In this chapter, different types of trajectory control and planning algorithms for mobile robots in static environments are analyzed and assessed. To this end, a mobile robot is made to plan and follow a route between two arbitrary points in an autonomous way. This work goes in depth into the discrete space techniques and those based on search trees. First, kinematics, trajectory planning and contour maps, robot control, etc. are reviewed. Second, computer simulations that validate these theoretical results are also designed and implemented. Finally, the strengths and weaknesses of each trajectory planning methodology are assessed.