关节臂式坐标测量机的数学建模及参数标定
|
摘要
关节臂式坐标测量机(AACMM)是一种便携式高精度测量设备,由于测量机末端探头中心坐标的关系且关节的旋转角度非常复杂,有必要建立准确的数学模型以达到所需的精度。其经典的数学模型是Denavit-Hartenberg(D-H)模型,但它在相邻关节轴平行时存在缺陷且忽略了静态柔性误差。为了消除D-H模型的不足,研究了一种基于广义几何误差理论的数学模型,并采用非常快速模拟退火算法对广义几何误差参数进行标定。对比实验结果表明,广义几何误差模型进行算法标定后平均误差减小了0.500 1 mm,标准偏差减小了0.337 3 mm;基于广义几何误差模型的长度测量的平均误差为0.045 4 mm,标准偏差为0.032 3 mm,均优于采用MDH模型测量的平均误差和标准偏差,验证了方法的有效性。
The articulated arm coordinate measuring machine is one of the portable high-precision coordinate measuring instruments. It is hence necessary to establish accurate mathematical model for achieving the required accuracy due to the relationship between the central coordinate of the probes at the end of the measuring machine and the complexity of rotation angle of the joints. The classic Denavit-Hartenberg(D-H) model has defects when adjacent axes are parallel and ignores static flexibility error. Thus, this paper focuses a new mathematical model based on the generalized geometric error model for improving the D-H model. Additionally, the very fast simulated annealing algorithm is applied to calibrate the generalized geometric error parameters. Experiments demonstrat that the average error, after the calibration by the generalized geometric error model, is reduced by 0.500 1 mm and the standard deviation is reduced by 0.337 3 mm. The average error of the measurement based on the generalized geometric error model is 0.045 4 mm and the standard deviation is 0.032 3 mm. Both of the methods are superior to the MDH model, which verifies the effectiveness of the proposed method.
The articulated arm coordinate measuring machine is one of the portable high-precision coordinate measuring instruments. It is hence necessary to establish accurate mathematical model for achieving the required accuracy due to the relationship between the central coordinate of the probes at the end of the measuring machine and the complexity of rotation angle of the joints. The classic Denavit-Hartenberg(D-H) model has defects when adjacent axes are parallel and ignores static flexibility error. Thus, this paper focuses a new mathematical model based on the generalized geometric error model for improving the D-H model. Additionally, the very fast simulated annealing algorithm is applied to calibrate the generalized geometric error parameters. Experiments demonstrat that the average error, after the calibration by the generalized geometric error model, is reduced by 0.500 1 mm and the standard deviation is reduced by 0.337 3 mm. The average error of the measurement based on the generalized geometric error model is 0.045 4 mm and the standard deviation is 0.032 3 mm. Both of the methods are superior to the MDH model, which verifies the effectiveness of the proposed method.
引文
[1] JOUBAIR A, SLAMANI M, BONEV I A. A novel XY-Theta precision table and a geometric procedure for its kinematic calibration[J]. Robots Computer-Integrated Manufacturing, 2012, 28(1): 57- 65.
[2] 罗哉,刘晖,田焜,等.关节臂式坐标测量机测量力误差分析及补偿[J].仪器仪表学报, 2017, 38(5):1159-1167.LUO Z, LIU H, TIAN K, et al. Error analysis and compensation of the measuring force of the articulated arm coordinate measuring machine[J]. Journal of University of Science and Technology of China, 2017,38(5):1159-1167.
[3] 赵磊,赵新华,王收军,等.柔性测量臂的RPY建模与误差标定[J].光学精密工程,2016,24(2): 365-371.ZHAO L, ZHAO X H, WANG SH J, et al. RPY modeling and error calibration of flexible measuring arm[J]. Optics and Precision Engineering, 2016, 24(2): 365-371.
