6R型工业机器人关节刚度辨识与实验研究
|
摘要
由于具有可编程性、适应性强、柔性强和花费少等优点,如今工业机器人已经广泛应用于各行各业,在加工任务中也逐渐使用机器人进行操作,比如研磨、去毛刺、抛光和铣削等基本加工任务。然而机器人成功应用于加工操作的事例却不多见,究其原因主要是工业机器人相对于传统的CNC加工中心来讲刚度非常低。典型的关节工业机器人的刚度通常都低于1N/μm,然而标准的CNC加工中心的刚度通常都高于50N/μm。本文主要工作是通过对柔性工业机器人的刚度进行分析进而提高机器人的加工能力。
本文首先分析了KUAK KR16机器人的结构特点,运用D-H方法建立了机器人的运动学方程,然后进行了机器人逆运动学的推导以及雅可比矩阵的详细推导。针对雅可比矩阵的行列式为零的情况,分析了机器人的两类奇异位姿。
其次分析了影响机器人末端绝对定位精度的误差来源,针对变形误差建立了机器人的关节刚度模型,建立关节刚度模型应满足下列要求:该模型能准确的预测任意外力作用下机器人结构变形值,并且刚度模型应该比较简单能够进行实时变形补偿。建立满足上述要求的关节刚度模型后,为保证辨识的准确性又提出了机器人关节刚度辨识的观测方法,保证了机器人关节刚度辨识实验的可行性。
然后设计了关节刚度的辨识实验。通过滑轮加载装置在机器人末端施加外载荷,并使用激光跟踪仪测量机器人末端位移。然后根据最小二乘法辨识出关节刚度的实际值,结果表明实验方法可行
最后设计了外载荷作用下机器人末端变形的补偿实验方法。在机器人末端直接加载重物块,通过补偿模型计算出变形的理论值再对机器人末端进行补偿,对补偿后的结果进行测量,发现得到较好的补偿结果。
Currently, the industrial robot has been applied to many kinds of industries due to its programmability, adaptivity, flexibility and low cost. And the industrial robot is already applied to machining tasks. However, it has not seen many success stories for such applications. The reason is that the stiffness of industrial robot is much lower than that of a traditional CNC machine. The stiffness for a typical articulated robot is usually less than1N/μm, while a standard CNC machine center often has stiffness greater than 50N/μm.This paper mainly analyzes the stiffness of flexible industrial robots in order to improve robotic machining performance.
Firstly in this paper considering KUKA KR16 robot’s geometrical structure, we establish the kinematics of the robot by means of D-H method. And then, detailed kinematics inverse solutions are calculated, and the Jacobian matrix is also solved. We also analyze two types of singular configuration of the robot when considering the determinant of the Jacobian matrix equals to zero.
Secondly aiming to increase the robot’s absolute accuracy, we analyze the error sources which mostly influence the robot’s absolute accuracy. And then, the joint stiffness model is established to consider the effect of elastic error in industrial robot, which is conducted by the principle of that the model should be accurate enough for the prediction of robot structure deformation under arbitrary load conditions and it needs to be simple enough for real time implementation. And we propose one observation strategy for joint stiffness identification, which can make sure each unknown parameter of joint stiffness is observable.
Then an experimental method is designed to identify the joint stiffness, which is composed by the API laser tracker and the cable pulley system. The external load is exerted on the end point of the robot by way of the cable pulley system and the displacement of the end point is measured via the API laser tracker. And then the joint stiffness is identified through the least squares method. The identification results are proved to be effective due to very small residual errors.
At last another experiment is implemented to give deformation compensation of the end point under the external load. The dead weight is exerted on the end point of the robot. Based on the stiffness model identified and the known payload before, the deformation due to the payload is calculated in MATALAB and the joint reference for the robot controller is updated. And we find the compensation results are proved to be effective.
