{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T10:08:39Z","timestamp":1788948519270,"version":"build-2803163510"},"reference-count":45,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T00:00:00Z","timestamp":1788912000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100019014","name":"Chengdu Science and Technology Program","doi-asserted-by":"publisher","award":["2025-YF08-00232-GX"],"award-info":[{"award-number":["2025-YF08-00232-GX"]}],"id":[{"id":"10.13039\/501100019014","id-type":"DOI","asserted-by":"publisher"}]},{"name":"People\u2019s Republic of China Central Military Commission","award":["62502010223"],"award-info":[{"award-number":["62502010223"]}]},{"award":["62502010223"],"award-info":[{"award-number":["62502010223"]}],"id":[{"id":"https:\/\/ror.org\/058tz9s83","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Aircraft wire-harness routing on fixture boards requires not only efficient large-workspace robot motion but also smooth and process-safe passage around densely distributed pins. Conventional robot trajectory optimization generally focuses on generic motion indices and cannot explicitly represent local over-bending risk and coupled wiring-process constraints. This paper proposes a process-safety-aware multi-objective trajectory optimization method for a seven-axis wiring robot composed of a linear rail and a six-DOF manipulator. An executable reference trajectory is parameterized using quintic B-splines, and execution time, normalized joint jerk, and a pin-neighborhood weighted bending-safety proxy are jointly optimized under robot-motion, pin-passing, board-clearance, and non-target-pin constraints. A constraint-guided adaptive DE-NSGA-II algorithm is developed to improve feasible-solution search in the resulting narrow and strongly coupled feasible region. Physical experiments show that, compared with MOPSO, the proposed method reduces normalized joint jerk by 35.8% and the bending-safety proxy by 77.0%, while completing all ten repeated trials without controller alarms. Vision-based measurements further show a strong correlation between the proposed proxy and the actual harness bending radius (R2=0.991). Additional routing layouts confirm the applicability of the method to more complex fixture-board configurations. These results demonstrate that the proposed method provides a practical balance among routing efficiency, trajectory smoothness, and process reliability.<\/jats:p>","DOI":"10.3390\/s26185714","type":"journal-article","created":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T09:24:02Z","timestamp":1788945842000},"page":"5714","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Objective Trajectory Optimization of a 7-DOF Wiring Robot for Aircraft Harness Layout on Fixture Boards"],"prefix":"10.3390","volume":"26","author":[{"given":"Jinhua","family":"Cai","sequence":"first","affiliation":[{"name":"School of Mechatronic Engineering, Changchun University of Science and Technology, No. 7089, Satellite Road, Chaoyang District, Changchun 130012, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Tao","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering, Changchun University of Science and Technology, No. 7089, Satellite Road, Chaoyang District, Changchun 130012, China"},{"name":"Chongqing Research Institute, Changchun University of Science and Technology, No. 5, Yulin Road, Liangjiang New Area, Chongqing 401120, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"software","vocabulary":"credit"},{"role":"conceptualization","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4659-8875","authenticated-orcid":false,"given":"Han","family":"Hou","sequence":"additional","affiliation":[{"name":"Chongqing Research Institute, Changchun University of Science and Technology, No. 5, Yulin Road, Liangjiang New Area, Chongqing 401120, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"}]},{"given":"Peng","family":"Gao","sequence":"additional","affiliation":[{"name":"High-End Aeronautical Equipment Technology Innovation Center (Sichuan) Co., Ltd., Chengdu 610000, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"}]},{"given":"Na","family":"Liu","sequence":"additional","affiliation":[{"name":"High-End Aeronautical Equipment Technology Innovation Center (Sichuan) Co., Ltd., Chengdu 610000, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"supervision","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"102596","DOI":"10.1016\/j.aei.2024.102596","article-title":"A systematic literature review of computer vision applications in robotized wire harness assembly","volume":"62","author":"Wang","year":"2024","journal-title":"Adv. Eng. Inform."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Navas-Reascos, G.E., Romero, D., Stahre, J., and Caballero-Ruiz, A. (2022). Wire harness assembly process supported by collaborative robots: Literature review and call for R&D. Robotics, 11.","DOI":"10.3390\/robotics11030065"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"696","DOI":"10.1016\/j.procir.2023.09.061","article-title":"Review of current status and future directions for collaborative and semi-automated automotive wire harnesses assembly","volume":"120","author":"Salunkhe","year":"2023","journal-title":"Procedia CIRP"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Navas-Reascos, G.E., Romero, D., Stahre, J., and Caballero-Ruiz, A. (2022). Wire harness assembly process supported by a collaborative robot: A case study focus on ergonomics. Robotics, 11.","DOI":"10.3390\/robotics11060131"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.jmsy.2021.10.003","article-title":"A novel vision-based method for 3D profile extraction of wire harness in robotized assembly process","volume":"61","author":"Nguyen","year":"2021","journal-title":"J. Manuf. