The problem of designing an accurate and reliable control for an Autonomous Underwater Vehicle (AUV), which is being subjected to environmental disturbances as well as configuration related changes, is critical in order to accomplish a successful mission. Any real-world problem solving system must deal with the issue of uncertainty, since the system's knowledge of the world is always incomplete, imprecise, and uncertain. This situation is aggravated for an AUV, due to the complex oceanic environment, and the inevitable noise of the sensory system.

Some major facts that contribute to the difficulty of the underwater vehicle control are:

• the dynamic behavior of the vehicle is highly nonlinear,

• hydrodynamic coefficients cannot be easily obtained, hence making up uncertainties in the model knowledge,

• the vehicle main body can be disturbed due to the ocean currents and vehicle motion. Therefore, it is difficult to obtain high performance by using the conventional control strategies. The control system should be able to learn and adapt itself to the changes in the dynamics of the vehicle and its environment.

Many control methods have been proposed by researchers during the last decade, and there still exists a trend towards finding a better control law to achieve exponential stability while accounting for environmental changes and vehicle uncertainties. Focusing on the low level motion control of AUVs, most of the proposed control schemes take into account the uncertainty in the model by resorting to an adaptive strategy ((Corradini & Orlando, 1997), (Fossen & Sagatun, 1991a) and (Narasimhan & Singh, 2006)), or a robust approach ((Marco & Healey, 2001) and (Healey & Lienard, 1993)). In (Healey & Lienard, 1993) an estimation of the dynamic parameters of the vehicle NPS AUV Phoenix is also provided. Other relevant works on the adaptive and robust control of underwater vehicles are (Cristi & Healey, 1989), and (Cristi et al., 1990). (Leonard & Krishnaprasad, 1994) considers the control of an AUV in the event of an actuator failure. Experimental results on underwater vehicle control have been addressed by many researchers (e.g. see (Antonelli et al., 1999), (Antonelli et al., 2001), and (Zhao & Yuh, 2005)). An overview of control techniques for AUVs is reported in (Fossen, 1994).

The aim of this chapter is to design a control system that would achieve perfect tracking for all configuration variables (e.g. sway and yaw motions) for any desired trajectory. To this end, we present the application of nonlinear control methods to an AUV that would lead to a successful uncertainty management, while accounting for the effect of saturation: an unwanted implementation problem which is seldom addressed by researchers. Three control methods are presented and applied to a two-dimensional model of an AUV, and their capabilities to cope with the issues of parameter uncertainties and environmental disturbances are studied and compared. The considered model is a nonlinear multi-input multi-output (MIMO) system, therefore we intend to shed a light on the complexities encountered when dealing with such systems. This model also serves as an example, and helps clarify the application of the given methods. All the methods presented, guarantee perfect tracking for all configuration variables of the system. The performance of the presented methods, are compared via simulation studies.

We begin by designing a control law using the computed torque control method. Although simple in design, the stability achieved by this method is sensitive to parameter variations and noise of the sensory system. Moreover, the maximum amount of disturbance waves that can be conquered by this method is somewhat lower relative to the other methods given here. Next we present the adaptive approach to computed torque control method. It will be shown that this method can withstand much higher values of disturbance waves and remain stable. Furthermore, parameter variations are compensated through an adaptation law. The third method presented, is the suction control method in which we employ the concepts of sliding surfaces, and boundary layers. This method, being robust in nature, achieves an optimal trade-off between control bandwidth and tracking precision. Compared to the computed torque control method, this method has improved performance with a more tractable controller design. Finally, the effect of saturation is studied through a novel approach, by considering the desired trajectory. A condition is derived under which saturation will not occur. The chapter will be closed by proposing topics for further research.

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