本文首先分析了KUAK KR16机器人的结构特点,运用D-H方法建立了机器人的运动学方程,然后进行了机器人逆运动学的推导以及雅可比矩阵的详细推导。针对雅可比矩阵的行列式为零的情况,分析了机器人的两类奇异位姿。
其次分析了影响机器人末端绝对定位精度的误差来源,针对变形误差建立了机器人的关节刚度模型,建立关节刚度模型应满足下列要求:该模型能准确的预测任意外力作用下机器人结构变形值,并且刚度模型应该比较简单能够进行实时变形补偿。建立满足上述要求的关节刚度模型后,为保证辨识的准确性又提出了机器人关节刚度辨识的观测方法,保证了机器人关节刚度辨识实验的可行性。
然后设计了关节刚度的辨识实验。通过滑轮加载装置在机器人末端施加外载荷,并使用激光跟踪仪测量机器人末端位移。然后根据最小二乘法辨识出关节刚度的实际值,结果表明实验方法可行
最后设计了外载荷作用下机器人末端变形的补偿实验方法。在机器人末端直接加载重物块,通过补偿模型计算出变形的理论值再对机器人末端进行补偿,对补偿后的结果进行测量,发现得到较好的补偿结果。
Currently, the industrial robot has been applied to many kinds of industries due to its programmability, adaptivity, flexibility and low cost. And the industrial robot is already applied to machining tasks. However, it has not seen many success stories for such applications. The reason is that the stiffness of industrial robot is much lower than that of a traditional CNC machine. The stiffness for a typical articulated robot is usually less than1N/μm, while a standard CNC machine center often has stiffness greater than 50N/μm.This paper mainly analyzes the stiffness of flexible industrial robots in order to improve robotic machining performance.
Firstly in this paper considering KUKA KR16 robot’s geometrical structure, we establish the kinematics of the robot by means of D-H method. And then, detailed kinematics inverse solutions are calculated, and the Jacobian matrix is also solved. We also analyze two types of singular configuration of the robot when considering the determinant of the Jacobian matrix equals to zero.
Secondly aiming to increase the robot’s absolute accuracy, we analyze the error sources which mostly influence the robot’s absolute accuracy. And then, the joint stiffness model is established to consider the effect of elastic error in industrial robot, which is conducted by the principle of that the model should be accurate enough for the prediction of robot structure deformation under arbitrary load conditions and it needs to be simple enough for real time implementation. And we propose one observation strategy for joint stiffness identification, which can make sure each unknown parameter of joint stiffness is observable.
Then an experimental method is designed to identify the joint stiffness, which is composed by the API laser tracker and the cable pulley system. The external load is exerted on the end point of the robot by way of the cable pulley system and the displacement of the end point is measured via the API laser tracker. And then the joint stiffness is identified through the least squares method. The identification results are proved to be effective due to very small residual errors.
At last another experiment is implemented to give deformation compensation of the end point under the external load. The dead weight is exerted on the end point of the robot. Based on the stiffness model identified and the known payload before, the deformation due to the payload is calculated in MATALAB and the joint reference for the robot controller is updated. And we find the compensation results are proved to be effective.
引文
[1] Siciliano, Bruno, Khatib, Oussama (Eds.). Springer handbook of robotics. Springer, 2008:287-288.
[2] Robert P. Judd and Al. B. Knasinski. A technique to calibrate industrial robots with experimental verification. In Proceedings of 1987 IEEE International Conference on Robotics and Automation, pp.351-357, April1987.
[3] Pashkevich A, Chablat D, Wenger P. Stiffness analysis of overconstrained parallel manipulators. Mechanism and Machine Theory 2009; 44: 966–982.
[4] Ostring M, Gunnnarsson S, Norrlof M. Closed-loop identification of an industrial robot containing flexibilities. Control Engineering Practice 2009; 11:291–300.
[5] M. Abderrahim, A. Khams, S. Garrido and L. Moreno,“Accuracy and calibration issues of industrial manipulators,”in Industrial Robotics: Programming, Simulation and Applications, L. K. Haut, Ed. Germany: Pro Literature Verlag, 2007, pp. 131-146.
[6] E. Abele, M. Wergild, and M. Kulak,“Increasing the accuracy of a milling industrial robot,”Production Engineering, vol. 13, no. 2, pp.221-224, 2006.
[7] M. Seltzer, O. von Stryker, E. Abele , J. Bauer, and M. Wergild,“High speed cutting with industrial robots: towards model based compensation of deviations,”in Proceedings of Robotic, Munich, Germany, 2008, pp. 143-146.
[8] E. Abele, M. Wergild and S. Rothenbücher,“Modeling and identification of an industrial robot for machining applications,”CIRP Annals - Manufacturing Technology, vol. 56, no. 1, pp. 387-390,2007.
[9] E. Abele, S. Rothenbücher, and M. Wergild,“Cartesian compliance model for industrial robots using virtual Joints,”Production Engineering, vol. 2, no. 3, pp. 339-343, 2008.
[10] T. Oiwa,“Error compensation system for joints, links and machine frame of parallel kinematics machines,”Int. J. Robotics Research, vol. 24, no. 12, pp. 1087-1102, 2005.
[11] T. Yang, H.S. Fan and S.C. Lin. Joint stiffness identification using FRF measurements, Computers and Structures. 2003, 81 :2549–2556.
