为了实现转向架实际线路运行状态室内台架模拟,对转向架动态测试的6自由度模拟平台位姿正解进行了研究.根据6自由度模拟平台几何结构和参数,利用基于欧拉角的齐次变换矩阵及杆长约束条件建立了以位姿变量为未知量、方程数等于作动器数的6自由度模拟平台位姿正解非线性数学模型,借助于Matlab/simulink仿真环境利用牛顿拉夫逊算法将以位姿元素为变量的非线性数学模型转化为以位姿元素增量为变量、Jacobian Matrix为系数矩阵的线性方程组来求取近似解,结合实例,验证了6自由度模拟平台正解数学模型及算法的准确性及高效性,为转向架测试6自由度模拟平台的运动控制提供了重要的理论基础.
Abstract
In order to realize real simulation of the bogie working state, the forward kinematics of 6DOF simulation platform for bogie test was investigated. According to geometry and parameters of 6DOF simulation platform, the nonlinear mathematical model for forward position solution of the platform was established by the homogeneous transformation matrix based on Euler angles and rod length constraints.The position variable was taken as unknown quantities with equation number equal to actuator number. By Matlab/simulink simulation, the approximate solution was achieved based on NewtonRaphson method to turn nonlinear mathematical model into linear equations with position variable as unknown quantities and Jacobian Matrix as coefficient matrix. Combined with example,the accuracy and efficiency of the algorithm and the nonlinear mathematical model for the forward kinematics solution were verified to provide important theoretical basis for the 6DOF platform motion control.
关键词
转向架 /
6自由度模拟平台 /
牛顿拉夫逊迭代 /
位姿正解 /
Matlab/simulink
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Key words
6-DOF simulation platform /
NewtonRaphson iteration /
forward kinematics /
Matlab/simulink
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参考文献
[1]王兴宇,苏建,梁树林,等.用于转向架刚度测试的6自由度加载平台控制策略[J].大连交通大学学报,2010,31(5):14-20.
Wang Xingyu, Su Jian, Liang Shulin, et al. Study of bogie stiffness test control strategy for sixDOF loading plate[J]. Journal of Dalian Jiaotong University, 2010,31(5):14-20. (in Chinese)
[2]王兴宇.高速列车转向架刚度测试模型及新型动态测试系统研究[D]. 长春:吉林大学交通学院,2009.
[3]Rad C R, Stan S D, Blan R,et al. Forward kinematics and workspace analysis of a 3RPS medical parallel robot[C]∥Proceedings of 2010 IEEE International Conference on Automation, Quality and Testing, Robotics. Piscataway,USA:IEEE Computer Society, 2010:301-306.
[4]Dalvand M M, Shirinzadeh B. Forward kinematics analysis of offset 6RRCRR parallel manipulators [C]∥Proceedings of the Institution of Mechanical Engineers.London,United Kingdom:SAGE Publications, 2011:3011-3018.
[5]Krishnamurthy P, Khorrami F, Fujikawa S.A modeling framework for six degreeoffreedom control of unmanned sea surface vehicles[C]∥Proceedings of the 2005 IEEE Conference on Decision and Control,and the European Control Conference. Piscataway. USA:IEEE Press,2005:2676-2681.
[6]Liu Yumei, Cao Xiaoning, Su Jian, et al. The pose realtime solution and control of the 6DOF loading platform for bogie test[C]∥Proceedings of 2011 International Conference on Transportation, Mechanical, and Electrical Engineering.Piscataway. USA:IEEE Computer Society, 2011:2294-2297.
[7]曹毅,李保坤,周辉,等. 6/6SPS型Stewart并联机构运动学正解的研究[J].安徽理工大学学报:自然科学版,2008,28(1):40-44.
Cao Yi, Li Baokun, Zhou Hui, et al. Direct kinetics analysis of a special class of the 6/6SPS stewart manipulators[J].Journal of Anhui University of Science and Technology:Natural Science Edition, 2008,28(1):40-44. (in Chinese)
[8]Yang Chifu, Huang Qitao, Ogbobe P O, et al. Forward kinematics analysis of parallel robots using global NewtonRaphson method[C]∥Proceedings of 2009 2nd International Conference on Intelligent Computing Technology and Automation.Piscataway,USA:IEEE Computer Society, 2009: 407-410.
[9]程佳.并联4TPS1PS型电动稳定跟踪平台的特性及控制研究[D]. 浙江:浙江大学机械与能源工程学院, 2008.
[10]米士彬,金振林.基于雅克比矩阵求解并联机器人位置正解方法[J].燕山大学学报, 2011,35(5): 391-395.
Mi Shibin, Jin Zhenlin. Seeking positional forward solution of parallel mechanism based on Jacobin matrix[J]. Journal of Yanshan University, 2011,35(5): 391-395. (in Chinese)
[11]张兆印.6DOF并联机器人位置正解的实用解法[J].计算机工程与应用,2009,45(9): 47-63.
Zhang Zhaoyin. Practical solution of 6DOF parallel robot position forward solution[J]. Computer Engineering and Applications,2009,45(9):47-63. (in Chinese)
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基金
“十一五”国家科技支撑计划项目(2006BAG01B03); 吉林省科技厅重点项目(20080356); 长春市科技支撑计划项目(2010018); 吉林大学研究生创新基金资助项目(20121076)
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