{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T18:13:22Z","timestamp":1773944002562,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,4]],"date-time":"2022-10-04T00:00:00Z","timestamp":1664841600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2021QE128"],"award-info":[{"award-number":["ZR2021QE128"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2019QEE042"],"award-info":[{"award-number":["ZR2019QEE042"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["2022CXGC010101"],"award-info":[{"award-number":["2022CXGC010101"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018532","name":"Major Scientific and Technological Innovation Project of Shandong Province","doi-asserted-by":"publisher","award":["ZR2021QE128"],"award-info":[{"award-number":["ZR2021QE128"]}],"id":[{"id":"10.13039\/501100018532","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018532","name":"Major Scientific and Technological Innovation Project of Shandong Province","doi-asserted-by":"publisher","award":["ZR2019QEE042"],"award-info":[{"award-number":["ZR2019QEE042"]}],"id":[{"id":"10.13039\/501100018532","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018532","name":"Major Scientific and Technological Innovation Project of Shandong Province","doi-asserted-by":"publisher","award":["2022CXGC010101"],"award-info":[{"award-number":["2022CXGC010101"]}],"id":[{"id":"10.13039\/501100018532","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Robotic machining has obtained growing attention recently because of the low cost, high flexibility and large workspace of industrial robots (IRs). Multiple degrees of freedom of IRs improve the dexterity of machining while causing the problem of redundancy. Meanwhile, the performance of IRs, such as their stiffness and dexterity, is affected by their position and posture obviously. Therefore, a redundant posture optimization method for robotic milling is proposed to improve the machining performance of the robot. The multiple characteristics of the robot are considered, including the joint-limit, singularity and stiffness, which have symmetry in its workspace. Firstly, the joint-limit is regarded as the constraint. And a symmetrical and effective constraint method is proposed to simply guarantee that all the interpolation points can avoid joint interference. Then, the performance indices of singularity and stiffness are designed as the optimization target. On this basis, the piecewise-global-optimization-strategy (PGOS) is proposed for redundant optimization. Owning to the PGOS, all the given planned tool points in their corresponding segment are considered simultaneously to avoid the gradual deterioration in traditional methods, which is especially suitable for the machining process with a continuous path. Moreover, the computational load of the optimization solution is considered and limited by the designed segmentation strategy. Finally, a series of comparative simulations are conducted to validate the good performance of the proposed method.<\/jats:p>","DOI":"10.3390\/sym14102066","type":"journal-article","created":{"date-parts":[[2022,10,11]],"date-time":"2022-10-11T03:32:56Z","timestamp":1665459176000},"page":"2066","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Redundant Posture Optimization for 6R Robotic Milling Based on Piecewise-Global-Optimization-Strategy Considering Stiffness, Singularity and Joint-Limit"],"prefix":"10.3390","volume":"14","author":[{"given":"Hepeng","family":"Ni","sequence":"first","affiliation":[{"name":"School of Mechanical and Electronic Engineering, Shandong Jianzhu University, Jinan 250101, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuai","family":"Ji","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingxin","family":"Ye","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electronic Engineering, Shandong Jianzhu University, Jinan 250101, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mikolajczyk, T. (2012). Manufacturing using robot. Advanced Materials Research, Trans Tech Publications Ltd.","DOI":"10.4028\/www.scientific.net\/AMR.463-464.1643"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1007\/s00170-019-03403-z","article-title":"Industrial robotic machining: A review","volume":"103","author":"Ji","year":"2019","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1007\/s001700050111","article-title":"Implementation of a robot system for sculptured surface cutting. Part 1. Rough machining","volume":"15","author":"Hu","year":"1999","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.cja.2020.12.030","article-title":"High precision and efficiency robotic milling of complex parts: Challenges, approaches and trends","volume":"35","author":"Zhu","year":"2021","journal-title":"Chin. J. Aeronaut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/j.rcim.2010.08.004","article-title":"The self-adaptation of weights for joint-limits and singularity avoidances of functionally redundant robotic-task","volume":"27","author":"Huo","year":"2011","journal-title":"Robot. Comput. Integr. Manuf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1109\/TCST.2011.2112661","article-title":"Robust force controller for industrial robots: Optimal design and real-time implementation on a KUKA robot","volume":"20","author":"Bigras","year":"2012","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.rcim.2015.02.006","article-title":"Stiffness-oriented posture optimization