# Kinesthetic Learning Based on Fast Marching Square Method for Manipulation
## 1 Introduction  
In today's robotics, the need for precise manipulation has encouraged the development of human-like robots. This has led to the emergence of manipulator arms of all kinds of shapes and configurations in order to achieve a system capable of reproducing natural human-inspired movements. To guarantee this similarity, robotic arms have a large number of degrees of freedom (DoF). For this reason, path planning and control for these platforms have become a very difficult task [1]. The most common way to solve this kind of problem in robotics is to use inverse kinematics. However, redundant manipulators carrying out complex tasks hinder classical methods from successfully solving this problem. The most common way to overcome this is based on the use of different learning methods. Learning algorithms would obtain a policy that works in a similar way as a human does. The main objective of these strategies is to identify patterns and then try to generalize the more relevant features for the given data. With that information, the algorithm tries to reproduce new behaviors resembling previous learned experiences, even if there is a change in the environment of the study or if it is unknown. When applying these methods to manipulation, the concept of learning in complex manipulating tasks lies in the use of knowledge taught by a human who shows how to solve a task and the generalization of that information for similar tasks [2, 3]. Traditional learning methods have shown good performance for the resolution of manipulation problems [4, 5]. However, the process needed in those methods to obtain the learning policy generates a mathematical model which usually relies on probabilisticterms, which makes these learning methods stochastic. Depending on what would need to be solved, this characteristic may not be a desirable property, since even with the same demonstrations, different solutions could be obtained in each test. This stochastic behavior may cause algorithms to end up obtaining a solution that does not converge. In this paper, we propose a learning-based solution that overcomes typical problems from both traditional planners and learning methods. It is an extension of a previous work proposed in [6; 7], which focuses on the generation of trajectories for a robotic manipulator for tasks in two dimensions and without the use of imitation learning techniques. We present the fast marching learning (FML) method, which is a deterministic and asymptotically globally stable learning algorithm created for learning point-to-point 2D and 3D tasks based on the fast marching square (\(FM^{2}\)) method [8; 9]. The proposed learning approach is either referred to in this work as fast marching learning or as learning based on the fast marching square. Initially, paths are kinesthetically taught to the robot by guiding its robotic manipulator. Then, these trajectories are represented by \(FM^{2}\), which is a path planner based on how the light propagates. This treats the environment where it is applied in a continuous way, deriving multiple benefits which will be discussed later. FML applies \(FM^{2}\) on every learned path to parameterize experience, which is later merged for obtaining a global knowledge representation. Additionally, some relevant optimizations are made with respect to our previous publications and a new concept of auto-learning is presented herein. A direct relation between the proposed method and common learning techniques, such as reinforcement learning (RL), is also carried out. Finally, a large amount of testing trials on a real robotic manipulator are performed to fully validate the functioning of the proposed strategy in 3D complex indoor environments. Regarding the state-of-the-art techniques and the previous work presented in [6; 7], the following advantages were obtained:  
* The generated trajectories are ensured to be smooth and local minima-free, which means that these always converge. * The path planner method is complete. If there is any solution, it is always found.