[4] 冯旭刚,徐驰,章家岩,等.虚拟关节臂式坐标测量机模型的构建与验证[J].重庆大学学报, 2016, 39(6):135-140.FENG X G, XU CH, ZHANG J Y, et al. The establishment and testing of a model called virtual articulated arm coordinate measuring machine[J]. Journal of Chongqing University, 2016, 39(6):135-140.
[5] RUGBANI A, SCHREVE K. The kinematics and error modelling of a novel micro-CMM[J]. International Journal of Advanced Manufacturing Technology, 2014, 78 (5- 8):961-969.
[6] RAMU P, YAGUE J A, HOCKEN R J, et al. Development of a parametric model and virtual machine to estimate task specific measurement uncertainty for a five-axis multisensory coordinate measuring machine[J]. Precision Engineering, 2011, 35(3): 431- 439.
[7] 郑大腾,费业泰.柔性坐标测量机空间误差模型研究[J].机械工程学报,2010,46(10):19- 24.ZHENG D T, FEI Y T. Research on spatial error model of flexible coordinate measuring machine[J]. Journal of Mechanical Engineering, 2010, 46(10):19- 24.
[8] FURUTANI R, SHIMOJIMA K, TAKAMASU K. Kinematical calibration of articulated cmm using multiple simple artifacts.[C]. Annual Review of Progress in Applied Computational Electromagnetics, 2003: 1789- 1801.
[9] MEGGIOLARO M A, DUBOWSKY S, MAVROIDIS C. Geometric and elastic error calibration of a high accuracy patient positioning system[J]. Mechanism & Machine Theory, 2005, 40(4): 415- 427.
[10] TIAN W, GAO W, ZHANG D, et al. A general approach for error modeling of machine tools[J]. International Journal of Machine Tools & Manufacture, 2014, 79(4):17- 23.
[11] 黄奎,莫健华,余立华,等.柔性测量臂运动学建模及参数标定方法[J].西安交通大学学报,2010,44(8):122-126.HUANG K, MO J H, YU L H, et al. Kinematic model and parameter calibration for flexible articulated coordinate measuring arm[J]. Journal of Xi′an Jiaotong University, 2010, 44(8): 122-126.
[12] ZHAO D, WEI Z, ZHAO H, et al. Structural parameter calibration for parallel dual-joint coordinate measuring machine[J]. Nanotechnology & Precision Engineering, 2015, 13(4):287- 292.
[13] 张光澄,王文娟,韩会磊,等.非线性最优化计算方法[M].北京:高等教育出版社,2005.ZHANG G CH, WANG W J, HAN H L, et al. Nonlinear optimization calculation method [M]. Beijing: Higher Education Press, 2005.
[14] 潘志康,祝连庆,郭阳宽.基于内点法实现关节式坐标测量机参数标定[J].仪器仪表学报,2018,39(3):117-123.PAN ZH K, ZHU L Q, GUO Y K. Parameter calibration for articulated arm coordinate measuring machine based on interior point algorithm[J]. Chinese Journal of Scientific Instrument, 2018,39(3):117-123.
[15] 吴霞,郑大腾.基于D-H矩阵的柔性坐标测量机多测量模型研究[J].电子测量与仪器学报,2015,29(5):760-765.WU X, ZHENG D T. Research on multiple measurement models based on D-H matrix in flexible coordinate measuring machine[J]. Journal of Electronic Measurement and Instrumentation, 2015,29(5):760-765.
[16] 柯龙.关节臂式柔性坐标测量机测量空间分析[J].电子世界,2013(4):100-101.KE L. Measurement space analysis of articulated arm flexible coordinate measuring machine[J]. Electronic World, 2013(4): 100-101.
[17] RUIBO H, ZHAO Y J, YANG SH N, et al. Kinematic-parameter identification for serial- robot calibration based on POE formula[J]. IEEE Transactions on Robotics, 2010, 26(3): 411- 423.
[18] ZHANG T, DU L, DAI X. Test of robot distance error and compensation of kinematic full parameters[J]. Advances in Mechanical Engineering, 2014 (22):1-9.
