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

Qiang Zhang; Dongchen Qin; Peng Zhou; Qiang Zhu; Jiangyi Chen

doi:10.16578/j.issn.1004.2539.2021.02.004

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

Theory·Reserach | 更新时间：2022-11-10

- Research on Modeling and Solving of Shield Tunneling Posture based on Homogeneous Transformation Matrix
- Journal of Mechanical Transmission Vol. 45, Issue 2, Pages: 23-27(2021)
- 作者机构：
  
  1.郑州大学机械与动力工程学院，河南郑州 450001
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2021.02.004
  CLC：
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张强,秦东晨,周鹏等.基于齐次变换矩阵的盾构机掘进位姿建模与求解研究[J].机械传动,2021,45(02):23-27.

Zhang Qiang,Qin Dongchen,Zhou Peng,et al.Research on Modeling and Solving of Shield Tunneling Posture based on Homogeneous Transformation Matrix[J].Journal of Mechanical Transmission,2021,45(02):23-27.
张强,秦东晨,周鹏等.基于齐次变换矩阵的盾构机掘进位姿建模与求解研究[J].机械传动,2021,45(02):23-27. DOI： 10.16578/j.issn.1004.2539.2021.02.004.

Zhang Qiang,Qin Dongchen,Zhou Peng,et al.Research on Modeling and Solving of Shield Tunneling Posture based on Homogeneous Transformation Matrix[J].Journal of Mechanical Transmission,2021,45(02):23-27. DOI： 10.16578/j.issn.1004.2539.2021.02.004.

摘要

为了更加精确快速地求解盾构机在掘进过程中的姿态变化，采用基于空间齐次变换矩阵元素的位姿正解求解方法建立盾构机位姿正解解算模型，并利用牛顿拉夫逊算法对得到的以齐次变换矩阵元素为未知量的非线性方程组进行逐次迭代求解，得到齐次变换矩阵各元素数值解；然后，根据齐次变换矩阵各元素与位姿映射关系求解对应位姿。并根据各个液压缸杆长约束条件建立位姿反解数学模型，在Matlab中对位姿正反解进行求解，并分析比较正反解结果的吻合度。结果表明，其误差在0.018%左右，在误差允许范围内，证明了所建立的盾构掘进位姿正反解数学模型的正确性。

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.

关键词

盾构机位姿位姿正解位姿反解齐次变换矩阵牛顿拉夫逊法

Keywords

Shield machine posePosture solutionPose inverse solutionHomogeneous transformation matrixNewton-Raphson algorithm

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