# Machine Learning Sequential Methodology for Robot Inverse Kinematic Modelling
## 1 Introduction
To improve the model's accuracy, further methodologies are the hybrid procedures based on ML models and optimization algorithms applied in the cascade form. In [32], [PERSON] et al. implemented a hybrid simulated annealing with GA to reduce the shallow network (46 hidden neurons in the hidden layer) error to 1.0 \(\upmu\)m for a 4-DOF manipulator. Similarly, a neuro annealing approach based on Elman recurrent networks for the Stanford and PUMA 560 robotic manipulator was applied in [33]. This study proposed a committee system with Elman networks as in [31], optimizing the final output using a simulated annealing and reducing the MSE from 2.10 to 0.0000079, in joint space. [PERSON] et al. [34] proposed the GA approach by applying an extreme learning machine (ELM), combined with a sequential mutation genetic algorithm (SGA). This work focused on a 6-DOF Stanford MT-ARM robot, highlighting a model error equal to 0.0225 mm with a standard deviation of 0.0081 mm. Although the literature shows promising methods and significant results in addressing ML strategies to achieve effective and robust manipulator's IK formulation, further studies are required to evaluate novel techniques for robot inverse kinematic modeling. In particular, the state of art shows that several ML methods are based on general models to compute all the joint values simultaneously, increasing the computational cost and complexity. In this way, the development of a sequential methodology focused on the single joint calculation may represent a novel paradigm [35; 36]. This paper aims to investigate and deploy an ML-model using a sequential procedure for an accurate IK formulation, addressing the model prediction using a data-driven approach. At each joint, the input vector includes the previously obtained actuators' values and the Cartesian coordinates with orientation. Moreover, the ANN architecture is defined through an optimization phase based on the GA technique. The main contribution of this study is to validate a complete sequential ML model methodology, assessing the results in terms of joint and Cartesian error. Additionally, the results are compared with the global approach. A further contribution is to integrate the Genetic Algorithm optimization into the IK procedure to define the network structure:the hidden layers and hidden neurons per layer. The GA score function depends on the normalized root mean square error, the maximum error, and the coefficient of determination. The novel sequential methodology is validated in a simulated environment (IRB140) and with a real physical robot (LR-Mate 200 iC). The paper is organized as follows: Section 2 presents the novel methodology to model the robot inverse kinematics, describing the sequential procedure. Following the proposed methodology, a simulated case study applied to an articulate robot (IRB140) is described in Section 3. Results are discussed and compared with other studies. Section 4 shows the experimental campaign performed on a 6 DOFs robot (FANUC LR-Mate 200 iC), evaluating the obtained results and validated the proposed sequential methodology for robot inverse kinematic modeling. Finally, Section 5 presents the conclusions discussing the study findings and prospective.