Abstract
This paper presents an efficient cascade calibration method with an improved Levenberg–Marquardt and sine–cosine hybrid algorithm to enhance the absolute positioning accuracy of robotic grinding systems. To expedite convergence in the Levenberg–Marquardt algorithm, a dynamic adaptive weight mechanism is introduced, enhancing global and local search capabilities. Furthermore, a novel learning rate, combining exponential and cosine functions, addresses local optima in the algorithm. The improved Levenberg–Marquardt algorithm is employed to obtain suboptimal values for robot kinematic parameter deviations. Subsequently, these values are used as central points for generating a candidate solution set in the sine–cosine algorithm, resulting in more accurate kinematic parameter deviation identification. This innovative dual-search optimization approach combines the two algorithms. Experimental results confirm the substantial improvements in absolute positioning accuracy and surface machining precision achieved by the proposed model, with the calibration method’s effectiveness verified through experimentation.












Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data availability
Data will be made available on request.
References
Deng Y, Hou X, Li B, Wang J, Zhang Y (2024) A highly powerful calibration method for robotic smoothing system calibration via using adaptive residual extended Kalman filter. Robot Comput Integr Manuf 86:102660
Li Z, Li S, Luo X (2021) An overview of calibration technology of industrial robots. IEEE/CAA J Automatica Sinica 8(1):23–36
Xie Z, Zong P, Yao P, Ren P (2019) Calibration of 6-DOF industrial robots based on line structured light. Optik 183:1166–1178
Gan Y, Duan J, Dai X (2019) A calibration method of robot kinematic parameters by drawstring displacement sensor. Int J Adv Rob Syst 16(5):1–9
Jiang Z, Zhou W, Li H, Mo Y, Ni W, Huang Q (2018) A new kind of accurate calibration method for robotic kinematic parameters based on the extended Kalman and particle filter algorithm. IEEE Trans Industr Electron 65(4):3337–3345
Ma L, Bazzoli P, Sammons P, Landers R, Bristow D (2018) Modeling and calibration of high-order joint-dependent kinematic errors for industrial robots. Robot Comput Integr Manuf 50:153–167
Sun T, Lian B, Zhang J, Song Y (2018) Kinematic calibration of a 2-DoF over-constrained parallel mechanism using real inverse kinematics. IEEE Access 6:67752–67761
Nonoyama K, Liu Z, Fujiwara T, Alam M, Nishi T (2022) Energy-efficient robot configuration and motion planning using genetic algorithm and particle swarm optimization. Energies 15(6):2074
Cao H, Nguyen H, Tran T, Tran H, Jeon J (2022) A robot calibration method using a neural network based on a butterfly and flower pollination algorithm. IEEE Trans Ind Electron 69(4):3865–3875
Wu G, Shi G (2019) Experimental statics calibration of a multi-constraint parallel continuum robot. Mech Mach Theory 136:72–85
Li Z, Li S, Bamasag O, Alhothali A, Luo X (2022) Diversified regularization enhanced training for effective manipulator calibration. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2022.3153039
Zhao H, Yu L, Jia H, Li W, Sun J (2016) A new kinematic model of portable articulated coordinate measuring machine. Appl Sci 6(7):181
Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133
Zhang J, Wang X, Wen K, Zhou Y, Yue Y, Yang J (2018) A simple and rapid calibration methodology for industrial robot based on kinematic constraint and two-step error. Ind Robot Int J 45:715–721
Deng Y, Hou X, Li B, Wang J, Zhang Y (2024) A novel positioning accuracy improvement method for polishing robot based on Levenberg–Marquardt and opposition-based learning squirrel search algorithm. J Intell Robot Syst 110:8
Wu L, Crawford R, Roberts J (2017) An analytic approach to converting POE parameters into D–H parameters for serial-link robots. IEEE Robot Autom Lett 2(4):2174–2179
Deng Y, Hou X, Li B, Wang J, Zhang Y (2023) A novel method for improving workpiece component smoothing quality in robotic smoothing systems by compensating path errors. Opt Express 31(19):30359–30378
Xu P, Cheung B, Li B (2019) A complete, continuous, and minimal product of exponentials-based model for five-axis machine tools calibration with a single laser tracker, an R-test, or a double ball-bar. J Manuf Sci Eng 141(4):041010
Huang B, Ma C (2019) A Shamanskii-like self-adaptive Levenberg–Marquardtt method for nonlinear equations. Comput Math Appl 77(2):357–373
Nielsen H (1999) Damping parameter in Marquardtt’s method. In: Informatics and mathematical modelling. Technical University of Denmark, DTU, pp 1–31
Park I, Lee B, Cho S, Hong Y, Kim J (2012) Laser-based kinematic calibration of robot manipulator using differential kinematics. IEEE-ASME Trans Mechatron 17(6):1059–1067
Deng X, Ge L, Li R, Liu Z (2020) Research on the kinematic parameter calibration method of industrial robot based on LM and PF algorithm. In: Proceedings of Chinese control and decision conference (CCDC), pp 2198–2203
Shang M, Luo X, Liu Z, Chen J, Yuan Y, Zhou M (2019) Randomized latent factor model for high-dimensional and sparse matrices from industrial applications. IEEE/CAA J Automatica Sinica 6(1):131–141
Deng Y, Hou X, Li B, Wang J, Zhang Y (2023) Review on mid-spatial frequency error suppression in workpiece components manufacturing. Int J Adv Manuf Technol 126:4827–4847
Wan S, Zhang X, Xu M, Wang W, Jiang X (2018) Region-adaptive path planning for precision workpiece polishing with industrial robots. Opt Express 26:23782–23795
Li W, Xie H, Zhang G, Yan S, Yin Z (2015) Hand-eye calibration in visually-guided robot grinding. IEEE Trans Cybern 46(11):2634–2642
Acknowledgements
This research was funded by the Collaborative Education Program of the Ministry of Education of China (202102145008, 202102145013), Innovation Fund for Industry-university Research of Chinese Universities (No. 2020ITA03041), National Natural Science Foundation of China (62101076); Sichuan Provincial Youth Science Foundation (2022NSFSC0920) and the Talents Start-up Project of Scientific Research in Chengdu University of Information Technology (KYTZ202102, 376157). The Quality of Personnel Training and Reform of Education & Teaching Program of Chengdu Technological University (No. 20210205), The Science and Technology Service Corps Program of Chengdu Technological University (No. 2023FW039).
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Ethical approval
Not applicable.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Liu, J., Deng, Y., Liu, Y. et al. A novel cascade calibration method for robotic grinding system. Intel Serv Robotics 17, 505–520 (2024). https://doi.org/10.1007/s11370-024-00534-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11370-024-00534-5