{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T10:15:18Z","timestamp":1777284918620,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T00:00:00Z","timestamp":1687132800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key R&amp;D Program of Zhejiang Province","award":["2022C04030"],"award-info":[{"award-number":["2022C04030"]}]},{"name":"Key R&amp;D Program of Zhejiang Province","award":["2020YFB1313300"],"award-info":[{"award-number":["2020YFB1313300"]}]},{"name":"Key R&amp;D Program of Zhejiang Province","award":["61836015"],"award-info":[{"award-number":["61836015"]}]},{"DOI":"10.13039\/501100012166","name":"National Key R&amp;D Program of China","doi-asserted-by":"publisher","award":["2022C04030"],"award-info":[{"award-number":["2022C04030"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key R&amp;D Program of China","doi-asserted-by":"publisher","award":["2020YFB1313300"],"award-info":[{"award-number":["2020YFB1313300"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key R&amp;D Program of China","doi-asserted-by":"publisher","award":["61836015"],"award-info":[{"award-number":["61836015"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022C04030"],"award-info":[{"award-number":["2022C04030"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2020YFB1313300"],"award-info":[{"award-number":["2020YFB1313300"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61836015"],"award-info":[{"award-number":["61836015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>MultiCal is an affordable, high-precision measuring device designed for the on-site calibration of industrial robots. Its design features a long measuring rod with a spherical tip that is attached to the robot. By restricting the rod\u2019s tip to multiple fixed points under different rod orientations, the relative positions of these points are accurately measured beforehand. A common issue with MultiCal is the gravitational deformation of the long measuring rod, which introduces measurement errors into the system. This problem becomes especially serious when calibrating large robots, as the length of the measuring rod needs to be increased to enable the robot to move in a sufficient space. To address this issue, we propose two improvements in this paper. Firstly, we suggest the use of a new design of the measuring rod that is lightweight yet has high rigidity. Secondly, we propose a deformation compensation algorithm. Experimental results have shown that the new measuring rod improves calibration accuracy from 20% to 39%, while using the deformation compensation algorithm, the accuracy increases from 6% to 16%. In the best configuration, the calibration accuracy is similar to that of a measuring arm with a laser scanner, producing an average positioning error of 0.274 mm and a maximum positioning error of 0.838 mm. The improved design is cost-affordable, robust, and has sufficient accuracy, making MultiCal a more reliable tool for industrial robot calibration.<\/jats:p>","DOI":"10.3390\/s23125717","type":"journal-article","created":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T02:26:56Z","timestamp":1687228016000},"page":"5717","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An Improved Design of the MultiCal On-Site Calibration Device for Industrial Robots"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3717-187X","authenticated-orcid":false,"given":"Ziwei","family":"Wan","sequence":"first","affiliation":[{"name":"College of Control Science and Engineering, Zhejiang University, Hangzhou 310063, China"},{"name":"Laboratory of Medical Robots, Huzhou Institute of Zhejiang University, Huzhou 313098, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6939-9732","authenticated-orcid":false,"given":"Chunlin","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Control Science and Engineering, Zhejiang University, Hangzhou 310063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaohui","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Zhejiang University, Hangzhou 310030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huapeng","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weixi","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Control Science and Engineering, Zhejiang University, Hangzhou 310063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zheng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Engineering, Huzhou University, Huzhou 313000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Control Science and Engineering, Zhejiang University, Hangzhou 310063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Icli, C., Stepanenko, O., and Bonev, I. (2020). New Method and Portable Measurement Device for the Calibration of Industrial Robots. Sensors, 20.","DOI":"10.3390\/s20205919"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.rcim.2016.02.008","article-title":"Kinematic calibration of a 3-DoF rotational parallel manipulator using laser tracker","volume":"41","author":"Sun","year":"2016","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1017\/S0263574713000714","article-title":"Comparison of two calibration methods for a small industrial robot based on an optical CMM and a laser tracker","volume":"32","author":"Nubiola","year":"2013","journal-title":"Robotica"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Cong, D., Yu, D., and Han, J. (2006, January 21\u201323). Kinematic Calibration of Parallel Robots Using CMM. Proceedings of the 2006 6th World Congress on Intelligent Control and Automation, Dalian, China.","DOI":"10.1109\/WCICA.2006.1713640"},{"key":"ref_5","unstructured":"Qiao, G., and Weiss, B.A. (2017, January 4\u20138). Accuracy Degradation Analysis for Industrial Robot Systems. Proceedings of the JSME\/ASME 2017 6th International Conference on Materials and Processing, Los Angeles, CA, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1631\/FITEE.2200172","article-title":"Development of an onsite calibration device for robot manipulators","volume":"24","author":"Wan","year":"2023","journal-title":"Front. Inf. Technol. Electron. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Chen, M., Hong, X., Wei, L., Liu, Y., and Xu, C. (2020, January 27\u201329). Robotic arm calibration and teaching method based on binocular vision. Proceedings of the 2020 39th Chinese Control Conference (CCC), Shenyang, China.","DOI":"10.23919\/CCC50068.2020.9189529"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.mechmachtheory.2013.09.005","article-title":"Optimal design and application of a low-cost wire-sensor system for the kinematic calibration of industrial manipulators","volume":"73","author":"Legnani","year":"2014","journal-title":"Mech. Mach. Theory"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/0921-8890(96)00011-5","article-title":"Autonomous robot calibration using a trigger probe","volume":"18","author":"Zhong","year":"1996","journal-title":"Robot. Auton. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Gaudreault, M., Joubair, A., and Bonev, I.A. (2016, January 16\u201321). Local and closed-loop calibration of an industrial serial robot using a new low-cost 3D measuring device. Proceedings of the 2016 IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden.","DOI":"10.1109\/ICRA.2016.7487629"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"113143","DOI":"10.1109\/ACCESS.2021.3104514","article-title":"A Comparative Review of Hand-Eye Calibration Techniques for Vision Guided Robots","volume":"9","author":"Enebuse","year":"2021","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/s00170-014-6448-5","article-title":"Kinematic calibration of a six-axis serial robot using distance and sphere constraints","volume":"77","author":"Joubair","year":"2014","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_13","unstructured":"Ikits, M., and Hollerbach, J.M. (1997, January 25\u201325). Kinematic calibration using a plane constraint. Proceedings of the International Conference on Robotics and Automation, Albuquerque, NM, USA."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Gaudreault, M., Joubair, A., and Bonev, I. (2018). Self-Calibration of an Industrial Robot Using a Novel Affordable 3D Measuring Device. Sensors, 18.","DOI":"10.3390\/s18103380"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.1177\/0954406220945728","article-title":"Kinematic modeling and parameter identification for a heavy gantry-type automated fiber placement machine considering gravity deformation","volume":"235","author":"Wu","year":"2020","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"90","DOI":"10.4028\/www.scientific.net\/AMM.552.90","article-title":"Modeling and Analysis of Key Geometric Error for Gravity Deformation of Heavy-Duty CNC Machine Tool","volume":"552","author":"Fu","year":"2014","journal-title":"Appl. Mech. Mater."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Vrhovec, M., Kovac, I., and Munih, M. (2010, January 25\u201327). Measurement and compensation of deformations in coordinate measurement arm. Proceedings of the 2010 International Symposium on Optomechatronic Technologies, Toronto, ON, Canada.","DOI":"10.1109\/ISOT.2010.5687319"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5156264","DOI":"10.1155\/2017\/5156264","article-title":"Modeling and Error Compensation of Robotic Articulated Arm Coordinate Measuring Machines Using BP Neural Network","volume":"2017","author":"Gao","year":"2017","journal-title":"Complexity"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1002\/rob.4620020406","article-title":"Improving the absolute positioning accuracy of robot manipulators","volume":"2","author":"Hayati","year":"1985","journal-title":"J. Robot. Syst."},{"key":"ref_20","unstructured":"Park, F.C., and Okamura, K. (1994). Advances in Robot Kinematics and Computational Geometry, Springer Netherlands."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6000","DOI":"10.1109\/TIE.2020.2994890","article-title":"Calibration for Precision Kinematic Control of an Articulated Serial Robot","volume":"68","author":"Sun","year":"2021","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"102165","DOI":"10.1016\/j.rcim.2021.102165","article-title":"A novel kinematic parameters calibration method for industrial robot based on Levenberg-Marquardt and Differential Evolution hybrid algorithm","volume":"71","author":"Luo","year":"2021","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_23","unstructured":"Fan, K.C., Liu, C.L., Wu, P.T., Chen, Y.C., and Wang, W.L. The Structure Design of a Micro-precision CMM with Abb\u00e9 Principle. Proceedings of the 35th International MATADOR Conference."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"161","DOI":"10.4271\/2013-01-2117","article-title":"Calibration Efficiency Analysis Based on Five Observability Indices and Two Calibration Models for a Six-Axis Industrial Robot","volume":"6","author":"Joubair","year":"2013","journal-title":"SAE Int. J. Aerosp."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/12\/5717\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:56:28Z","timestamp":1760126188000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/12\/5717"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,19]]},"references-count":24,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["s23125717"],"URL":"https:\/\/doi.org\/10.3390\/s23125717","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,19]]}}}