The advancement of robotics in recent years has driven the growth of robotic applications for more complex tasks requiring manipulation capabilities. Recent works have focused on adapting learning methods to manipulation applications which are stochastic and may not converge. In this paper, a kinesthetic learning method based on fast marching square is presented. This method poses great advantages such as ensuring convergence and is based on learning from the experience of a human demonstrator. For this purpose, the demonstrator teaches paths by physically guiding one of the UR3 arms of a mobile manipulator. After this first phase, the fast marching Learning method is used to make the robot learn from this experience. As a novelty, an auto-learning functionality is presented, which provides the kinesthetic learning algorithm with an exploration capacity. The base of this algorithm is not only using the information provided by the taught trajectories, but also expanding its ability in order to explore unknown states of the environment. The effectiveness of the proposed method has been evaluated through simulations in 2D and 3D environments and in a real mobile manipulator. The learning process is analyzed with other 2D learning approaches using the LASA dataset and it is tested in complex 3D scenarios with different obstacles, proving its effectiveness.