Two robot arms working in a common workspace may collide because each of them is a dynamic obstacle for the other one. Motion Path Planning (MPP) is the process of finding a track that a robot/robot arm can follow to get to the target starting from any point in its workspace. In this Thesis, a collision-free MPP for two manipulators sharing a workspace is trained with reinforcement learning, specifically a Team Q-Learning algorithm, and two methods are considered for state discretization. For complicated models, a great deal of machine time is spent on calculation and decision making, while Look Up tables are usually fast on fly. In this approach, initially, the moving manipulator knows nothing about the workspace and the obstacles, but after enough exploration it learns optimal collision-free paths. Here, two methods are considered for state discretization, namely General State Discretization (GSD) and Tile Coding Discretization (TCD) in terms of Q-learning methods, both single-agent and multi-agent approaches are tested for 2-link manipulators. It is shown that the proposed GSD will end in smaller sets of states compared to TCD and a faster learning process. Without GSD a Q-learning approach could be very hard to apply to the model of two manipulators in a common workspace.