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A Simple Two-step Geometric Approach for the Kinematic Calibration of the 3-PRS Parallel Manipulator

Published online by Cambridge University Press:  14 January 2019

Genliang Chen Open the ORCID record for Genliang Chen [Opens in a new window] ,
Lingyu Kong ,
Qinchuan Li  and
Hao Wang
Genliang Chen*
Affiliation:
State Key Laboratory of Mechanical Systems and Vibration, Shanghai Key Laboratory of Digital Manufacturing for Thin-Wall Structures, Shanghai Jiao Tong University, Shanghai 200240, China
Lingyu Kong
Affiliation:
Intelligent Robot Research Center, Zhejiang Lab, Hangzhou 311100, China
Qinchuan Li
Affiliation:
The Mechatronic Institute, Zhejiang Sci-Tech University, Hangzhou 310018, China
Hao Wang
Affiliation:
State Key Laboratory of Mechanical Systems and Vibration, Shanghai Key Laboratory of Digital Manufacturing for Thin-Wall Structures, Shanghai Jiao Tong University, Shanghai 200240, China
*
*Corresponding author. E-mail: leungchan@sjtu.edu.cn
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Summary

Kinematic calibration plays an important role in the improvement of positioning accuracy for parallel manipulators. Based on the specific geometric constraints of limbs, this paper presents a new kinematic parameter identification method for the widely studied 3-PRS parallel manipulator. In the proposed calibration method, the planes where the PRS limbs exactly located are identified firstly as the geometric characteristics of the studied parallel manipulator. Then, the limbs can be considered as planar PR mechanisms whose kinematic parameters can be determined conveniently according to the limb planes identified in the first step. The main merit of the proposed calibration method is that the system error model which relates the manipulator’s kinematic errors to the output ones is not required for kinematic parameter identification. Instead, only two simple geometric problems need to be established for identification, which can be solved readily using gradient-based searching algorithms. Hence, another advantage of the proposed method is that parameter identification of the manipulator’s limbs can be accomplished individually without interactive impact on each other. In order to validate the effectiveness and efficiency of the proposed method, calibration experiments are conducted on an apparatus of the studied 3-PRS parallel manipulator. The results show that using the proposed two-step calibration method, the kinematic parameters can be identified quickly by means of gradient searching algorithm (converge within five iterations for both steps). The positioning accuracy of the studied 3-PRS parallel manipulator has been significantly improved by compensation according to the identified parameters. The mean position and orientation errors at the validation configurations have been reduced to 1.56 × 10−4 m and 1.13 × 10−3 rad, respectively. Further, the proposed two-step kinematic calibration method can be extended to other limited-degree-of-freedom parallel manipulators, if proper geometric constraints can be characterized for their kinematic limbs.

Keywords

Kinematic calibrationParallel manipulatorError modelingGeometric approach
Type
Articles
Information
Robotica , Volume 37 , Issue 5 , May 2019 , pp. 837 - 850
Copyright
Copyright © Cambridge University Press 2019 