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/j.jmsy.2023.12.002","article-title":"Revolutionizing robotized assembly for wire harness: A 3D vision-based method for multiple wire-branch detection","volume":"72","author":"Nguyen","year":"2024","journal-title":"J. Manuf. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"102924","DOI":"10.1016\/j.rcim.2024.102924","article-title":"Strategic algorithm for cable wiring using dual arm with compliance control","volume":"93","author":"Cho","year":"2025","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Gonz\u00e1lez Huarte, J., Ortiz de Zarate, M., and Ibarguren, A. (2023). CAD-based robot programming solution for wire harness manufacturing in aeronautic sector. Robotics, 12.","DOI":"10.3390\/robotics12050130"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Song, J., Kumar, P., Kim, Y., and Kim, H.S. (2024). A fault detection system for wiring harness manufacturing using artificial intelligence. Mathematics, 12.","DOI":"10.3390\/math12040537"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/j.jmsy.2025.10.008","article-title":"A dual-arm robotic system for automated multi-branch wire harness assembly in automotive industry","volume":"83","author":"Vasudevan","year":"2025","journal-title":"J. Manuf. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"102645","DOI":"10.1016\/j.rcim.2023.102645","article-title":"Design and motion planning of a 7-DOF assembly robot with heavy load in spacecraft module","volume":"86","author":"Liu","year":"2024","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1163\/016918610X551782","article-title":"Robotized assembly of a wire harness in a car production line","volume":"25","author":"Jiang","year":"2011","journal-title":"Adv. Robot."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1177\/0278364918779698","article-title":"Robotic manipulation and sensing of deformable objects in domestic and industrial applications: A survey","volume":"37","author":"Sanchez","year":"2018","journal-title":"Int. J. Robot. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3426","DOI":"10.1109\/LRA.2018.2852770","article-title":"A framework for manipulating deformable linear objects by coherent point drift","volume":"3","author":"Tang","year":"2018","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/LRA.2019.2944304","article-title":"Robotic manipulation planning for shaping deformable linear objects with environmental contacts","volume":"5","author":"Zhu","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"104652","DOI":"10.1016\/j.robot.2024.104652","article-title":"Robotic co-manipulation of deformable linear objects for large deformation tasks","volume":"175","author":"Almaghout","year":"2024","journal-title":"Robot. Auton. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1177\/0278364904041882","article-title":"Static modeling of linear object deformation based on differential geometry","volume":"23","author":"Wakamatsu","year":"2004","journal-title":"Int. J. Robot. Res."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Hu, F., Kou, Z., Sefene, E.M., and Mikolajczyk, T. (2023). An Origami Flexiball-Inspired Soft Robotic Jellyfish. J. Mar. Sci. Eng., 11.","DOI":"10.3390\/jmse11040714"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wang, J., Zhang, Y., Zhu, S., and Wang, J. (2024). A Novel Multi-Objective Trajectory Planning Method for Robots Based on the Multi-Objective Particle Swarm Optimization Algorithm. Sensors, 24.","DOI":"10.3390\/s24237663"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/j.mechmachtheory.2017.11.006","article-title":"Optimal time-jerk trajectory planning for industrial robots","volume":"121","author":"Huang","year":"2018","journal-title":"Mech. Mach. Theory"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1186\/s10033-021-00669-x","article-title":"Multi-objective trajectory planning method based on the improved elitist non-dominated sorting genetic algorithm","volume":"35","author":"Wang","year":"2022","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1761","DOI":"10.1017\/S0263574724000481","article-title":"Multi-objective optimal trajectory planning for robot manipulator attention to end-effector path limitation","volume":"42","author":"Ye","year":"2024","journal-title":"Robotica"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"107223","DOI":"10.1016\/j.engappai.2023.107223","article-title":"Time-energy-jerk optimal trajectory planning for high-speed parallel manipulator based on quantum-behaved particle swarm optimization algorithm and quintic B-spline","volume":"126","author":"Chen","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4382","DOI":"10.1177\/0954406220969734","article-title":"Optimum time-energy-jerk trajectory planning for serial robotic manipulators by reparameterized quintic NURBS curves","volume":"235","author":"Wu","year":"2021","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1007\/s43684-024-00077-7","article-title":"Multi-objective optimal trajectory planning for manipulators based on CMOSPBO","volume":"4","author":"Bao","year":"2024","journal-title":"Auton. Intell. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, M., Liu, J., Wu, Y., Hou, T., and Li, T. (2025). Multi-objective trajectory planning for robotic arms based on MOPO algorithm. Electronics, 14.","DOI":"10.3390\/electronics14122371"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Fan, Y., Peng, Y., and Liu, J. (2025). Advanced multi-objective trajectory planning for robotic arms using a multi-strategy enhanced NSGA-II algorithm. PLoS ONE, 20.","DOI":"10.1371\/journal.pone.0324567"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"111216","DOI":"10.1016\/j.asoc.2023.111216","article-title":"Multi-objective trajectory planning for segment assembly robots using a B-spline interpolation- and infeasible-updating non-dominated sorting-based method","volume":"152","author":"Sun","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"86923","DOI":"10.1109\/ACCESS.2020.2992640","article-title":"Robot time-optimal trajectory planning based on improved cuckoo search algorithm","volume":"8","author":"Wang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1186\/s10033-024-01130-5","article-title":"Multi-Objective Trajectory Optimization for Rigid-Flexible Coupling Spray-Painting Robot Integrated with Coating Process Constraints","volume":"37","author":"Xu","year":"2024","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"110894","DOI":"10.1016\/j.ress.2025.110894","article-title":"Bayesian Inference-Assisted Reliability Analysis Framework for Robotic Motion Systems in Future Factories","volume":"258","author":"Shen","year":"2025","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1016\/j.actaastro.2026.06.021","article-title":"Convex Set-Based Reliability Evaluation for Manipulator Positioning Accuracy with Limited and Bounded Uncertain Data","volume":"248","author":"Yang","year":"2026","journal-title":"Acta Astronaut."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","article-title":"A fast and elitist multi-objective genetic algorithm: NSGA-II","volume":"6","author":"Deb","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential evolution\u2014A simple and efficient heuristic for global optimization over continuous spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Glob. Optim."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2518","DOI":"10.1109\/TCYB.2019.2925534","article-title":"Dynamic MOPSO-Based Optimal Control for Wastewater Treatment Process","volume":"51","author":"Han","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/S0045-7825(99)00389-8","article-title":"An efficient constraint handling method for genetic algorithms","volume":"186","author":"Deb","year":"2000","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1109\/TEVC.2003.810758","article-title":"Performance assessment of multiobjective optimizers: An analysis and review","volume":"7","author":"Zitzler","year":"2003","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1109\/TEVC.2007.892759","article-title":"MOEA\/D: A multiobjective evolutionary algorithm based on decomposition","volume":"11","author":"Zhang","year":"2007","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1016\/j.ejor.2008.09.022","article-title":"An improved multiobjective differential evolution based on Pareto-adaptive epsilon-dominance and orthogonal design","volume":"198","author":"Gong","year":"2009","journal-title":"Eur. J. Oper. Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/TEVC.2020.2991040","article-title":"A grid-based inverted generational distance for multi\/many-objective optimization","volume":"25","author":"Cai","year":"2021","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.swevo.2011.10.001","article-title":"Constraint-handling in nature-inspired numerical optimization: Past, present and future","volume":"1","year":"2011","journal-title":"Swarm Evol. Comput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"108952","DOI":"10.1109\/ACCESS.2020.2998358","article-title":"Digital twin: Enabling technologies, challenges and open research","volume":"8","author":"Fuller","year":"2020","journal-title":"IEEE Access"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2405","DOI":"10.1109\/TII.2018.2873186","article-title":"Digital twin in industry: State-of-the-art","volume":"15","author":"Tao","year":"2019","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Guo, Q., Grigorev, M.A., and Kholodilin, I. (2024). Construction Method of a Digital-Twin Simulation System for SCARA Robots Based on Modular Communication. Sensors, 24.","DOI":"10.3390\/s24227183"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"116440","DOI":"10.1016\/j.apm.2025.116440","article-title":"Auxiliary-based dual-stage constrained multiobjective evolutionary algorithm for obstacle-avoidance inverse kinematics of redundant welding manipulators","volume":"151","author":"He","year":"2025","journal-title":"Appl. Math. Model."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/18\/5714\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T09:32:55Z","timestamp":1788946375000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/18\/5714"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,9]]},"references-count":45,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["s26185714"],"URL":"https:\/\/doi.org\/10.3390\/s26185714","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,9]]}}}