新型可重构混联机器人Tricept-IV运动学标定方法研究
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摘要
本文密切结合汽车工业对先进零部件制造装备的重大需求,在国家863计划重点项目课题的资助下,系统研究了新型五坐标可重构混联机器人Tricept-IV的运动学标定方法,内容涉及机构位置分析、误差映射模型、参数辨识、几何误差源分析、误差补偿及相应的计算机仿真等。论文取得以下研究成果:
1)利用矢量法建立了含冗余驱动副的5自由度混联机器人Tricept-IV的位置正逆解模型,并借助数值迭代法与全空间比例分配法获得其位置正逆解算法。
2)将Tricept-IV并联机构各支链被动关节的姿态误差矢量分解为与位形无关的结构误差和随位形变化的许动方向误差两部分,利用闭环约束方程得到各被动关节许动误差与几何误差参数间的约束关系,进而得到动平台位姿误差与几何误差参数间的误差映射模型,结合串联结构误差传递关系最终构造出Tricept-IV机器人全误差参数映射模型。
3)建立了基于激光跟踪仪的误差参数辨识模型,根据误差参数数量级将误差源分为测量坐标系误差、机器人零位误差和几何误差三类,并将其辨识与补偿过程分为三个阶段逐级进行;利用辨识矩阵的最简阶梯行列式的性质将几何误差源分为独立项、相关项和零项三类,并选用了修正系统输入的在线补偿策略。
4)以简化误差参数辨识矩阵的条件数为评价指标,综合考虑辨识精度和效率,对测量点位置和数目进行了优化,有效地提高了辨识模型的鲁棒性;计算机仿真结果验证了本文所述运动学标定方法的正确性和有效性。
This thesis deals with the kinematic analysis, error modeling, parameter identification, source error analysis, error compensation and computer simulation of a novel reconfigurable hybrid robot—Tricept-IV. The following creative work has been completed.
1) The inverse and forward position analysis of Tricept-IV is carried out using vector based method with the consideration of the redundant translational degree of freedom. The corresponding algorithm is programmed using numerical iterative method and proportional distribution principle.
2) The orientation error vector of any passive joints in Tricept-IV robot can be decomposed to two parts—constant structural error vector and variable movable error vector. Using the above assumption, the linear mapping between the variable movable error vectors and all of the constant geometrical error parameters has been derived through the closed-loop constraint equations. Applying the linear mapping to one of kinematic chains of the robot, the full geometric error mapping model of the hybrid robot has been obtained.
3) The laser tracker is employed to the error measurement and the corresponding parameter identification model is also formulated. According to the size of the source errors, the procedure of the parameter identification and compensation are divided into three steps to identify measurement coordinate system errors, the home position error of the robot and the geometric errors respectively. By analyzing the reduced row echelon form of parameter identification matrix, the source errors are separated to independent, relevant and zero ones. The strategy of the error compensation is carried out by modifying the system input.
4) The locations and number of the measurement points is optimized using the condition number of the identification matrix as the evaluation index in order to achieve proper efficiency and robustness. The feasibility and effectiveness of the proposed kinematic calibration method is verified by simulation results.
1)利用矢量法建立了含冗余驱动副的5自由度混联机器人Tricept-IV的位置正逆解模型,并借助数值迭代法与全空间比例分配法获得其位置正逆解算法。
2)将Tricept-IV并联机构各支链被动关节的姿态误差矢量分解为与位形无关的结构误差和随位形变化的许动方向误差两部分,利用闭环约束方程得到各被动关节许动误差与几何误差参数间的约束关系,进而得到动平台位姿误差与几何误差参数间的误差映射模型,结合串联结构误差传递关系最终构造出Tricept-IV机器人全误差参数映射模型。
3)建立了基于激光跟踪仪的误差参数辨识模型,根据误差参数数量级将误差源分为测量坐标系误差、机器人零位误差和几何误差三类,并将其辨识与补偿过程分为三个阶段逐级进行;利用辨识矩阵的最简阶梯行列式的性质将几何误差源分为独立项、相关项和零项三类,并选用了修正系统输入的在线补偿策略。
4)以简化误差参数辨识矩阵的条件数为评价指标,综合考虑辨识精度和效率,对测量点位置和数目进行了优化,有效地提高了辨识模型的鲁棒性;计算机仿真结果验证了本文所述运动学标定方法的正确性和有效性。
This thesis deals with the kinematic analysis, error modeling, parameter identification, source error analysis, error compensation and computer simulation of a novel reconfigurable hybrid robot—Tricept-IV. The following creative work has been completed.