[19] 于连栋,赵会宁.关节类坐标测量机关键技术及进展[J].仪器仪表学报,2017,38(8):1879-1888.YU L D, ZHAO H N. Key technologies and advances of articulated coordinate measuring machines[J]. Chinese Journal of Scientific Instrument, 2017, 38(8):1879-1888.
[20] 高贯斌,王文,林铿,等.应用改进模拟退火算法实现关节臂式坐标测量机的参数辨识[J].光学精密工程,2009,17(10):2499- 2505.GAO G B, WANG W, LIN K, et al. Parameter identification based on modified annealing algorithm for articulated arm CMMs[J]. Optics and Precision Engineering, 2009, 17(10): 2499- 2505.
[21] 童树之,王咏梅.坐标测量机精度校准方法的分析与比较[J].国外电子测量技术,2018, 37 (1):24- 28.TONG SH ZH, WANG Y M. Analysis and comparison of calibration methods for coordinate measuring machines[J]. Foreign Electronic Measurement Technology, 2018, 37 (1):24- 28.
[22] ZHAO H N, YU L D, JIA H K, et al. A new Kinematic model of portable articulated coordinate measuring machine[J]. Applied Sciences, 2016, 6(7):181.
[23] 陆晓芳,程顺有.模拟退火算法及其在多层密度界面反演中的应用[J].中国西部科技, 2011, 10(7):27- 29,51.LU X F, CHENG SH Y. Application of simulated annealing algorithm in the gravity inversion of multi-layer density interface[J]. Science and Technology of West China, 2011, 10(7): 27- 29,51.
[2] 罗哉,刘晖,田焜,等.关节臂式坐标测量机测量力误差分析及补偿[J].仪器仪表学报, 2017, 38(5):1159-1167.LUO Z, LIU H, TIAN K, et al. Error analysis and compensation of the measuring force of the articulated arm coordinate measuring machine[J]. Journal of University of Science and Technology of China, 2017,38(5):1159-1167.
[3] 赵磊,赵新华,王收军,等.柔性测量臂的RPY建模与误差标定[J].光学精密工程,2016,24(2): 365-371.ZHAO L, ZHAO X H, WANG SH J, et al. RPY modeling and error calibration of flexible measuring arm[J]. Optics and Precision Engineering, 2016, 24(2): 365-371.
[4] 冯旭刚,徐驰,章家岩,等.虚拟关节臂式坐标测量机模型的构建与验证[J].重庆大学学报, 2016, 39(6):135-140.FENG X G, XU CH, ZHANG J Y, et al. The establishment and testing of a model called virtual articulated arm coordinate measuring machine[J]. Journal of Chongqing University, 2016, 39(6):135-140.
[5] RUGBANI A, SCHREVE K. The kinematics and error modelling of a novel micro-CMM[J]. International Journal of Advanced Manufacturing Technology, 2014, 78 (5- 8):961-969.
[6] RAMU P, YAGUE J A, HOCKEN R J, et al. Development of a parametric model and virtual machine to estimate task specific measurement uncertainty for a five-axis multisensory coordinate measuring machine[J]. Precision Engineering, 2011, 35(3): 431- 439.
[7] 郑大腾,费业泰.柔性坐标测量机空间误差模型研究[J].机械工程学报,2010,46(10):19- 24.ZHENG D T, FEI Y T. Research on spatial error model of flexible coordinate measuring machine[J]. Journal of Mechanical Engineering, 2010, 46(10):19- 24.
[8] FURUTANI R, SHIMOJIMA K, TAKAMASU K. Kinematical calibration of articulated cmm using multiple simple artifacts.[C]. Annual Review of Progress in Applied Computational Electromagnetics, 2003: 1789- 1801.
[9] MEGGIOLARO M A, DUBOWSKY S, MAVROIDIS C. Geometric and elastic error calibration of a high accuracy patient positioning system[J]. Mechanism & Machine Theory, 2005, 40(4): 415- 427.
