ABSTRACT
This chapter provides an overview of the dynamic mathematical model of an underwater vehicle is presented. The dynamic model is presented for the motion planning tasks. The chapter discusses the dynamic model of the underwater vehicle. The three-dimensional equations of motion for hydrodynamically shaped underwater vehicles can be developed using a body fixed coordinate frame and a global reference frame. The chapter addresses the control design for the problem of motion point-to-point stabilization. The system is supposed to reach a final desired configuration starting from an initial point, without the need to plan a trajectory. The Lyapunov function will be used as a stability analysis tool as well as a feedback control design tool for this system. The design of feedback control is done in such a way that the Lyapunov function or its derivative has certain properties that guarantee boundedness or convergence to an equilibrium point.
