The Calibration Algorithms for Industrial Robots Based on a Novel Self-calibration Device
GU Lefeng1,2, YANG Guilin1,2, FANG Zaojun1, WANG Rencheng1, ZHENG Tianjiang1
1. Zhejiang Key Laboratory of Robotics and Intelligent Equipment Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China; 2. University of Chinese Academy of Sciences, Beijing 100049, China
Abstract：Considering the problem that the conventional robot self-calibration device based on geometric constraints can only measure and calibrate partial robot poses in the local robot workspace, a novel portable robot self-calibration device is proposed, which consists of a ball center measuring device installed at the flange of robot and a movable ball bar. By utilizing spherical and distance constraints, it can measure and calibrate a large range of robot targets in large workspace, which improves the reliability of the calibration results. According to the single-ball and double-ball arrangements of the movable ball bar, two robot self-calibration models as well as algorithms based on vector difference and distance difference are established respectively. By using the local product of exponential (POE) formula and introducing position adjoint transformation matrix, both the self-calibration models are simplified, which reduces the linearizing calculation of the kinematic equations. Finally, a simulation experiment on a 6-DOF (degree of freedom) serial manipulator is implemented and the simulation results show that both the proposed self-calibration algorithms can converge quickly, which verifies that both the calibration algorithms are effective and robust.
 周炜,廖文和,田威.基于空间插值的工业机器人精度补偿方法理论与试验[J].机械工程学报,2013,49(3):42-48.Zhou W, Liao W H, Tian W. Theory and experiment of industrial robot accuracy compensation method based on spatial interpolation[J]. Journal of Mechanical Engineering, 2013, 49(3):42-49.  高涵,张明路,张小俊,等. 机械臂绝对定位精度标定关键技术综述[J].计算机应用研究,2017,34(9):2570-2576.Gao H, Zhang M L, Zhang X J, et al. Review on key technology of manipulator absolute positioning accuracy calibration[J]. Application Research of Computers, 2017, 34(9):2570-2576.  Judd R P, Knasinski A B. A technique to calibrate industrial robots with experimental-verification[J]. IEEE Transactions on Robotics and Automation, 1990, 6(1):20-30.  周学才,张启先.距离误差模型在机器人精度研究中的应用[J].机器人,1995,17(1):1-6.Zhou X C, Zhang Q X. Distance error model in the study on the positioning accuracy of robots[J]. Robot, 1995, 17(1):1-6.  Mustafa S K, Tao P Y, Yang G, et al. A geometrical approach for online error compensation of industrial manipulators[C]//IEEE/ASME International Conference on Advanced Intelligent Mechatronics. Piscataway, USA:IEEE, 2010:738-743.  Siciliano B, Khatib O. Springer handbook of robotics[M]. New York, USA:Springer, 2016.  Chen G, Li T, Chu M, et al. Review on kinematics calibration technology of serial robots[J]. International Journal of Precision Engineering and Manufacturing, 2014, 15(8):1759-1774.  He R, Li X, Shi T, et al. A kinematic calibration method based on the product of exponentials formula for serial robot using position measurements[J]. Robotica, 2015, 33(6):1295-1313.  Wu L, Yang X, Chen K, et al. A minimal POE-based model for robotic kinematic calibration with only position measurements[J]. IEEE Transactions on Automation Science and Engineering, 2015, 12(2):758-763.  Gaudreault M, Joubair A, Bonev I. Self-calibration of an industrial robot using a novel affordable 3D measuring device[J]. Sensors, 2018, 18(10):3380.  Hu S, Zhang M, Zhou C, et al. A novel self-calibration method with POE-based model and distance error measurement for serial manipulators[J]. Journal of Mechanical Science and Technology, 2017, 31(10):4911-4923.  Gaudreault M, Joubair A, Bonev I A. Local and closed-loop calibration of an industrial serial robot using a new low-cost 3D measuring device[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2016:4312-4319.  Nubiola A, Bonev I A. Absolute robot calibration with a single telescoping ballbar[J]. Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology, 2014, 38(3):472-480.  Nubiola A, Slamani M, Bonev I A. A new method for measuring a large set of poses with a single telescoping ballbar[J]. Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology, 2013, 37(2):451-460.  Wang R, Yang G, Zhao H, et al. Robot kinematic calibration with plane constraints based on POE formula[C]//IEEE International Conference on Information and Automation. Piscataway, USA:IEEE, 2016:1887-1892.  Hage H, Bidaud P, Jardin N. Practical consideration on the identification of the kinematic parameters of the Stäubli TX90 robot[C]//Proceedings of the 13th World Congress in Mechanism and Machine Science. Guanajuato, Mexique:IFToMM, 2011:43.  Joubair A, Bonev I A. Non-kinematic calibration of a six-axis serial robot using planar constraints[J]. Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology, 2015, 40:325-333..  Meng Y, Zhuang H Q. Self-calibration of camera-equipped robot manipulators[J]. International Journal of Robotics Research, 2001, 20(11):909-921.  Okamura K, Park F C. Kinematic calibration using the product of exponentials formula[J]. Robotica, 1996, 14(4):415-421.  He R, Zhao Y, Yang S, et al. Kinematic-parameter identification for serial-robot calibration based on POE formula[J]. IEEE Transactions on Robotics, 2010, 26(3):411-423.  高文斌,王洪光,姜勇. 一种基于指数积的串联机器人标定方法[J].机器人, 2013, 35(2):156-161.Gao W B, Wang H G, Jiang Y. A calibration method for serial robots based on POE formula[J]. Robot, 2013, 35(2):156-161.  Chiu Y J, Perng M H. Self-calibration of a general hexapod manipulator using cylinder constraints[J]. International Journal of Machine Tools and Manufacture, 2003, 43(10):1051-1066.  Liu Y, Xi N. Low-cost and automated calibration method for joint offset of industrial robot using single-point constraint[J]. Industrial Robot, 2011, 38(6):577-584.  Du S, Ding J, Liu Y, et al. Industrial robot kinematic calibration using virtual line-based sphere surface constraint approach[C]//IEEE International Conference on Cyber Technology in Automation, Control, and Intelligent Systems. Piscataway, USA:IEEE, 2015:48-53.  Chen G, Kong L, Li Q, et al. Complete, minimal and continuous error models for the kinematic calibration of parallel manipulators based on POE formula[J]. Mechanism and Machine Theory, 2018, 121:844-856.  Liu H, Zhu W, Dong H, et al. An improved kinematic model for serial robot calibration based on local POE formula using position measurement[J]. Industrial Robo, 2018, 45(5):573-584.  Chen I M, Yang G L, Tan C T, et al. Local POE model for robot kinematic calibration[J]. Mechanism and Machine Theory, 2001, 36(11/12):1215-1239.  Lynch K M, Park F C. Modern robotics[M]. Cambridge, UK:Cambridge University Press, 2017.