in robotic machining applications","volume":"35","author":"Guo","year":"2015","journal-title":"Robot. Comput. Integr. Manuf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.mechmachtheory.2016.01.015","article-title":"Off-line programming of six-axis robots for optimum five-dimensional tasks","volume":"100","author":"Angeles","year":"2016","journal-title":"Mech. Mach. Theory"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"106981","DOI":"10.1016\/j.ast.2021.106981","article-title":"Online-learning control with weakened saturation response to attitude tracking: A variable learning intensity approach","volume":"117","author":"Zhang","year":"2021","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"106441","DOI":"10.1016\/j.ast.2020.106441","article-title":"On low-complexity control design to spacecraft attitude stabilization: An online-learning approach","volume":"110","author":"Zhang","year":"2021","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_11","unstructured":"Xie, H., Li, W., and Yin, Z. (2021, January 22\u201325). Posture optimization based on both joint parameter error and stiffness for robotic milling. Proceedings of the International Conference on Intelligent Robotics and Applications, Yantai, China."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1751","DOI":"10.1007\/s11431-019-1529-x","article-title":"Smoothness-oriented path optimization for robotic milling processes","volume":"63","author":"Peng","year":"2020","journal-title":"Sci. China Technol. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2535","DOI":"10.1007\/s00170-013-4873-5","article-title":"An off-line programming system for robotic drilling in aerospace manufacturing","volume":"68","author":"Zhu","year":"2013","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.robot.2018.09.002","article-title":"Processing configuration off-line optimization for functionally redundant robotic drilling tasks","volume":"110","author":"Jiao","year":"2018","journal-title":"Robot. Auton. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.precisioneng.2017.04.001","article-title":"Stiffness analysis and optimization in robotic drilling application","volume":"49","author":"Bu","year":"2017","journal-title":"Precis. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.rcim.2017.02.002","article-title":"Posture optimization methodology of 6R industrial robots for machining using performance evaluation indexes","volume":"48","author":"Lin","year":"2017","journal-title":"Robot. Comput. Integr. Manuf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10846-020-01171-7","article-title":"On maximizing manipulability index while solving a kinematics task","volume":"100","author":"Dufour","year":"2020","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/s12206-017-1202-1","article-title":"Optimal design of a six-axis vibration isolator via Stewart platform by using homogeneous Jacobian matrix formulation based on dual quaternions","volume":"32","author":"Li","year":"2018","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"102076","DOI":"10.1016\/j.rcim.2020.102076","article-title":"Stiffness-oriented performance indices defined on two-dimensional manifold for 6-DOF industrial robot","volume":"68","author":"Li","year":"2021","journal-title":"Robot. Comput. Integr. Manuf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3253","DOI":"10.1007\/s00170-017-9991-z","article-title":"Modeling and experimental investigation of Cartesian compliance characterization for drilling robot","volume":"91","author":"Yin","year":"2017","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Mikolajczyk, T. (2012). System to surface control in robot machining. Advanced Materials Research, Trans Tech Publications Ltd.","DOI":"10.4028\/www.scientific.net\/AMR.463-464.708"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.rcim.2018.07.003","article-title":"Stiffness performance index based posture and feed orientation optimization in robotic milling process","volume":"55","author":"Chen","year":"2019","journal-title":"Robot. Comput. Integr. Manuf."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Xiong, G., Ding, Y., and Zhu, L. (2017, January 16\u201318). A feed-direction stiffness based trajectory optimization method for a milling robot. Proceedings of the International Conference on Intelligent Robotics and Applications, Wuhan, China.","DOI":"10.1007\/978-3-319-65292-4_17"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.rcim.2018.07.001","article-title":"Stiffness-based pose optimization of an industrial robot for five-axis milling","volume":"55","author":"Xiong","year":"2019","journal-title":"Robot. Comput. Integr. Manuf."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"101953","DOI":"10.1016\/j.rcim.2020.101953","article-title":"Region-based toolpath generation for robotic milling of freeform surfaces with stiffness optimization","volume":"64","author":"Liao","year":"2020","journal-title":"Robot. Comput. Integr. Manuf."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/2066\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:46:16Z","timestamp":1760143576000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/2066"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,4]]},"references-count":25,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["sym14102066"],"URL":"https:\/\/doi.org\/10.3390\/sym14102066","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,4]]}}}