Research on Modeling and Solving of Shield Tunneling Posture based on Homogeneous Transformation Matrix

Abstract

In order to more accurately and quickly solve the shield machine pose change during the tunneling process， a positive solution method for the pose of the shield machine based on the spatial homogeneous transformation matrix element is used to establish a positive solution model of the shield machine pose， and the Newton-Raphson algorithm is used to obtain the nonlinear equations with homogeneous transformation matrix elements as unknown quantities are solved successively， and the numerical solutions of the elements of the homogeneous transformation matrix are obtained. Then， the corresponding poses are solved according to the mapping relationship between the elements of the homogeneous transformation matrix and the poses. According to the constraints of the length of each hydraulic cylinder rod， the mathematical model of the inverse posture solution is established， and the positive and negative solutions of the posture are solved in Matlab. The results show that the error is about 0.018%， within the allowable range of error， which proves the correctness of the mathematical model of the forward and reverse solutions of the shield tunneling position and pose.

Keywords

• Shield machine pose;Posture solution;Pose inverse solution;Homogeneous transformation matrix;Newton-Raphson algorithm