The trajectory planning methods presented in Chaps. 4 and 7, respectively, for manipulators and mobile robots, operate under the simplifying assumption that the workspace is empty. In the presence of obstacles, it is necessary to plan motions that enable the robot to execute the assigned task without colliding with them. This problem, referred to as motion planning, is the subject of this chapter. After defining a canonical version of the problem, a selection of representative planning techniques is presented. The method based on the notion of retraction characterizes the connectivity of the free configuration space using a roadmap, i.e., a set of collision-free paths, while the cell decomposition method identifies a network of channels with the same property. The PRM and bidirectional RRT techniques are probabilistic in nature and rely on randomized sampling of the configuration space and memorization of samples that do not cause a collision between the robot and the obstacles. The artificial potential method is also described as a heuristic approach particularly suited to online planning problems, where the geometry of the workspace obstacles is unknown in advance. The chapter ends with a discussion of the application of the presented planning methods to the robot manipulator case.