# A Neural Network Based Approach to Inverse Kinematics Problem for General Six-Axis Robots
## 1 Introduction
As a brief summary of the previous work, we sort and summarize their features in Table 1. It can be observed that, despite the high precision showcased by their IKP solutions, a common limitation accompanies: the robot models being studied are simple, being either decoupled or low DoF. Testing the learning-based algorithms on these robot models is inappropriate. On the one hand, for these decoupled or low-DoF models, the compact, elegant and high-efficiency analytical IKP solutions are always the optimal choice, making the learning-based approaches somewhat meaningless in this scenario. Furthermore, inverse kinematics functions under low-DoF or decoupled case are relatively simple and easier to be learnt from training data. Hence, performance of these NN-based methods on general high-DoF robots, the IKP of which deserves most attentions, is still not clear and worth discussing. In this paper, a novel NN-based approach combining the regression and classification model was proposed to solve the IKP of general six-axis robots. Due to the complexity of the problem, the underlying IK function was first simplified by joint space segmentation, with the respective training data generated via FKP on each subspace. Then, the prediction system, comprising several sets of NNs, was trained on these data to learn the problem in piece. Meanwhile, a set of classification models was trained to determine which foregoing NNs, representing different joint spaces, should be selected for prediction given a desired pose. Considering the precision requirement of some sensitive tasks, an iterative process was applied to minimize the prediction error subsequently. With this configuration, we hypothesized that our algorithm can achieve high precision and stability. This hypothesis is verified by simulations with comparison to other models reported in the literature. Our contributions are twofold: On the one hand, the performance of neural network methods for IKP is further explored and improved for six-joint general robots. Due to the complexity of our robot model, the existing methods in the literature, which fit the problem directly, are not capable of solving the IKP of the aforementioned type of robots accurately. Our novel NN-based method as a robust integration of the regression and classification model can solve the problem efficiently and the precision of the algorithm is secured by the idea of joint space segmentation. In addition, an error minimization method is investigated \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Reference** & **Robot Model** & **Analytical Solution** & **Accuracy** \\ \hline ANN & [16; 20; 22; 23; 24; 25; 27; 28; 30] & Low-DoF or 6-DoF decoupled & Yes & low to extremely high \\ RNN & [18; 21] & 6-DoF decoupled & Yes & fair to extremely high \\ RFB & [17; 19] & 6-DoF decoupled & Yes & fair to high \\ GAN & [26] & Low-DoF & Yes & high \\ \hline Our work & & 6-DoF general robot & No & extremely high \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the previous and present work. based on the classic Newton-Raphson (NR) algorithm. One novelty of this approach is its robustness in minimizing the singularity in the IKP problem. Moreover, the method also has advantages in the sense of overcoming underlying drawbacks associated with the commonly used error minimization algorithm, such as the efficiency. The rest of this paper is organized as follows: Section 2 covers the robot model and kinematic analysis. Section 3 gives a brief introduction about the mathematical model of neural networks and the Newton-Raphson based error minimization method. In Section 4, some details during implementation are covered while the simulation results are shown and discussed in Section 5. Finally, Section 6 concludes the paper.