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References

Nabat, V., Rodriguez, M., Company, O., Krut, S. and Pierrot, F., “Par4: Very High Speed Parallel Robot for Pick-and-Place,” 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, Edmonton, Canada (2005) pp. 553–558.CrossRefGoogle Scholar
Chu, X., Gao, F., Guo, W. and Yan, C., “Complexity of heavy-payload forging manipulator based on input/output velocity relationship,” Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 224(11), 2468–2476 (2010).CrossRefGoogle Scholar
Chen, G., Wang, H., Zhao, K. and Lin, Z., “Modular calculation of the Jacobian matrix and its application to the performance analyses of a forging robot,” Adv. Rob. 23(10), 1261–1279 (2009).CrossRefGoogle Scholar
Kong, L., Chen, G., Wang, H. and Zhao, Y., “An Experimental Comparison for the Accuracy Improvement of a 6-PSS Parallel Manipulator by Choosing Different Sets of Measurement Data,” International Conference on Intelligent Robotics and Applications (Springer, 2015) pp. 173–184.CrossRefGoogle Scholar
Li, T., Li, F., Jiang, Y., Zhang, J. and Wang, H., “Kinematic calibration of a 3-P(Pa)S parallel-type spindle head considering the thermal error,” Mechatronics 43, 86–98 (2017).CrossRefGoogle Scholar
Wu, J., Wang, J., Wang, L. and Li, T., “Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy,” Mech. Mach. Theory 44(4), 835–849 (2009).CrossRefGoogle Scholar
Wu, J., Yu, G., Gao, Y. and Wang, L., “Mechatronics modeling and vibration analysis of a 2-DOF parallel manipulator in a 5-DOF hybrid machine tool,” Mech. Mach. Theory 121, 430–445 (2018).CrossRefGoogle Scholar
Wu, J., Wang, J. and You, Z., “An overview of dynamic parameter identification of robots,” Rob. Comput. Integr. Manuf. 26(5), 414–419 (2010).CrossRefGoogle Scholar
Khalil, W. and Dombre, E., Modeling, Identification and Control of Robots (Hermes Penton, London, UK, 2002).Google Scholar
Liu, Y., Wu, J., Wang, L., Wang, J., Wang, D. and Yu, G., “Kinematic calibration of a 3-DOF parallel tool head,” Ind. Rob. Int. J. 44(2), 231–241 (2017).CrossRefGoogle Scholar
Zhang, H., Cheng, G., Shan, X. and Guo, F., “Kinematic accuracy research of 2(3HUS+S) parallel manipulator for simulation of hip joint motion,” Robotica 36(9), 1386–1401 (2018).CrossRefGoogle Scholar
Kong, L., Chen, G., Zhang, Z. and Wang, H., “Kinematic calibration and investigation of the influence of universal joint errors on accuracy improvement for a 3-DOF parallel manipulator,” Rob. Comput. Integr. Manuf. 49, 388–397 (2018).CrossRefGoogle Scholar
Chen, G., Kong, L., Li, Q., Wang, H. and Lin, Z., “Complete, minimal and continuous error models for the kinematic calibration of parallel manipulators based on poe formula,” Mech. Mach. Theory 121, 844–856 (2018).CrossRefGoogle Scholar
Nubiola, A. and Bonev, I., “Absolute calibration of an ABB IRB 1600 robot using a laser tracker,” Rob. Comput. Integr. Manuf. 29(1), 236–245 (2013).CrossRefGoogle Scholar
Chen, G., Wang, H. and Lin, Z., “Determination of the identifiable parameters in robot calibration based on the POE formula,” IEEE Trans. Rob. 30(5), 1066–1077 (2014).CrossRefGoogle Scholar
Wang, W., Song, H., Yan, Z., Sun, L. and Du, Z., “A universal index and an improved PSO algorithm for optimal pose selection in kinematic calibration of a novel surgical robot,” Rob. Comput. Integr. Manuf. 50, 90–101 (2018).CrossRefGoogle Scholar
Wang, J. and Masory, O., “On the Accuracy of a Stewart Platform. I. The Effect of Manufacturing Tolerances,” Proceedings of the 1993 IEEE International Conference on Robotics and Automation, Atlanta, Georgia (1993) pp. 114–120.Google Scholar
Masory, O., Wang, J. and Zhuang, H., “On the Accuracy of a Stewart Platform. II. Kinematic Calibration and Compensation,” 1993 IEEE International Conference on Robotics and Automation, 1993, Proceedings, Atlanta, Georgia (IEEE, 1993) pp. 725–731.CrossRefGoogle Scholar