1) The inverse and forward position analysis of Tricept-IV is carried out using vector based method with the consideration of the redundant translational degree of freedom. The corresponding algorithm is programmed using numerical iterative method and proportional distribution principle.
2) The orientation error vector of any passive joints in Tricept-IV robot can be decomposed to two parts—constant structural error vector and variable movable error vector. Using the above assumption, the linear mapping between the variable movable error vectors and all of the constant geometrical error parameters has been derived through the closed-loop constraint equations. Applying the linear mapping to one of kinematic chains of the robot, the full geometric error mapping model of the hybrid robot has been obtained.
3) The laser tracker is employed to the error measurement and the corresponding parameter identification model is also formulated. According to the size of the source errors, the procedure of the parameter identification and compensation are divided into three steps to identify measurement coordinate system errors, the home position error of the robot and the geometric errors respectively. By analyzing the reduced row echelon form of parameter identification matrix, the source errors are separated to independent, relevant and zero ones. The strategy of the error compensation is carried out by modifying the system input.
4) The locations and number of the measurement points is optimized using the condition number of the identification matrix as the evaluation index in order to achieve proper efficiency and robustness. The feasibility and effectiveness of the proposed kinematic calibration method is verified by simulation results.
引文
[1] Weck M, Staimer D, Parallel kinematic machine tools --- current state and future potentials, Annals of the CIRP, 2002, 51(2): 671-683
[2]汪劲松,黄田,并联机床——机床行业面临的机遇与挑战,中国机械工程, 1999, 10(10): 1103-1107
[3]马晓丽,陈艾华,并联机器人机构的创新与应用研究进展,机床与液压, 2007, (2): 235-237
[4] Weck M, Staimer D, Accuracy issues of parallel kinematic machine tools, IMechE Journal of Multi-body Dynamics, Part K, 2002, 216: 51-57
[5]何小妹,丁洪生,并联机床运动学标定研究综述,机床与液压, 2004, (10): 9-11
[6] Huang T, Whitehouse D J, Chetwynd D, A unified error modeling for tolerance design, assembly and error compensation of a class of parallel kinematic machines with parallelogram struts, Annals of the CIRP, 2002, 52(1): 297-301
[7] Mooring B W, Roth Z S, Driels M R, Fundamentals of Manipulator Calibration, John Wiley & Sons, New York, 1991
[8] Huang T, Chetwynd D G, Whitehouse D J, A general and novel approach for parameter identification of 6-DOF parallel kinematic machines. Mechanism and Machine Theory, 2005, 40: 219-239
[9]于大永,韩俊伟,丛大成,基于三坐标测量机的并联机器人运动学标定,全国先进制造技术高层论坛暨制造业自动化信息化技术研讨会论文集, 2005,239-243
[10]王东署,迟健男,机器人运动学标定综述,计算机应用研究, 2007, 24(9): 8-11
[11] Huang T, Whitehouse D J, A Simple yet effective approach for error compensation of a tripod-based parallel kinematic machine, Annals of the CIRP, 2000, 49(1): 285-288
[12]唐国宝,黄田, Delta并联机构精度标定方法研究,机械工程学报, 2003, 39(8): 55-60
[13]史长虹,张同庄,丁洪生,变轴数控机床精度研究进展,组合机床与自动化技术, 200l, (4): 8-10
[14]石则昌,刘深厚,机构精确度,北京:高等教育出版社, 1995
[15]徐卫良,张启先,空间机构运动误差的概率分析和蒙特卡洛模拟,机械工程学报, 1988, 24(3): 97-104
[16] Wang J, Masory O, On the accuracy of a Stewart platform --- Part I: The effect of manufacturing tolerances, IEEE International Conference on Robotics and Automation, Atlanta, USA, 1993, 114-120
[17] Patel A J, Ehmann K F, Volumetric error of a Stewart platform-based machine tool, Annals of the CIRP, 1997, 46(1): 287-290
