Path Planning methods for autonomous control of Unmanned Aerial Vehicle (UAV) swarms are on the rise because of all the advantages they bring. There are more and more scenarios where autonomous control of multiple UAVs is required. Most of these scenarios present a large number of obstacles, such as power lines or trees. If all UAVs can be operated autonomously, personnel expenses can be decreased. In addition, if their flight paths are optimal, energy consumption is reduced. This ensures that more battery time is left for other operations. In this paper, a Reinforcement Learning based system is proposed for solving this problem in environments with obstacles by making use of Q-Learning. This method allows a model, in this particular case an Artificial Neural Network, to self-adjust by learning from its mistakes and achievements. Regardless of the size of the map or the number of UAVs in the swarm, the goal of these paths is to ensure complete coverage of an area with fixed obstacles for tasks, like field prospecting. Setting goals or having any prior information aside from the provided map is not required. For experimentation, five maps of different sizes with different obstacles were used. The experiments were performed with different number of UAVs. For the calculation of the results, the number of actions taken by all UAVs to complete the task in each experiment is taken into account. The lower the number of actions, the shorter the path and the lower the energy consumption. The results are satisfactory, showing that the system obtains solutions in fewer movements the more UAVs there are. For a better presentation, these results have been compared to another state-of-the-art approach.