In last decades, great technology advances have been done related to the automotive sector, especially in Advanced Driver Assistance Systems (ADAS) developed to improve mobility in terms of comfort and safety during driving process; hence, automated driving is presented as an evolution of those systems in the present and upcoming years. The aim of this work is to present a complete framework of motion planning for automated vehicles, considering different constraints with parametric curves for lateral and longitudinal planners. Parametric Bézier curves are used as the core approach for trajectory design in intersections, roundabouts, and lane change maneuvers. Additionally, a speed planner algorithm is presented using the same parametric curve approach, considering comfort and safety. A simulation environment is used for testing the planning method in urban conditions. Finally, tests with the real platform in automated mode have been performed showing goods results.