Modeling of Inverse Kinematic of 3-DoF Robot, Using Unit Quaternions and Artificial Neural Network

Abstract

SUMMARY This paper presents a novel method for modeling a 3-degree of freedom open kinematic chain using quaternions algebra and neural network to solve the inverse kinematic problem. The structure of the network was composed of 3 hidden layers with 25 neurons per layer and 1 output layer. The network was trained using the Bayesian regularization backpropagation. The inverse kinematic problem was modeled as a system of six nonlinear equations and six unknowns. Finally, both models were tested using a straight path to compare the results between the Newton–Raphson method and the network training.

[Retracted] Application of Artificial Neural Network Algorithm in Facial Biological Image Information Scanning and Recognition

“…In combination with the biological feature invariance of the face, the noise separation output binary image of the face is obtained, and the result is as follows ( 8 ): where G ( σ I ) represents the pixel intensity of the exposure area block of the multipose face image; For the edge pixel ( x , y ), σ I is used to represent the edge wheel integral scale of the multipose face image, σ D is the differential scale, and x , y is the binary pixel of the original image sequence; L ( x , y , σ D ) represents the information entropy in the image sequence, L x ( x , y , σ D ) and L y ( x , y , σ D ) represent the weight fusion results of the multipose face image in the horizontal translation x direction and the vertical translation y direction respectively, L xx ( x , y , σ D ) and L yy ( x , y , σ D ) are the cross-correlation feature quantities of the corner distribution of the face [ 11 ].…”

“…where G(σ I ) represents the pixel intensity of the exposure area block of the multipose face image; For the edge pixel (x, y), σ I is used to represent the edge wheel integral scale of the multipose face image, σ D is the differential scale, and x, y is the binary pixel of the original image sequence; L(x, y, σ D ) represents the information entropy in the image sequence, L x (x, y, σ D ) and L y (x, y, σ D ) represent the weight fusion results of the multipose face image in the horizontal translation x direction and the vertical translation y direction respectively, L xx (x, y, σ D ) and L yy (x, y, σ D ) are the crosscorrelation feature quantities of the corner distribution of the face [11]. According to the above analysis, the dynamic corner features of multipose face images are extracted, and the geometric difference eigenvalues of faces are calculated for face feature analysis and classification recognition.…”

“…Carry out highlight detection and information fusion of multipose face image, select appropriate feature registration function to describe the feature points of multipose face image at different scales, and get the expression of face feature distribution as follows (11):…”

Nonlinear model identification and statistical verification using experimental data with a case study of the UR5 manipulator joint parameters

“…Then, the corresponding probability value (p − value) k of the calculated test statistic value (Z k ) from the distribution under the null hypothesis ( (Z k )) is calculated using Eq. (10).…”

Robust Sliding Mode Fuzzy Control of Industrial Robots Using an Extended Kalman Filter Inverse Kinematic Solver

“…Geometrical approaches to solve inverse kinematic have already been used for planar hyper-redundant manipulators [18,19], the 7R 6-DOF Robot-Manipulator [20], and hybrid parallel-serial five-axis machine tools [21]. Neural networks [22][23][24], neuro-fuzzy approaches [25], and deep neural networks [26,27] can be put in the second category of inverse kinematic solvers. The third category is the one that uses estimation algorithms to solve the inverse kinematic.…”