Modeling of Remotely Operated Vehicle

Abstract

In this chapter, nonlinear dynamic model of an ROV with perturbation due to hydrodynamic forces is discussed. In general, there are two methods to derive the dynamic model: the Lagrange formulation using the energy method and Newtonian’s formulation using the Newton’s Second Law of Motion. The latter method gives an equation using the angular velocities about the body-fixed axes; unlike the generalized variables used in the Lagrange equation, the angular velocities cannot be integrated to obtain angular displacements about these axes and are therefore unsatisfactory to describe fully the orientation of a rigid body in three-dimensional (3D) space. However, the body-fixed angular velocities can be solved and transformed to give the orientation of the vehicle in 3D space using the Euler’s angles. The Euler’s transformation (or commonly known as kinematics equation) provides the relationship between the dynamics derived in the earth-fixed and the body-fixed coordinates. There are practical advantages to derive the dynamics in the body-fixed coordinate for the following reasons. First, most sensors and actuators mounted on the ROV measure the body parameters, such as the ROV velocities, and provide propelling forces. Secondly, the dynamic equation is inherently parameterized and hence less complicated because this parameterized form is not Euler’s angle-dependent. Unfortunately, due to modeling uncertainties, the model derived by either method can be inadequate for control system design. These uncertainties are mainly due to the hydrodynamic forces which are experimentally and theoretically difficult to obtain. Nevertheless, for control design purposes, there is a need to consider a simplified nominal model with additive perturbation bounds that are accurate enough to represent the ROV dynamic behavior.