Model Predictive Control (MPC) has had an increasing role in autonomous driving applications over the last decade, enabled by the continuous rising of the computational power in microcontrollers. In this thesis a collision avoidance trajectory generation algorithm based in MPC formulation is developed. The operating environment consists in a one-way highway with two lanes. The overall system is equipped with a low-level controller capable of tracking the trajectory generated by the MPC planner. In the path towards this goal, a MPC based lane changing application in an obstacle-free highway environment has been developed. A point-mass kinematic vehicle model is used as the MPC plant model for its simplicity and enabled by the usage of a low-level controller. This thesis studies several obstacle representation approaches and then, explains in detail the development process of the collision avoidance trajectory generation application, defining and discussing simulation results for each intermediate approach obtained. Both applications have been implemented in a BeagleBone Black online board situated in small-scale trucks (1:12) for testing purpose. The experimental results have been studied and discussed to prove the algorithms functionalities, as well as to check the board capabilities to run online MPC applications in comparison with polynomials based approaches.