{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T22:11:00Z","timestamp":1769551860189,"version":"3.49.0"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T00:00:00Z","timestamp":1769472000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basic Scientific Research Project of Higher EducationInstitutions of Liaoning Province","award":["JYTQN2023064"],"award-info":[{"award-number":["JYTQN2023064"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In contemporary semiconductor manufacturing, wafer-handling robots are essential for achieving high-speed and high-precision wafer transportation. However, the demand for rapid motion and lightweight design introduces flexible transmission components that are prone to residual vibrations, which degrade positioning accuracy and system stability. To address this challenge, this paper proposes a vibration-suppression trajectory planning method based on the Gray Goose Optimization (GGO) algorithm. The proposed algorithm integrates grouped global search with local optimization capabilities, making it well suited for solving multi-objective optimization problems. Comparative tests conducted on eight randomly selected multimodal benchmark functions from the CEC2013 test suite verify the effectiveness and robustness of the GGO algorithm. Establishing a multi-objective function that considers both motion time and vibration energy enables the GGO algorithm to determine the switching time points of an S-shaped velocity profile, thereby generating smooth trajectories with continuous velocity and acceleration. By varying different initial conditions, the trade-off between motion time and vibration energy is systematically analyzed with respect to angular displacement, initial acceleration, and time-weighting factors. Simulation results indicate that the planned trajectories exhibit negligible displacement variation under zero-mean disturbances. The velocity error remains within 0.1 deg\u00b7s\u22121, and the acceleration error is confined within 0.2 deg\u00b7s\u22122. Consequently, Pareto-optimal solutions are successfully obtained with respect to both motion time and residual vibration energy.<\/jats:p>","DOI":"10.3390\/s26030829","type":"journal-article","created":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T09:05:27Z","timestamp":1769504727000},"page":"829","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Wafer Handing Robotic Arm Vibration Trajectory Planning Based on Graylag Goose Optimization"],"prefix":"10.3390","volume":"26","author":[{"given":"Yujie","family":"Ji","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Shenyang Ligong University, Shenyang 110159, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peiyan","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shenyang Ligong University, Shenyang 110159, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,27]]},"reference":[{"key":"ref_1","first-page":"344","article-title":"A Survey of Semiconductor Wafer Fabrication Technologies: Advances and Future Trends","volume":"10","author":"Chandu","year":"2023","journal-title":"Int. J. Res. Anal. Rev."},{"key":"ref_2","first-page":"2025010","article-title":"Ultraprecision machining for single-crystal silicon carbide wafers: State-of-the-art and prospectives","volume":"5","author":"Wang","year":"2025","journal-title":"J. Adv. Manuf. Sci. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"12031","DOI":"10.1007\/s12633-022-01940-z","article-title":"Silicon wafers; its manufacturing processes and finishing techniques: An overview","volume":"14","author":"Pandey","year":"2022","journal-title":"Silicon"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Chen, D., Tang, L., Cong, D., and Qiao, J. (2023, January 26\u201327). AcArm: A Novel Semiconductor Wafer Handling Robot. Proceedings of the 2023 China Semiconductor Technology International Conference (CSTIC), Shanghai, China.","DOI":"10.1109\/CSTIC58779.2023.10219280"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2401432","DOI":"10.1002\/admt.202401432","article-title":"Crystal Damage and Surface Morphology in Industrial Diamond Wire Slicing of 300 mm Monocrystalline Silicon Wafers for Microelectronic Devices","volume":"10","author":"Oberhans","year":"2025","journal-title":"Adv. Mater. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6320","DOI":"10.1109\/LRA.2022.3168936","article-title":"Advanced 2-DOF counterbalance mechanism based on gear units and springs to minimize required torques of robot arm","volume":"7","author":"Kim","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Yanga, C., and Banb, L. (2021, January 22\u201324). Vibration control of piezoelectric flexible manipulator based on machine vision and improved PID. Proceedings of the 2021 IEEE International Conference on Power Electronics, Computer Applications (ICPECA), Shenyang, China.","DOI":"10.1109\/ICPECA51329.2021.9362620"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Guo, X., Li, Z., and Sun, G. (2019, January 21\u201322). The robot arm control based on RBF with incremental PID and sliding mode robustness. Proceedings of the 2019 WRC Symposium on Advanced Robotics and Automation (WRC SARA), Beijing, China.","DOI":"10.1109\/WRC-SARA.2019.8931971"},{"key":"ref_9","first-page":"3746","article-title":"PID controller with robotic arm using optimization algorithm","volume":"7","author":"Wazzan","year":"2022","journal-title":"Int. J. Mech. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhang, S., Xia, Q., Chen, M., and Cheng, S. (2023). Multi-objective optimal trajectory planning for robotic arms using deep reinforcement learning. Sensors, 23.","DOI":"10.3390\/s23135974"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Yu, C., Cao, J., Peng, H., Liu, Y., Xu, Q., and Wang, S. (2025, January 18\u201321). ELM-PSO-GA based inverse solution algorithm for robotic arm. Proceedings of the 2025 International Conference of Clean Energy and Electrical Engineering (ICCEEE), Changchun, China.","DOI":"10.1109\/ICCEEE63357.2025.11156491"},{"key":"ref_12","first-page":"404","article-title":"Trajectory Optimization of Robotic Arm Based on Improved Simulated Annealing Genetic Algorithm","volume":"37","author":"Xu","year":"2025","journal-title":"J. Syst. Simul."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2968","DOI":"10.1016\/j.ifacol.2022.10.183","article-title":"Genetic Algorithm-Based Sliding Mode Control of a Human Arm Model","volume":"55","author":"Kheshti","year":"2022","journal-title":"IFAC-PapersOnLine"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wu, N., Jia, D., Li, Z., and He, Z. (2024). Trajectory planning of robotic arm based on particle swarm optimization algorithm. Appl. Sci., 14.","DOI":"10.3390\/app14188234"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Nonoyama, K., Liu, Z., Fujiwara, T., Alam, M.M., and Nishi, T. (2022). Energy-efficient robot configuration and motion planning using genetic algorithm and particle swarm optimization. Energies, 15.","DOI":"10.3390\/en15062074"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"14275","DOI":"10.1007\/s00521-023-08481-5","article-title":"A systematic review of the emerging metaheuristic algorithms on solving complex optimization problems","volume":"35","author":"Turgut","year":"2023","journal-title":"Neural Comput. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s41324-022-00500-2","article-title":"Intelligent control of robotic manipulators: A comprehensive review","volume":"31","author":"Rawat","year":"2023","journal-title":"Spat. Inf. Res."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Yue, Z., and Zhai, W. (2025, January 19\u201321). Trajectory planning of the robotic arm using improved grey wolf algorithm. Proceedings of the 2025 International Conference on Mechatronics, Robotics, and Artificial Intelligence (MRAI), Jinan, China.","DOI":"10.1109\/MRAI65197.2025.11135727"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2687","DOI":"10.1007\/s13369-022-07002-1","article-title":"Jerk optimized motion planning of redundant space robot based on grey-wolf optimization approach","volume":"48","author":"Shrivastava","year":"2023","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"113092","DOI":"10.1016\/j.chaos.2022.113092","article-title":"An optimal robust fuzzy adaptive integral sliding mode controller based upon a multi-objective grey wolf optimization algorithm for a nonlinear uncertain chaotic system","volume":"167","author":"Mahmoodabadi","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1007\/s40430-024-04694-4","article-title":"Robotic arm time\u2013jerk optimal trajectory based on improved dingo optimization","volume":"46","author":"Pu","year":"2024","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1007\/s40430-024-05304-z","article-title":"A novel hybrid improved dingo algorithm for unmanned aerial vehicle path planning","volume":"47","author":"Wang","year":"2025","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3488","DOI":"10.1017\/S0263574725102208","article-title":"Improved dung beetle optimization algorithm based inverse kinematics solution for robotic arm","volume":"43","author":"Lv","year":"2025","journal-title":"Robotica"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Widyianto, A., Yazid, E., Mirdanies, M., Ardiansyah, R.A., and Ramadiansyah, M.L. (2022, January 13\u201314). Optimization of PD controller using ACO for the trajectory tracking of a ship-mounted two-DOF manipulator system. Proceedings of the 2022 6th International Conference on Information Technology, Information Systems and Electrical Engineering (ICITISEE), Yogyakarta, Indonesia.","DOI":"10.1109\/ICITISEE57756.2022.10057756"},{"key":"ref_25","first-page":"70","article-title":"A Hybrid PSO-ACO Algorithm for Precise