In modern society cars are one of the most important means of transportation. Unfortunately, many people die in car accidents around the world. Research shows that the number of fatal casualties in car accidents has been increasing for the past decade and that the largest cause of these accidents is the human driver. For this reason, research on fully autonomous vehicles has gained a lot of attention. However, currently autonomous driving is only implemented to reduce the errors of human drivers. More research is necessary in order for fully autonomous vehicles to be implemented and to remove the human driver completely. A robust navigation algorithm which is able to run in real time is one of the challenges in development of fully autonomous vehicles. Important topics in navigation of autonomous vehicles include the path planner and the motion controller. The path planner finds a path for the vehicle from its current location to the target location. At the same time the path planner avoids obstacles and fulfills the non-holonomic constraints of the autonomous vehicle. The motion controller tries to follow the path the path planner made as close as possible by controlling the vehicle. These two topics influence each other and are therefore dependent. In literature little research is done on integrated algorithms that combine path planning and motion control. Therefore, this thesis will research navigation of autonomous vehicles by using an integrated algorithm that includes both path planning and motion control. The objective of this thesis is to develop a Lyapunov stable control algorithm that is capable of planning a path for all possible vehicle maneuvers. Besides path planning the proposed algorithm must be capable of controlling the vehicle along this path. Furthermore, the algorithm needs to include obstacles and the non-holonomic dynamics of an autonomous vehicle. The main contribution of this thesis is an integrated path planner and motion controller for navigation of autonomous vehicles. The stability of the proposed algorithm is proven by using the Lyapunov method. Simulation results prove that the algorithm is capable of planning the path and the motion of the autonomous vehicle with non-holonomic constraints and with the presence of obstacles.