## Introduction

Underwater vehicles (UVs) lately found their use in many activities such as underwater mapping, habitat exploration, different types of inspections (underwater cables, dams, ship hulls), rescue missions and many others. All of these applications speeded up the research related to modeling and control of UVs. Modeling of UVs is important because many applications demand that the mission is carefully planned in a simulated environment. Control, on the other hand, is essential if higher level tasks are to be performed effectively. Finding a mathematical model describing an underwater vehicle dynamics can be a tedious task. The greatest problem is the complexity of the rigid body dynamics which is augmented by additional forces and effects which appear in fluid. The hydrodynamics observe this problem with great care, paying extra attention to dependencies between different variables. Another problem are the couplings that appear due to motion in different degrees of freedom simultaneously. For the control purposes, most of these dependencies are often neglected in order to obtain a simple model which can later be used for designing autopilots.

This chapter deals with methods for obtaining a precise enough mathematical model, which can be used for control purposes, using cheap and commercially available sensors such as cameras or compasses. First section deals with description of a full mathematical model of an underwater vehicle, starting with actuators (thrusters) and methods of determining their static characteristics. The section is followed by actuator allocation where some common configurations and allocation matrices are mentioned. Kinematic model is briefly addressed and dynamic model is presented in its full form. The coupling effects are observed in the horizontal plane and a short methodology of determining dominant parameters in the coupled model is given. For the uncoupled case, two model equations are taken into account: linear and nonlinear. In section two, three vision-based data acquisition methods are presented. Here it is explained which equipment is needed for making a laboratory apparatus for data acquisition, and the process of data acquisition via image analysis is presented. The following section deals with the identification algorithms which use the data obtained via the vision-based methods. Here we present in short the least-squares method (used for determining the coupled model), open loop, zig-zag methods and identification based on the self-oscillations. All of these methods are followed with results obtained either from real vehicles or simulations.

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