## 1 Introduction  
In recent years, the use of underwater robotics as a technological tool for solving a wide variety of problems in underwater environments has experienced a great increase. These types of robots are known as Autonomous Underwater Vehicles (AUVs) or Unmanned Underwater Vehicles (UUVs). Some operations carried out in shallow and deep water such as ship hull inspections, surveillance operations in harbor areas, three dimensional mapping of coral reefs, and deep water archaeology are only a few examples of the current issues in different fields of interest. Recent advances in technology and science in this domain has made this type of vehicle increasingly accessible for the scientific community and for people in general. One of the most important features of AUVs is their ability to operate without human management. Control theory aims to provide underwater vehicles with the capacity to execute autonomous maneuvering operations in underwater environments where an adequate performance is achieved. In this sense, there exists a wide range of control approaches, most of them based mainly on adaptive or robust techniques. This is due to the AUV dynamics having parametric and/or modelling uncertainties. In general, the mathematical model of underwater vessels dynamics ([1; 2; 3]) depends on characteristics such as weight, buoyancy, frame geometry, number, and configuration of the propellers and hydrodynamic effects, among others. In the majority of cases, it is challenging to obtain complete model dynamics of underwater vehicles mostly due to the difficulty in obtaining the hydrodynamic parameters (added mass, and linear and nonlinear damping coefficients) with sufficient accuracy according to real operations [4]. This difficulty stems largely from the fact that vehicles such as AUVs move at low speeds, describing a uniform translation motion or a stationary state, due to their slow thruster dynamics [5]. The most common method to obtain hydrodynamic parameters is by using experimental tests with a planar motion mechanism (PMM) [6; 7], based on measurements of the reaction forces when the vehicle is moving through water. However, experiment-based methods require complicated and expensive setups [7; 8; 9]. An estimation of these parameters can be approximated by computational fluid dynamic (CFD) simulations [10; 11] to obtain nominal values for specific conditions. Analytical derivation and identification schemes of these values represent a very complex issue and are generally applied for quite simple cases that do not reflect realistic conditions [12; 13]. Nevertheless, it is common that AUVs replace their equipment with a diversity of sensors and technological devices depending on the mission to be carried out; in consequence, physical characteristics such as mass and shape are modified. Therefore, nominal values of the hydrodynamic parameters are of limited practical utility [14]. Furthermore, it is necessary to consider that the vehicle experiences external disturbances when its body moves in underwater environments such as waves or currents. The mixed effect of all these phenomena for an underwater vehicle results in a highly nonlinear model subject to uncertainties and external disturbances. From the control theory point of view, the hydrodynamic phenomena (the coefficients of which are taken to be unknown but constant) are considered as external disturbances to the vehicle dynamics. Motivated by the great challenges associated with the problem of AUV control subject to uncertainties, the research community has increased its efforts to find new strategies to achieve solutions for different control objectives related to underwater robots such depth control, station-keeping, trajectory tracking, path-following, fault tolerant control, or docking operations [15; 16; 17; 18]. Research studies have demonstrated that intelligent control techniques ([19; 20]) are highly effective to deal with this type of problem because of their adaptive and robustness nature.