[12] Swerves, et al. Optimal robot excitation and identification. IEEE Transactions on Robotics and Automation, 1997, 13:730-40.
[13]王世军,黄玉美,王凯.柔性机械臂关节刚度的一种间接测量方法.机床与液压. 2004, (8):154-177.
[14] F. Demister and H. van Brussel. Experimental compliance breakdown of industrialrobots, Trans. ASME, J. Mech. Des. 1994, 116:1065-1072.
[15] Abele E, Wergild M, Rothenbücher S. Modeling and identification of an industrial robot for machining applications. Ann CIRP, 2007, 56(1):387–390。
[16] T. Tsumugiwa, R. Yokogawa, and K. Hara. Measurement Method for Compliance of Vertical-Multi-Articulated Robot-Application to 7-DOF Robot PA-10. Proceeding of the IEEE International Conference on Robotics and Automation, 2003:2741-2746.
[17]黄心汉.机器人刚度的测试方法.机器人, 1988, (3):45-50.
[18] G. Alici and B. Shirinzadeh,“Enhanced stiffness modeling, identification and characterization for robot manipulators,”IEEE Trans. Robotics, vol. 21, no. 4, pp. 554-564, Aug. 2005.
[19]熊有伦.机器人技术基础.武汉:华中科技大学出版社,1996
[20] John J. Craig.机器人学导论.贠超等译.北京:机械工业出版社,2006
[21] J. Denavit and R. S. Hartenberg,“A Kinematics Notation for Lower-Pair Mechanisms Based on Metrics”, Journal of Applied Mechanics, pp.215-221, June 1955.
[22] J. Colson and N.D. Perreira,“Kinematics Arrangements Used in Industrial Robots”, 13th Industrial Robots Conference Proceedings,April1983
[23]杨达毅, 6R工业机器人的运动学研究:[硕士学位论文].长春:吉林大学图书馆,2005
[24]程永伦,朱世强,罗利佳等.基于Matlab的QJ-6R焊接机器人运动学分析及仿真[J].机电工程,2007,24(11): 107~110
[25]孙祥,徐流美,吴清. MATLAB 7.0基础教程.北京:清华大学出版社,2005
[26]施晓红,周佳.精通GUI图形界面编程.北京:北京大学出版社,2003
[27] D. Piper and B. Roth,“The kinematics of Manipulators Under Computer Control”, Proceeding of the Second International Congress on Theory of Machines and Mechanisms,Vol.2,Zakopane,Poland, 1969,pp.159-169.
[28] D. Piper,“The kinematics of Manipulators Under Computer Control”, Unpublished Ph.D. Thesis, Stanford University, 1968
[29] R.P. Pual, B. Shimano, and G. Mayer,“Kinematics Control Equations for Simple Manipulators”, IEEE Transactions on Systems, Man, and Cybernetics, Vol.SMC-11, 6, 1981
[30] B. Gorla and M. Renaaud, Robots Manipulators, Cepadues-Editions, Toulouse, 1984
[31] C. Wampler,“Wrist Singularities: Theory and Practice”, In the Robotics Review 2, , MIT press,Cambridge,MA,1992
[32] J. Hollerbach,“A Survey of Kinematic Calibration”, In the Robotics Review, MIT Press, Cambridge, MA, 1989.
[33] J. Flanz, et al., 1996. Design approach for a highly accurate patient positioning system for NPTC, in: Proceedings of the PTOOG XXV and Hadrontherapy Symposium, Belgium, pp. 1–5.
[34] W. Hamel, S. Marland, T. Widner, 1997. A model-based concept for telerobotic control of decontamination and dismantlement tasks, in: Proceedings of the 1997 IEEE International Conference of Robotics and Automation, Albuquerque, New Mexico.
[35] Slocum A, precision machine design, Englewood cliffs, 1992.
[36] Robert P. Judd and Al. B. Knasinski. A technique to calibrate industrial robots with experimental verification. In Proceedings of 1987 IEEE International Conference on Robotics and Automation, pp.351-357, April, 1987.
[37] Marco A. Meggiolaro, Steven Dubowsky, Constantinos Mavroidis. Geometric and elastic error calibration of a high accuracy patient positioning system, Mechanism and Machine Theory, 2005,40: 415-427.
[38]费仁元,张慧慧.机器人机械设计和分析.北京:北京工业大学出版社,1998
[39] Jianjun Wang, Hui Zhang, and Thomas Fuhlbrigge. Improving Machining Accuracy with Robot Deformation Compensation, The 2009 IEEE International Conference on Intelligent Robots and Systems, pp: 11-15, October, 2009.