[18] Soons J A, Error analysis of a hexapod machine tool, Laser Metrology and Machine Performance, 1997: 346-358
[19] Wang S M, Ehmann K F, Error model and accuracy analysis of a six-DOF Stewart platform, ASME Journal of Manufacturing Science and Engineering, 2002, 124(2): 286-295
[20] Nahvi A N, Hollerbach J M, Hayward V, Calibration of a parallel robot using multiple kinematic closed loops, Proc. IEEE International Conference on Robotics and Automation, 1994, 142-148
[21] Maurine P, Dombre E, A calibration procedure for the parallel robot delta 4, Proc. IEEE International Conference on Robotics and Automation, Atlanta, USA, 1996, 975-980
[22]李亚, 3-HSS并联机床精度设计与运动学标定方法研究[博士学位论文],天津:天津大学, 2002
[23]李思维,黄田,一种含平行四边形支链的3自由度并联机构姿态精度综合与装配工艺设计,机械工程学报, 2003, 39(7): 38-42
[24] Everett L J, Driels M, Mooring W, Kinematic modeling for robot calibration. IEEE Trans. on Robotics and Automation, 1987, 4: 183-189
[25] Judd R P, Knasinski A B, A technique to calibrate industrial robots with experimental verification. IEEE Trans. on Robotics and Automation, 1990, 6: 20-30
[26] Mooring B W, Padavala S S, Effect of kinematic model complexity on manipulator accuracy, Proc. IEEE Inter. Conf. on Robotics and Automation, 1989, 593-598
[27] Masory O, Wang J, Zhuang H, On the accuracy of a Stewart platform --- Part II: kinematic calibration and compensation, Proc. IEEE Inter. Conf. on Robotics and Automation,1993, 725-731
[28]彭斌彬,高峰,并联机器人的标定建模,机械工程学报, 2005, 41(8): 132-135
[29] Patel A J, Ehmann K F, Calibration of a hexapod machine tool using a redundant leg, International Journal of Machine Tools & Manufacture, 2000, 40: 489-512
[30] Ota H, Shibukawa T, Tooyama T, Forward kinematic calibration and gravity compensation for parallel-mechanism-based machine tools, IMechE Journal of Multi-body Dynamics, Part K, 2002, 216: 39-49
[31] Yukio T, Gang S, Hiroaki F, DBB-Based kinematic calibration method for in-parallel actuated mechanisms using a Fourier series, ASME Journal of Mechanical Design, 2004, 126: 856-865
[32] Ihara Y, Ishida T, Kakino Y, Kinematic calibration of a hexapod machine tool by using circular test, Proc. Japan-USA Flexible Automation Conference, Michigan, USA, 2000, 1-4
[33] Zhuang H, Yan J, Masory O, Calibration of Stewart platforms and other parallel manipulators by minimizing inverse kinematic residuals, Journal of Robotic Systems, 1998, 15(7): 395-405
[34] Morris R. Vision-based automatic theodolite for robot calibration, IEEE Transactions on Robotics and Automation, 1991, 7(3):351-360
[35] Fraczek J. Calibration of multi robot system without and under load using electronic theodolites, Proc. IEEE International Conference on Robotics and Automation, 1999, 71-75
[36] Driels M R, Swayze L W. Full-pose calibration of a robot manipulator using a coordinate measuring machine, International Journal of Advanced Manufacturing Technology, 1993, 8: 34-41
[37]白月飞,高青松,金伟,浅谈三坐标测量机及其应用,现代制造技术与装备, 2009, 6, 29-31
[38]叶声华,王一,任永杰,基于激光跟踪仪的机器人运动学参数标定方法,天津大学学报, 2007, 40(2): 202-205
[39]孙华德,陈五一,陈鼎昌,用激光跟踪仪标定并联机床的理论探讨,机床与液压, 2002, (5): 16-18
[40] Veitschegger W K, Wu C H. Robot calibration and compensation, IEEE Trans on Robotics and Automation, 1988, 4(6): 643-656
[41] Char K S, Young K, Tuersley I, A practical calibration process using partial information for commercial Stewart platform, Robotica, 2002, 20(3): 315-322
[42]黄田,汪劲松, David J,并联构型装备几何参数可辨识性研究,机械工程学报, 2004, 38(S): 1-6
