{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T20:37:34Z","timestamp":1772051854201,"version":"3.50.1"},"reference-count":21,"publisher":"Emerald","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,8,9]]},"abstract":"<jats:sec>\n                  <jats:title>Purpose<\/jats:title>\n                  <jats:p>This paper aims to address the issue of model discontinuity typically encountered in traditional Denavit-Hartenberg (DH) models. To achieve this, we propose the use of a local Product of Exponentials (POE) approach. Additionally, a modified calibration model is presented which takes into account both kinematic errors and high-order joint-dependent kinematic errors. Both kinematic errors and high-order joint-dependent kinematic errors are analyzed to modify the model.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Design\/methodology\/approach<\/jats:title>\n                  <jats:p>Robot positioning accuracy is critically important in high-speed and heavy-load manufacturing applications. One essential problem encountered in calibration of series robot is that the traditional methods only consider fitting kinematic errors, while ignoring joint-dependent kinematic errors.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Findings<\/jats:title>\n                  <jats:p>Laguerre polynomials are chosen to fitting kinematic errors and high-order joint-dependent kinematic errors which can avoid the Runge phenomenon of curve fitting to a great extent. Levenberg\u2013Marquard algorithm, which is insensitive to overparameterization and can effectively deal with redundant parameters, is used to quickly calibrate the modified model. Experiments on an EFFORT ER50 robot are implemented to validate the efficiency of the proposed method; compared with the Chebyshev polynomial calibration methods, the positioning accuracy is improved from 0.2301 to 0.2224\u2009mm.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Originality\/value<\/jats:title>\n                  <jats:p>The results demonstrate the substantial improvement in the absolute positioning accuracy achieved by the proposed calibration methods on an industrial serial robot.<\/jats:p>\n               <\/jats:sec>","DOI":"10.1108\/ir-11-2022-0284","type":"journal-article","created":{"date-parts":[[2023,5,19]],"date-time":"2023-05-19T00:00:17Z","timestamp":1684454417000},"page":"753-764","source":"Crossref","is-referenced-by-count":8,"title":["Modeling and calibration of high-order joint-dependent kinematic errors of serial robot based on local POE"],"prefix":"10.1108","volume":"50","author":[{"given":"Yujie","family":"Zhang","sequence":"first","affiliation":[{"name":"Beijing University of Technology Department of Materials and Manufacturing, , Beijing, and Hebei Key Laboratory for Mine Equipment Safety Monitoring, , Hebei,","place":["China China"]},{"name":"North China Institute of Science and Technology Department of Materials and Manufacturing, , Beijing, and Hebei Key Laboratory for Mine Equipment Safety Monitoring, , Hebei,","place":["China China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Cui","sequence":"additional","affiliation":[{"name":"Beijing University of Technology Department of Materials and Manufacturing, , Beijing,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Li","sequence":"additional","affiliation":[{"name":"Beijing University of Technology Department of Materials and Manufacturing, , Beijing,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongyi","family":"Chu","sequence":"additional","affiliation":[{"name":"Beihang University Schoool of Instrumentation and Optoelectronic Engineering, , Beijing,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2023,5,22]]},"reference":[{"issue":"1\/2","key":"2025072819425853700_ref001","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10589-013-9573-4","article-title":"A Levenberg-Marquardt method with approximate projections","volume":"59","author":"Behling","year":"2014","journal-title":"Computational Optimization and Applications"},{"key":"2025072819425853700_ref002","first-page":"93","volume-title":"Robotic Manipulators and the Product of Exponentials Formula","author":"Brockett","year":"1984"},{"issue":"4","key":"2025072819425853700_ref003","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1109\/TIE.2021.3073312","article-title":"A robot calibration method using a neural network based on a butterfly and flower pollination algorithm","volume":"69","author":"Cao","year":"2022","journal-title":"IEEE Transactions on Industrial Electronics"},{"issue":"5","key":"2025072819425853700_ref004","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.1109\/TRO.2014.2319560","article-title":"Determination of the identifiable parameters in robot calibration based on the POE formula","volume":"30","author":"Chen","year":"2014","journal-title":"IEEE Transactions on Robotics"},{"issue":"11\/12","key":"2025072819425853700_ref005","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1016\/S0094-114X(01)00048-9","article-title":"Local POE model for robot kinematic calibration","volume":"36","author":"Chen","year":"2001","journal-title":"Mechanism and Machine Theory"},{"issue":"7","key":"2025072819425853700_ref006","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.rcim.2018.07.002","article-title":"Non-kinematic calibration of industrial robots using a rigid\u2013flexible coupling error model and a full pose measurement method","volume":"57","author":"Chen","year":"2019","journal-title":"Robotics and Computer-Integrated