A future transportation service for Aalborg University (AAU) is imagined as Autonomous Mobility on Demand (AMoD). This thesis in- tends to build a solid foundation to such a ser- vice by addressing the basics of autonomous driving. The problem is derived specifically for the available platform, which is a golf cart. A first-principles model of a cart is derived for simulation purposes. Furthermore, a sim- plified model is derived to ease the controller design. To bind this model with the actual platform, the models for the actuators are derived. Nonlinear controllers are designed to fulfil the path-following problem and are tested in simulation. The actuator models are used to extend these controllers to implement them in the actual platform. As the controllers needs feedback, the measurements provided by the equipped sensors are fused together using an Extended Kalman Filter (EKF). The combination of the controllers and the EKF is tested in the platform. An exhaustive review of the state-of-the-art path-planners is per- formed. Based on this, an optimal Rapidly- exploring Random Trees algorithm (RRT*) with kinodynamic constraints is implemented and tested in simulation. The environment for it is constructed as an occupancy-map. This is performed with two LIDARs using the Cartographer library for Robot Operating System (ROS).