{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T03:04:46Z","timestamp":1760151886497,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,11,30]],"date-time":"2022-11-30T00:00:00Z","timestamp":1669766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LGG22F030001"],"award-info":[{"award-number":["LGG22F030001"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents a novel algorithm about the industrial robot contouring control based on the NURBS (non-uniform rational B-spline) curve. First, aiming at the error between the industrial robot\u2019s actual trajectory and the desired trajectory, the contour error is proposed as the trajectory evaluation index, and the estimation algorithm of contour error based on the tangent approximation is proposed. Based on the tangent approximation algorithm, the estimation algorithm of contour error in the local task coordinate frame is proposed to realize the transformation from the Cartesian coordinate frame to the local task coordinate frame. Second, according to the configuration of the industrial robot, a modified cross-coupling control scheme based on the local task coordinate frame is designed. Finally, the Bernoulli\u2019s lemniscate curves are constructed by NURBS curve and five-order polynomial curve, respectively, and they are symmetrical. The contrast experiment is designed using the two types of constructed Bernoulli\u2019s lemniscate curves as the incentive trajectory. Through the analysis and comparison between the obtained uniaxial tracking error and the contour error curve of the two incentive trajectories, it is concluded that the incentive trajectory constructed by the NURBS curve has better contour control performance than that constructed by the five-order polynomial curve. The results drawn from this paper lay a certain foundation for the future high-precision contouring control of industrial robots.<\/jats:p>","DOI":"10.3390\/sym14122533","type":"journal-article","created":{"date-parts":[[2022,11,30]],"date-time":"2022-11-30T04:32:53Z","timestamp":1669782773000},"page":"2533","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Industrial Robot Contouring Control Based on Non-Uniform Rational B-Spline Curve"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2353-6241","authenticated-orcid":false,"given":"Guirong","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mechanical and Electrical Engineering, China Jiliang University, Hangzhou 310018, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2148-2865","authenticated-orcid":false,"given":"Jiahao","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, China Jiliang University, Hangzhou 310018, China"}]},{"given":"Kun","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, China Jiliang University, Hangzhou 310018, China"}]},{"given":"Zhihui","family":"Pang","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, China Jiliang University, Hangzhou 310018, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"228628","DOI":"10.1109\/ACCESS.2020.3042890","article-title":"Trajectory Planning in Joint Space for a Pointing Mechanism Based on a Novel Hybrid Interpolation Algorithm and NSGA-II Algorithm","volume":"8","author":"Sun","year":"2020","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"102257","DOI":"10.1016\/j.rcim.2021.102257","article-title":"Contour error-based optimization of the end-effector pose of a 6 degree-of-freedom serial robot in milling operation","volume":"73","author":"Lin","year":"2022","journal-title":"Robot. 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