[10] TIAN W, GAO W, ZHANG D, et al. A general approach for error modeling of machine tools[J]. International Journal of Machine Tools & Manufacture, 2014, 79(4):17- 23.
[11] 黄奎,莫健华,余立华,等.柔性测量臂运动学建模及参数标定方法[J].西安交通大学学报,2010,44(8):122-126.HUANG K, MO J H, YU L H, et al. Kinematic model and parameter calibration for flexible articulated coordinate measuring arm[J]. Journal of Xi′an Jiaotong University, 2010, 44(8): 122-126.
[12] ZHAO D, WEI Z, ZHAO H, et al. Structural parameter calibration for parallel dual-joint coordinate measuring machine[J]. Nanotechnology & Precision Engineering, 2015, 13(4):287- 292.
[13] 张光澄,王文娟,韩会磊,等.非线性最优化计算方法[M].北京:高等教育出版社,2005.ZHANG G CH, WANG W J, HAN H L, et al. Nonlinear optimization calculation method [M]. Beijing: Higher Education Press, 2005.
[14] 潘志康,祝连庆,郭阳宽.基于内点法实现关节式坐标测量机参数标定[J].仪器仪表学报,2018,39(3):117-123.PAN ZH K, ZHU L Q, GUO Y K. Parameter calibration for articulated arm coordinate measuring machine based on interior point algorithm[J]. Chinese Journal of Scientific Instrument, 2018,39(3):117-123.
[15] 吴霞,郑大腾.基于D-H矩阵的柔性坐标测量机多测量模型研究[J].电子测量与仪器学报,2015,29(5):760-765.WU X, ZHENG D T. Research on multiple measurement models based on D-H matrix in flexible coordinate measuring machine[J]. Journal of Electronic Measurement and Instrumentation, 2015,29(5):760-765.
[16] 柯龙.关节臂式柔性坐标测量机测量空间分析[J].电子世界,2013(4):100-101.KE L. Measurement space analysis of articulated arm flexible coordinate measuring machine[J]. Electronic World, 2013(4): 100-101.
[17] RUIBO H, ZHAO Y J, YANG SH N, et al. Kinematic-parameter identification for serial- robot calibration based on POE formula[J]. IEEE Transactions on Robotics, 2010, 26(3): 411- 423.
[18] ZHANG T, DU L, DAI X. Test of robot distance error and compensation of kinematic full parameters[J]. Advances in Mechanical Engineering, 2014 (22):1-9.
[19] 于连栋,赵会宁.关节类坐标测量机关键技术及进展[J].仪器仪表学报,2017,38(8):1879-1888.YU L D, ZHAO H N. Key technologies and advances of articulated coordinate measuring machines[J]. Chinese Journal of Scientific Instrument, 2017, 38(8):1879-1888.
[20] 高贯斌,王文,林铿,等.应用改进模拟退火算法实现关节臂式坐标测量机的参数辨识[J].光学精密工程,2009,17(10):2499- 2505.GAO G B, WANG W, LIN K, et al. Parameter identification based on modified annealing algorithm for articulated arm CMMs[J]. Optics and Precision Engineering, 2009, 17(10): 2499- 2505.
[21] 童树之,王咏梅.坐标测量机精度校准方法的分析与比较[J].国外电子测量技术,2018, 37 (1):24- 28.TONG SH ZH, WANG Y M. Analysis and comparison of calibration methods for coordinate measuring machines[J]. Foreign Electronic Measurement Technology, 2018, 37 (1):24- 28.
[22] ZHAO H N, YU L D, JIA H K, et al. A new Kinematic model of portable articulated coordinate measuring machine[J]. Applied Sciences, 2016, 6(7):181.
[23] 陆晓芳,程顺有.模拟退火算法及其在多层密度界面反演中的应用[J].中国西部科技, 2011, 10(7):27- 29,51.LU X F, CHENG SH Y. Application of simulated annealing algorithm in the gravity inversion of multi-layer density interface[J]. Science and Technology of West China, 2011, 10(7): 27- 29,51.