This paper presents model predictive control of an autonomous vehicle. Simulation and experimental results have been shown and compared with input-output linearization method. The results obtained show that the MPC is an efficient method that allows for accurate control and navigation of an autonomous vehicle. Model based predictive control is tested in simulations for motion on an inclined plane. This is done to prepare future work regarding the avoidance of the violation of the smoothness condition for exact linearization, while at the same time by modifying the input commands the geometric path planning results are conserved. The approach is presented for the wheel-ground slippage and tip-over avoidance of the three-wheeled vehicle for inclined plane motion. A complete three-dimensional dynamic model using Newtonian dynamics is also presented. Simulation results using a three-wheeled vehicle built in our laboratory illustrate the performance of the proposed controller.