Hollerbach, J. and Lokhorst, D., “Closed-loop kinematic calibration of the RSI 6-DOF hand controller,” IEEE Trans. Rob. Autom. 11(3), 352–359 (1995).CrossRefGoogle Scholar
Hu, Y., Gao, F., Zhao, X., Wei, B., Zhao, D. and Zhao, Y., “Kinematic calibration of a 6-DOF parallel manipulator based on identifiable parameters separation (IPS),” Mech. Mach. Theory 126, 61–78 (2018).CrossRefGoogle Scholar
Guo, J., Wang, D., Fan, R., Chen, W. and Zhao, G., “Kinematic calibration and error compensation of a hexaglide parallel manipulator,” Proc. Inst. Mech. Eng. Part B: J. Eng. Manuf. 233(1), 215–225 (2019).CrossRefGoogle Scholar
Zhuang, H., “Self-calibration of parallel mechanisms with a case study on stewart platforms,” IEEE Trans. Rob. Autom. 13(3), 387–397 (1997).CrossRefGoogle Scholar
Zhuang, H., Yan, J. and Masory, O., “Calibration of stewart platforms and other parallel manipulators minimizing inverse kinematic residuals,” J. Rob. Syst. 15(7), 395–405 (1998).3.0.CO;2-H>CrossRefGoogle Scholar
Chiu, Y. and Perng, M., “Self-calibration of a general hexapod manipulator using cylinder constraints,” Int. J. Mach. Tools Manuf. 43(10), 1051–1066 (2003).CrossRefGoogle Scholar
Rauf, A. and Ryu, J., “Fully Autonomous Calibration of Parallel Manipulators by Imposing Position Constraint,” Proceedings of the 2001 IEEE International Conference on Robotics and Automation, vol. 3, Seoul, South Korea (2001) pp. 2389–2394.Google Scholar
Huang, T., Chetwynd, D., Whitehouse, D. and Wang, J., “A general and novel approach for parameter identification of 6-DOF parallel kinematic machines,” Mech. Mach. Theory 40(2), 219–239 (2005).CrossRefGoogle Scholar
Chen, G., Wang, H. and Lin, Z., “Optimal kinematic calibration of the 6-UPS parallel manipulator”, In: Intelligent Robotics and Applications. ICIRA 2013. Lecture Notes in Computer Science (Lee, J., Lee, M. C., Liu, H., and Ryu, J. H., eds.), vol. 8102 (Springer, Berlin, Heidelberg).Google Scholar
Verner, M., Xi, F. and Mechefske, C., “Optimal calibration of parallel kinematic machines,” J. Mech. Des. 127(1), 62–69 (2005).CrossRefGoogle Scholar
Wang, H. and Fan, K.-C., “Identification of strut and assembly errors of a 3-PRS serial–parallel machine tool,” Int. J. Mach. Tools Manuf. 44(11), 1171–1178 (2004).CrossRefGoogle Scholar
Yu, L., Yan, Y., Ren, S. and Zhao, J., “Vision-Based Method of Kinematic Calibration and Image Tracking of Position and Posture for 3-RPS Parallel Robot,” 2017 IEEE International Conference on Mechatronics and Automation (ICMA), Takamatsu, Japan (2017) pp. 1757–1762.CrossRefGoogle Scholar
Pashkevich, A., Chablat, D. and Wenger, P., “Kinematic calibration of Orthoglide-type mechanisms from observation of parallel leg motions,” Mechatronics 19(4), 478–488 (2009).CrossRefGoogle Scholar
Gojtan, G., Furtado, G. and Hess-Coelho, T., “Error analysis of a 3-DOF parallel mechanism for milling applications,” J. Mech. Rob. 5(3), 034501 (2013).CrossRefGoogle Scholar
Bai, P., Mei, J., Huang, T. and Chetwynd, D. G., “Kinematic calibration of Delta robot using distance measurements,” Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 230(3), 414–424 (2016).CrossRefGoogle Scholar
Joubair, A., Slamani, M. and Bonev, I. A., “Kinematic calibration of a five-bar planar parallel robot using all working modes,” Rob. Comput. Integr. Manuf. 29(4), 15–25 (2013).CrossRefGoogle Scholar
Jiang, Y., Li, T., Wang, L. and Chen, F., “Kinematic error modeling and identification of the over-constrained parallel kinematic machine,” Rob. Comput. Integr. Manuf. 49, 105–119 (2018).CrossRefGoogle Scholar
Zhang, J., Chen, Q., Wu, C. and Li, Q., “Kinematic calibration of a 2-DOF translational parallel manipulator,” Adv Rob. 28(10), 707–714 (2014).CrossRefGoogle Scholar