydrodynamic effects affecting the tracking performance. To this aim, a suitable adaptive action based on appropriate kinematic transformations between the earth-fixed frame and the vehicle-fixed frame is developed. The proposed control law adopts quaternions to represent attitude errors, thus avoiding representation singularities that occur when using instead Euler angles. The stability of the designed control law is demonstrated by means of a Lyapunov-based argument. In view of practical implementation, a simplified version of the developed control law is also proposed that compensates only the persistent hydrodynamic terms, namely, the restoring generalized forces and the ocean current. Finally, the tracking performance of the proposed control law is analyzed in comparison to that of other existing control laws available in the literature. The obtained simulation results confirm the effectiveness of the proposed technique.