Research on Measurement Modeling of Spherical Joint Rotation Angle Based on RBF–ELM Network

Abstract

The acquisition of rotation angle and pose information of precision spherical joint is of great importance for error motion prediction analysis and motion control. In the early stage, an analytical measurement model based on the equivalent magnetic charge method has been purposed to realize the rotation direction identification and rotation angle measurement. However, several shortcomings were observed such as complicated calculations and time-consuming, and the solution accuracy of the theoretical model was decreasing with the expansion of measurement range. To improve this situation, new modeling methods based on artificial neural network have been researched. This paper employs radial basis function (RBF), extreme learning machine (ELM), and RBF–ELM hybrid neural networks to construct measurement models, then analyzes and compares their effectiveness to obtain the optimal algorithm. Analysis results show that the RBF–ELM hybrid neural network has a better calculation accuracy than the others. Finally, the experimental data are used to train and test the network model, and the error between output angle of the model and the actual measured rotation angle is calculated. The comparison results show that the measurement model based on the RBF–ELM hybrid neural network has a higher calculation accuracy and generalization capability. Within the range of ±20°, the maximum error of rotation angle around the X and Y axes are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$9'~48''$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6'~55''$ </tex-math></inline-formula> , respectively, and the root mean squared error is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1' 59''$ </tex-math></inline-formula> .