Localization and Geometric Error Reduction in Industrial Robots","volume":"12","author":"Abro","year":"2025","journal-title":"Instrumentation"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Wang, F., Wu, Z., and Bao, T. (2022). Time-jerk optimal trajectory planning of industrial robots based on a hybrid WOA-GA algorithm. Processes, 10.","DOI":"10.3390\/pr10051014"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ni, Z., Wang, G., and Ye, H. (2024, January 26\u201328). Optimal Trajectory Planning for Robotic Arm Based on Improved Whale Optimization Algorithm. Proceedings of the 2024 3rd International Conference on Service Robotics (ICoSR), Hangzhou, China.","DOI":"10.1109\/ICoSR63848.2024.00013"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"122147","DOI":"10.1016\/j.eswa.2023.122147","article-title":"Greylag goose optimization: Nature-inspired optimization algorithm","volume":"238","author":"Khodadadi","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Sharma, A., Gupta, K., Jangir, K., Jain, P., and Malakar, P. (2024, January 2\u20133). Multi-objective Greylag Goose Optimization. Proceedings of the 2024 2nd International Conference on Advancement in Computation & Computer Technologies (InCACCT), Gharuan, India.","DOI":"10.1109\/InCACCT61598.2024.10551106"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Han, B.Y., Zhao, B., and Sun, R.H. (2023). Research on Motion Control and Wafer-Centering Algorithm of Wafer-Handling Robot in Semiconductor Manufacturing. Sensors, 23.","DOI":"10.3390\/s23208502"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1109\/TMECH.2024.3411629","article-title":"Hybrid hard-soft robotic joint and robotic arm based on pneumatic origami chambers","volume":"30","author":"Oh","year":"2024","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Bassett, L., Apostle, M., and Aveta, F. (2024, January 17\u201319). High-Precision Robotic Arm for Silicon Wafer Handling and Alignment in Small-Scale Semiconductor Fabrication. Proceedings of the 2024 IEEE 15th Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON), Yorktown Heights, NY, USA.","DOI":"10.1109\/UEMCON62879.2024.10754678"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1109\/TASE.2024.3349380","article-title":"Virtual cell-based scheduling approach to single-robotic-arm cluster tools subject to wafer residency time constraints","volume":"22","author":"Wang","year":"2024","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"50100","DOI":"10.1109\/ACCESS.2022.3172953","article-title":"A fully automatic calibration for vision-based selective compliance assembly robot arm and its application to intelligent wafer inspection scheduling","volume":"10","author":"Su","year":"2022","journal-title":"IEEE Access"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"7714","DOI":"10.1109\/ACCESS.2023.3238663","article-title":"Influence of dynamic accuracy constraints of manipulator of wafer transmission robot on scheduling and control of single-armed cluster tools","volume":"11","author":"Li","year":"2023","journal-title":"IEEE Access"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"160","DOI":"10.21608\/erjeng.2023.237586.1256","article-title":"Path planning for a 6 DOF robotic arm based on whale optimization algorithm and genetic algorithm","volume":"7","author":"Mousa","year":"2023","journal-title":"J. Eng. Res."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Soleimani Amiri, M., and Ramli, R. (2021). Intelligent trajectory tracking behavior of a multi-joint robotic arm via genetic\u2013swarm optimization for the inverse kinematic solution. Sensors, 21.","DOI":"10.3390\/s21093171"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Lin, Y., Xu, Q., Ju, W., and Zhang, T. (2024). Inverse kinematics of large hydraulic manipulator arm based on ASWO optimized BP neural network. Appl. Sci., 14.","DOI":"10.3390\/app14135551"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.cogr.2023.05.003","article-title":"Optimization of energy consumption in industrial robots, a review","volume":"3","author":"Soori","year":"2023","journal-title":"Cogn. Robot."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"13695","DOI":"10.1007\/s00500-021-06007-6","article-title":"An improved particle swarm optimization algorithm for inverse kinematics solution of multi-DOF serial robotic manipulators","volume":"25","author":"Deng","year":"2021","journal-title":"Soft Comput."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/3\/829\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T09:07:43Z","timestamp":1769504863000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/3\/829"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,27]]},"references-count":40,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["s26030829"],"URL":"https:\/\/doi.org\/10.3390\/s26030829","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,27]]}}}