Manufacturing"},{"key":"2025072819425853700_ref007","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1155\/2008\/942391","article-title":"A modified Levenberg-Marquardt method for nonsmooth equations with finitely many maximum functions","volume":"2008","author":"Du","year":"2008","journal-title":"Mathematical Problems in Engineering"},{"key":"2025072819425853700_ref008","first-page":"37","article-title":"Levenberg-Marquardt method for solving inverse problem of MRE based on the modified stationary stokes system","volume":"12","author":"Jiang","year":"2021","journal-title":"Inverse Problems"},{"key":"2025072819425853700_ref009","article-title":"Kinematic model and metrology system for modular robot calibration","author":"Kang","year":"2004"},{"key":"2025072819425853700_ref010","article-title":"Kinematic calibration of a 7-DOF self-calibrated modular cable-driven robotic arm","author":"Kurbanhusen","year":"2008"},{"issue":"5","key":"2025072819425853700_ref011","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1108\/IR-07-2018-0141","article-title":"An improved kinematic model for serial robot calibration based on local POE formula using position measurement","volume":"45","author":"Liu","year":"2018","journal-title":"Industrial Robot: An International Journal"},{"issue":"4","key":"2025072819425853700_ref012","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.rcim.2017.09.006","article-title":"Modeling and calibration of high-order joint-dependent kinematic errors for industrial robots","volume":"50","author":"Ma","year":"2018","journal-title":"Robotics and Computer-Integrated Manufacturing"},{"issue":"1","key":"2025072819425853700_ref013","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.rcim.2012.06.004","article-title":"Absolute calibration of an ABB IRB 1600 robot using a laser tracker","volume":"29","author":"Nubiola","year":"2013","journal-title":"Robotics and Computer-Integrated Manufacturing"},{"issue":"3","key":"2025072819425853700_ref014","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/j.precisioneng.2013.02.003","article-title":"Self-alignment of on-board measurement sensors for robot kinematic calibration","volume":"37","author":"Santolaria","year":"2013","journal-title":"Precision Engineering"},{"issue":"6","key":"2025072819425853700_ref015","doi-asserted-by":"crossref","first-page":"377","DOI":"10.2306\/scienceasia1513-1874.2017.43.377","article-title":"On the local convergence of a Levenberg-Marquardt method for nonsmooth nonlinear complementarity problems","volume":"43","author":"Song","year":"2017","journal-title":"ScienceAsia"},{"issue":"5","key":"2025072819425853700_ref016","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1109\/70.466613","article-title":"An implicit loop method for kinematic calibration and its application to closed-chain mechanisms","volume":"11","author":"Wampler","year":"1995","journal-title":"IEEE Transactions on Robotics and Automation"},{"issue":"2","key":"2025072819425853700_ref017","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1108\/01439911211201609","article-title":"A screw axis identification method for serial robot calibration based on the POE model","volume":"39","author":"Wang","year":"2012","journal-title":"Industrial Robot: An International Journal"},{"issue":"2","key":"2025072819425853700_ref018","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1109\/TASE.2014.2328652","article-title":"A minimal POE-based model for robotic kinematic calibration with only position measurements","volume":"12","author":"Wu","year":"2015","journal-title":"IEEE Transactions on Automation Science and Engineering"},{"issue":"6","key":"2025072819425853700_ref019","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1177\/1729881417743555","article-title":"A product-of-exponential-based robot calibration method with optimal measurement configurations","volume":"14","author":"Xiong","year":"2017","journal-title":"International Journal of Advanced Robotic Systems"},{"issue":"3","key":"2025072819425853700_ref020","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/j.rcim.2013.11.002","article-title":"A minimal kinematic model for serial robot calibration using POE formula","volume":"30","author":"Yang","year":"2014","journal-title":"Robotics and Computer-Integrated Manufacturing"},{"key":"2025072819425853700_ref021","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1108\/IR-05-2018-0102","article-title":"A simple and rapid calibration methodology for industrial robot based on geometric constraint and two-step error","volume":"45","author":"Zhang","year":"2018","journal-title":"Industrial Robot"}],"container-title":["Industrial Robot: the international journal of robotics research and application"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/IR-11-2022-0284\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/ir\/article-pdf\/50\/5\/753\/1187971\/ir-11-2022-0284.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/ir\/article-pdf\/50\/5\/753\/1187971\/ir-11-2022-0284.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T23:43:05Z","timestamp":1753746185000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/ir\/article\/50\/5\/753\/175125\/Modeling-and-calibration-of-high-order-joint"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,22]]},"references-count":21,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,8,9]]}},"URL":"https:\/\/doi.org\/10.1108\/ir-11-2022-0284","relation":{},"ISSN":["0143-991X","1758-5791"],"issn-type":[{"value":"0143-991X","type":"print"},{"value":"1758-5791","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,22]]}}}