[40]杨世兴,张宝泉,赵永秀. MATLAB在最小二乘参数辨识中的应用[J].电子技术,2003,7(11): 44~45
[41]王可,毛志坚.基于MATLAB实现最小二乘曲线拟合[J].北京广播学院学报(自然科学版),2005,12(2): 52~54
[42] [42]许启发. MATLAB中方程组的解与回归模型的最小二乘估计[J].统计与决策,2005,3(下): 21~24
[43] Morris R. Driels, Uday S. Pathre. Vision-based automatic theodolite for robot calibration [C]. IEEE transaction on robotic and automation, 1991, 7(3): 351~360
[44]康继平.自动经纬仪跟踪测量中运动目标的跟踪算法设计.内蒙古工业大学硕士论文,2009.
[45]宋开臣.三坐标测量机动态误差补偿的研究[J].仪器仪表学报,1999,7(1):10-15.
[46] M. Vincze, J. P. Prenninger, H. Gander. A Laser Tracking System to Measure Position and Orientation of Robot End Effectors Under Motion. The International Journal of Robotics Research, Vol.13, No.4, August 1994, pp: 305-314.
[2] Robert P. Judd and Al. B. Knasinski. A technique to calibrate industrial robots with experimental verification. In Proceedings of 1987 IEEE International Conference on Robotics and Automation, pp.351-357, April1987.
[3] Pashkevich A, Chablat D, Wenger P. Stiffness analysis of overconstrained parallel manipulators. Mechanism and Machine Theory 2009; 44: 966–982.
[4] Ostring M, Gunnnarsson S, Norrlof M. Closed-loop identification of an industrial robot containing flexibilities. Control Engineering Practice 2009; 11:291–300.
[5] M. Abderrahim, A. Khams, S. Garrido and L. Moreno,“Accuracy and calibration issues of industrial manipulators,”in Industrial Robotics: Programming, Simulation and Applications, L. K. Haut, Ed. Germany: Pro Literature Verlag, 2007, pp. 131-146.
[6] E. Abele, M. Wergild, and M. Kulak,“Increasing the accuracy of a milling industrial robot,”Production Engineering, vol. 13, no. 2, pp.221-224, 2006.
[7] M. Seltzer, O. von Stryker, E. Abele , J. Bauer, and M. Wergild,“High speed cutting with industrial robots: towards model based compensation of deviations,”in Proceedings of Robotic, Munich, Germany, 2008, pp. 143-146.
[8] E. Abele, M. Wergild and S. Rothenbücher,“Modeling and identification of an industrial robot for machining applications,”CIRP Annals - Manufacturing Technology, vol. 56, no. 1, pp. 387-390,2007.
[9] E. Abele, S. Rothenbücher, and M. Wergild,“Cartesian compliance model for industrial robots using virtual Joints,”Production Engineering, vol. 2, no. 3, pp. 339-343, 2008.
[10] T. Oiwa,“Error compensation system for joints, links and machine frame of parallel kinematics machines,”Int. J. Robotics Research, vol. 24, no. 12, pp. 1087-1102, 2005.
[11] T. Yang, H.S. Fan and S.C. Lin. Joint stiffness identification using FRF measurements, Computers and Structures. 2003, 81 :2549–2556.
[12] Swerves, et al. Optimal robot excitation and identification. IEEE Transactions on Robotics and Automation, 1997, 13:730-40.
[13]王世军,黄玉美,王凯.柔性机械臂关节刚度的一种间接测量方法.机床与液压. 2004, (8):154-177.
[14] F. Demister and H. van Brussel. Experimental compliance breakdown of industrialrobots, Trans. ASME, J. Mech. Des. 1994, 116:1065-1072.
[15] Abele E, Wergild M, Rothenbücher S. Modeling and identification of an industrial robot for machining applications. Ann CIRP, 2007, 56(1):387–390。
[16] T. Tsumugiwa, R. Yokogawa, and K. Hara. Measurement Method for Compliance of Vertical-Multi-Articulated Robot-Application to 7-DOF Robot PA-10. Proceeding of the IEEE International Conference on Robotics and Automation, 2003:2741-2746.
[17]黄心汉.机器人刚度的测试方法.机器人, 1988, (3):45-50.
[18] G. Alici and B. Shirinzadeh,“Enhanced stiffness modeling, identification and characterization for robot manipulators,”IEEE Trans. Robotics, vol. 21, no. 4, pp. 554-564, Aug. 2005.