[43] David D, Emiris I Z, Robust parallel robot calibration with partial information, Proc. 2001 IEEE International Conference on Robotics and Automation, Seal, Korea, 2001, 5(3): 262-267
[44]魏世民,廖启征,黄靖远,平面3-RPR机构运动学标定的矩阵重构法,清华大学学报(自然科学版), 2001, 41(8): 33-36
[45] Grotjahn M, Daemi M, Heimann B. Friction and rigid body identification of robot dynamics, International Journal of Solids and Structures, 2001, 38(10): 1889- 1902
[46] Martinele A, Tomatis N, Simultaneous localization and geometry calibration for mobile robot, Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, USA, 2003: 1499-1504
[47] Renders J M, Kinematic calibration and geometrical parameter identification for robots, IEEE Trans. on Robotics and Automation, 1997, 7(6): 721-731
[48] Horning R J, A comparison of identification techniques for robot calibration, Case Western Reserve University, 1998
[49]黄真,孔令富,方跃法,并联机器人机构学理论及控制,北京:机械工业出版社, 1997
[50] Zhuang H Q, Wu W C, Roth Z S, Camera-assisted calibration of SCARA arms, IEEE , 1995, 1: 507-51
[2]汪劲松,黄田,并联机床——机床行业面临的机遇与挑战,中国机械工程, 1999, 10(10): 1103-1107
[3]马晓丽,陈艾华,并联机器人机构的创新与应用研究进展,机床与液压, 2007, (2): 235-237
[4] Weck M, Staimer D, Accuracy issues of parallel kinematic machine tools, IMechE Journal of Multi-body Dynamics, Part K, 2002, 216: 51-57
[5]何小妹,丁洪生,并联机床运动学标定研究综述,机床与液压, 2004, (10): 9-11
[6] Huang T, Whitehouse D J, Chetwynd D, A unified error modeling for tolerance design, assembly and error compensation of a class of parallel kinematic machines with parallelogram struts, Annals of the CIRP, 2002, 52(1): 297-301
[7] Mooring B W, Roth Z S, Driels M R, Fundamentals of Manipulator Calibration, John Wiley & Sons, New York, 1991
[8] Huang T, Chetwynd D G, Whitehouse D J, A general and novel approach for parameter identification of 6-DOF parallel kinematic machines. Mechanism and Machine Theory, 2005, 40: 219-239
[9]于大永,韩俊伟,丛大成,基于三坐标测量机的并联机器人运动学标定,全国先进制造技术高层论坛暨制造业自动化信息化技术研讨会论文集, 2005,239-243
[10]王东署,迟健男,机器人运动学标定综述,计算机应用研究, 2007, 24(9): 8-11
[11] Huang T, Whitehouse D J, A Simple yet effective approach for error compensation of a tripod-based parallel kinematic machine, Annals of the CIRP, 2000, 49(1): 285-288
[12]唐国宝,黄田, Delta并联机构精度标定方法研究,机械工程学报, 2003, 39(8): 55-60
[13]史长虹,张同庄,丁洪生,变轴数控机床精度研究进展,组合机床与自动化技术, 200l, (4): 8-10
[14]石则昌,刘深厚,机构精确度,北京:高等教育出版社, 1995
[15]徐卫良,张启先,空间机构运动误差的概率分析和蒙特卡洛模拟,机械工程学报, 1988, 24(3): 97-104
[16] Wang J, Masory O, On the accuracy of a Stewart platform --- Part I: The effect of manufacturing tolerances, IEEE International Conference on Robotics and Automation, Atlanta, USA, 1993, 114-120
[17] Patel A J, Ehmann K F, Volumetric error of a Stewart platform-based machine tool, Annals of the CIRP, 1997, 46(1): 287-290
[18] Soons J A, Error analysis of a hexapod machine tool, Laser Metrology and Machine Performance, 1997: 346-358
[19] Wang S M, Ehmann K F, Error model and accuracy analysis of a six-DOF Stewart platform, ASME Journal of Manufacturing Science and Engineering, 2002, 124(2): 286-295
[20] Nahvi A N, Hollerbach J M, Hayward V, Calibration of a parallel robot using multiple kinematic closed loops, Proc. IEEE International Conference on Robotics and Automation, 1994, 142-148
[21] Maurine P, Dombre E, A calibration procedure for the parallel robot delta 4, Proc. IEEE International Conference on Robotics and Automation, Atlanta, USA, 1996, 975-980
[22]李亚, 3-HSS并联机床精度设计与运动学标定方法研究[博士学位论文],天津:天津大学, 2002
[23]李思维,黄田,一种含平行四边形支链的3自由度并联机构姿态精度综合与装配工艺设计,机械工程学报, 2003, 39(7): 38-42
[24] Everett L J, Driels M, Mooring W, Kinematic modeling for robot calibration. IEEE Trans. on Robotics and Automation, 1987, 4: 183-189
