# A Neural Network Based Approach to Inverse Kinematics Problem for General Six-Axis Robots
## 1 Introduction
While the mean squared error (MSE) of the whole system was 0.015687, the reliability was claimed to be 99.99993664% after training. Although this reliability seems perfect, it is computed by simple multiplications of the reliabilities from each trained network, ignoring the fact that the probability behind each component is not independent. [PERSON] and [PERSON] [19] trained a novel RBF network to tackle IKP. Unlike traditional networks using the goal pose as input and joint state as output, their model was additionally fed with incremental change of the pose in order to predict the increment of joint angles. Simulation results on KUKA-Kr robot revealed the improvement of their model over traditional networks. To get rid of the kinematic singularities, a single hidden layer NN was trained to solve the IKP and the kinematics Jacobian simultaneously in [20]. Implementing on a 6-DOF manipulator, maximum IK errors of 4.81% in the joint space, as well as 6.72% and 5.79% for position and orientation, respectively, in the Cartesian space, were observed. [PERSON] investigated the idea of combining NN and genetic algorithm (GA) for IKP [21]. The integer portion of the solution was first obtained from NNs while the floating-point portion was further improved by GA. With this workflow, the precision of the solver can reach the micrometer level. Take a further step, [PERSON] [22] optimized the previous GA error minimization procedure by introducing simulated annealing algorithm as a genetic operator. Hence, the number of epochs reaching the optimal solution was reduced to a half of the method without using annealing algorithm. [PERSON] et al. proposed a novel approach to solve IKP with the single hidden layer feedforward neural networks (SLFNs) in [23]. Within their scheme, an electromagnetism-like method was used to generate the training within the joint subspace while the extreme learning machine analytically determined the weights of the SLFNs instead of back propagation (BP) training. Although this approach was proved to be highly precise, the SLFNs need to be retrained every time given a new target pose, which limited its application. [PERSON] et al. [24] took the current joint state into consideration during implementing ANN and verified their modification can be helpful to achieve better performance for ANN system. In [25], the performance of NN for IKP was compared with those of GA and adaptive neuro-fuzzy inference system (ANFIS). The results from the drawing spring shape task demonstrated that NN was much more faster than GAand had a better accuracy in contrast to ANFIS. A model based on generative adversarial networks (GAN) was proposed for IKP and inverse dynamics (ID) in [26]. A comparative test was conducted between the proposed model and the traditional feedforward network (FFN). Ignoring the ID part, GAN showed no obvious advantages over FFN for IKP and the minimum MSE was 0.0256 in their work. [PERSON] et al. [27] utilized MLP to determinate the IKP solution of a 6-DoF industrial robot, as well as the best architecture for the NN; they also discussed the effect of choosing different solvers, activation functions, and hidden layers sizes. However, error minimization was not considered for their NN prediction and the mean absolute error for the last joint was up to 1.56557\({}^{\circ}\). In [28], a 3-DoF robot arm was modeled with unit quaternions instead of D-H convention for IKP training. After learning the respective features with an MLP, the maximum IKP prediction error is 0.0669\({}^{\circ}\) in the joint space. Additionally, some researchers lay their emphases on the training process, and the heuristic algorithms are applied to train the model for IKP, such as the PSO-optimized NN in [29] and the FOA-optimized NN in [30]. Maximum observed prediction error for these two models were \(-0.1859^{\circ}\) and 0.1271\({}^{\circ}\), respectively.