[19]熊有伦.机器人技术基础.武汉:华中科技大学出版社,1996
[20] John J. Craig.机器人学导论.贠超等译.北京:机械工业出版社,2006
[21] J. Denavit and R. S. Hartenberg,“A Kinematics Notation for Lower-Pair Mechanisms Based on Metrics”, Journal of Applied Mechanics, pp.215-221, June 1955.
[22] J. Colson and N.D. Perreira,“Kinematics Arrangements Used in Industrial Robots”, 13th Industrial Robots Conference Proceedings,April1983
[23]杨达毅, 6R工业机器人的运动学研究:[硕士学位论文].长春:吉林大学图书馆,2005
[24]程永伦,朱世强,罗利佳等.基于Matlab的QJ-6R焊接机器人运动学分析及仿真[J].机电工程,2007,24(11): 107~110
[25]孙祥,徐流美,吴清. MATLAB 7.0基础教程.北京:清华大学出版社,2005
[26]施晓红,周佳.精通GUI图形界面编程.北京:北京大学出版社,2003
[27] D. Piper and B. Roth,“The kinematics of Manipulators Under Computer Control”, Proceeding of the Second International Congress on Theory of Machines and Mechanisms,Vol.2,Zakopane,Poland, 1969,pp.159-169.
[28] D. Piper,“The kinematics of Manipulators Under Computer Control”, Unpublished Ph.D. Thesis, Stanford University, 1968
[29] R.P. Pual, B. Shimano, and G. Mayer,“Kinematics Control Equations for Simple Manipulators”, IEEE Transactions on Systems, Man, and Cybernetics, Vol.SMC-11, 6, 1981
[30] B. Gorla and M. Renaaud, Robots Manipulators, Cepadues-Editions, Toulouse, 1984
[31] C. Wampler,“Wrist Singularities: Theory and Practice”, In the Robotics Review 2, , MIT press,Cambridge,MA,1992
[32] J. Hollerbach,“A Survey of Kinematic Calibration”, In the Robotics Review, MIT Press, Cambridge, MA, 1989.
[33] J. Flanz, et al., 1996. Design approach for a highly accurate patient positioning system for NPTC, in: Proceedings of the PTOOG XXV and Hadrontherapy Symposium, Belgium, pp. 1–5.
[34] W. Hamel, S. Marland, T. Widner, 1997. A model-based concept for telerobotic control of decontamination and dismantlement tasks, in: Proceedings of the 1997 IEEE International Conference of Robotics and Automation, Albuquerque, New Mexico.
[35] Slocum A, precision machine design, Englewood cliffs, 1992.
[36] Robert P. Judd and Al. B. Knasinski. A technique to calibrate industrial robots with experimental verification. In Proceedings of 1987 IEEE International Conference on Robotics and Automation, pp.351-357, April, 1987.
[37] Marco A. Meggiolaro, Steven Dubowsky, Constantinos Mavroidis. Geometric and elastic error calibration of a high accuracy patient positioning system, Mechanism and Machine Theory, 2005,40: 415-427.
[38]费仁元,张慧慧.机器人机械设计和分析.北京:北京工业大学出版社,1998
[39] Jianjun Wang, Hui Zhang, and Thomas Fuhlbrigge. Improving Machining Accuracy with Robot Deformation Compensation, The 2009 IEEE International Conference on Intelligent Robots and Systems, pp: 11-15, October, 2009.
[40]杨世兴,张宝泉,赵永秀. MATLAB在最小二乘参数辨识中的应用[J].电子技术,2003,7(11): 44~45
[41]王可,毛志坚.基于MATLAB实现最小二乘曲线拟合[J].北京广播学院学报(自然科学版),2005,12(2): 52~54
[42] [42]许启发. MATLAB中方程组的解与回归模型的最小二乘估计[J].统计与决策,2005,3(下): 21~24
[43] Morris R. Driels, Uday S. Pathre. Vision-based automatic theodolite for robot calibration [C]. IEEE transaction on robotic and automation, 1991, 7(3): 351~360
[44]康继平.自动经纬仪跟踪测量中运动目标的跟踪算法设计.内蒙古工业大学硕士论文,2009.
[45]宋开臣.三坐标测量机动态误差补偿的研究[J].仪器仪表学报,1999,7(1):10-15.
[46] M. Vincze, J. P. Prenninger, H. Gander. A Laser Tracking System to Measure Position and Orientation of Robot End Effectors Under Motion. The International Journal of Robotics Research, Vol.13, No.4, August 1994, pp: 305-314.