[25] Judd R P, Knasinski A B, A technique to calibrate industrial robots with experimental verification. IEEE Trans. on Robotics and Automation, 1990, 6: 20-30
[26] Mooring B W, Padavala S S, Effect of kinematic model complexity on manipulator accuracy, Proc. IEEE Inter. Conf. on Robotics and Automation, 1989, 593-598
[27] Masory O, Wang J, Zhuang H, On the accuracy of a Stewart platform --- Part II: kinematic calibration and compensation, Proc. IEEE Inter. Conf. on Robotics and Automation,1993, 725-731
[28]彭斌彬,高峰,并联机器人的标定建模,机械工程学报, 2005, 41(8): 132-135
[29] Patel A J, Ehmann K F, Calibration of a hexapod machine tool using a redundant leg, International Journal of Machine Tools & Manufacture, 2000, 40: 489-512
[30] Ota H, Shibukawa T, Tooyama T, Forward kinematic calibration and gravity compensation for parallel-mechanism-based machine tools, IMechE Journal of Multi-body Dynamics, Part K, 2002, 216: 39-49
[31] Yukio T, Gang S, Hiroaki F, DBB-Based kinematic calibration method for in-parallel actuated mechanisms using a Fourier series, ASME Journal of Mechanical Design, 2004, 126: 856-865
[32] Ihara Y, Ishida T, Kakino Y, Kinematic calibration of a hexapod machine tool by using circular test, Proc. Japan-USA Flexible Automation Conference, Michigan, USA, 2000, 1-4
[33] Zhuang H, Yan J, Masory O, Calibration of Stewart platforms and other parallel manipulators by minimizing inverse kinematic residuals, Journal of Robotic Systems, 1998, 15(7): 395-405
[34] Morris R. Vision-based automatic theodolite for robot calibration, IEEE Transactions on Robotics and Automation, 1991, 7(3):351-360
[35] Fraczek J. Calibration of multi robot system without and under load using electronic theodolites, Proc. IEEE International Conference on Robotics and Automation, 1999, 71-75
[36] Driels M R, Swayze L W. Full-pose calibration of a robot manipulator using a coordinate measuring machine, International Journal of Advanced Manufacturing Technology, 1993, 8: 34-41
[37]白月飞,高青松,金伟,浅谈三坐标测量机及其应用,现代制造技术与装备, 2009, 6, 29-31
[38]叶声华,王一,任永杰,基于激光跟踪仪的机器人运动学参数标定方法,天津大学学报, 2007, 40(2): 202-205
[39]孙华德,陈五一,陈鼎昌,用激光跟踪仪标定并联机床的理论探讨,机床与液压, 2002, (5): 16-18
[40] Veitschegger W K, Wu C H. Robot calibration and compensation, IEEE Trans on Robotics and Automation, 1988, 4(6): 643-656
[41] Char K S, Young K, Tuersley I, A practical calibration process using partial information for commercial Stewart platform, Robotica, 2002, 20(3): 315-322
[42]黄田,汪劲松, David J,并联构型装备几何参数可辨识性研究,机械工程学报, 2004, 38(S): 1-6
[43] David D, Emiris I Z, Robust parallel robot calibration with partial information, Proc. 2001 IEEE International Conference on Robotics and Automation, Seal, Korea, 2001, 5(3): 262-267
[44]魏世民,廖启征,黄靖远,平面3-RPR机构运动学标定的矩阵重构法,清华大学学报(自然科学版), 2001, 41(8): 33-36
[45] Grotjahn M, Daemi M, Heimann B. Friction and rigid body identification of robot dynamics, International Journal of Solids and Structures, 2001, 38(10): 1889- 1902
[46] Martinele A, Tomatis N, Simultaneous localization and geometry calibration for mobile robot, Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, USA, 2003: 1499-1504
[47] Renders J M, Kinematic calibration and geometrical parameter identification for robots, IEEE Trans. on Robotics and Automation, 1997, 7(6): 721-731
[48] Horning R J, A comparison of identification techniques for robot calibration, Case Western Reserve University, 1998
[49]黄真,孔令富,方跃法,并联机器人机构学理论及控制,北京:机械工业出版社, 1997
[50] Zhuang H Q, Wu W C, Roth Z S, Camera-assisted calibration of SCARA arms, IEEE , 1995, 1: 507-51