In this thesis we study the methods for motion planning for nonholonomic systems. These systems are characterized by nonholonomic constraints on their generalized velocities. The motion planning problem with constraints on the velocities is transformed into a control problem having fewer control inputs than the degrees of freedom. The main focus of the thesis is on the study of motion planning and design of the feedback control laws for an autonomous underwater vehicle: a nonholonomic system. The nonlinear controllability issues for the system are also studied. For the design of feedback controllers, the system is transformed into chained and power forms. The methods of transforming a nonholonomic system into these forms are discussed. The work presented in this thesis is a step towards the initial study concerning the applicability of kinematic-based control on underwater vehicles.