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Province","award":["F2021202016"],"award-info":[{"award-number":["F2021202016"]}]},{"name":"Natural Science Foundation of Hebei Province","award":["F2021202062"],"award-info":[{"award-number":["F2021202062"]}]},{"name":"Natural Science Foundation of Hebei Province","award":["E2022202130"],"award-info":[{"award-number":["E2022202130"]}]},{"name":"Natural Science Foundation of Hebei Province","award":["EERI_OY2021004"],"award-info":[{"award-number":["EERI_OY2021004"]}]},{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment","award":["52275016"],"award-info":[{"award-number":["52275016"]}]},{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment","award":["52275017"],"award-info":[{"award-number":["52275017"]}]},{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment","award":["U1913211"],"award-info":[{"award-number":["U1913211"]}]},{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment","award":["226Z1801G"],"award-info":[{"award-number":["226Z1801G"]}]},{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment","award":["226Z1811G"],"award-info":[{"award-number":["226Z1811G"]}]},{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment","award":["F2021202016"],"award-info":[{"award-number":["F2021202016"]}]},{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment","award":["F2021202062"],"award-info":[{"award-number":["F2021202062"]}]},{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment","award":["E2022202130"],"award-info":[{"award-number":["E2022202130"]}]},{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment","award":["EERI_OY2021004"],"award-info":[{"award-number":["EERI_OY2021004"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In recent years, many wall-climbing robots have been developed in the field of petrochemical storage tank maintenance. However, it is difficult for most of them to be widely used due to common problems such as poor adsorption capacity, poor adaptation to elevation, and low trajectory tracking accuracy. In order to solve the problem of the robot not being able to achieve high-precision operation on curved surfaces, a new wall-climbing robot system is designed. Based on the magnetic wheel adsorption method, a passive adaptive motion mechanism that can adapt to walls with different curvatures is proposed. In order to improve the trajectory tracking accuracy of the wall-climbing robot, the kinematic model of the wall-climbing robot is simplified, a velocity compensation controller is designed, and the stability of the controller is proved by introducing the Lyapunov equation. Through experiments, the controller designed in this paper is compared with the conventional controller to verify the effectiveness and superiority of the controller. The experimental results show that the robot can move safely and stably on curved surfaces, with improved tracking accuracy and reduced trajectory deviation caused by response time lag, and meets the maintenance operation requirements of wall-climbing robots.<\/jats:p>","DOI":"10.3390\/sym15020255","type":"journal-article","created":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T02:58:16Z","timestamp":1673924296000},"page":"255","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Optimization Design and Trajectory Error Compensation of a Facade-Adaptive Wall-Climbing Robot"],"prefix":"10.3390","volume":"15","author":[{"given":"Dong","family":"Zhang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China"},{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhihao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pei","family":"Jia","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yueshuo","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shixin","family":"Liu","sequence":"additional","affiliation":[{"name":"China Nuclear Power Technology Research Institute Co., Ltd., Shenzhen 518028, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minglu","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Manhong","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China"},{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,17]]},"reference":[{"key":"ref_1","unstructured":"Wang, S. (2021, January 22\u201324). Research status and future development of wall-climbing robot. Proceedings of the 2021 International Conference on Electronics, Circuits and Information Engineering (ECIE), Zhengzhou, China."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"168","DOI":"10.54097\/hset.v9i.1741","article-title":"Automation Solution to Wall-climbing Robot Working for Large-scale Metal Spherical Tanks","volume":"9","author":"Chen","year":"2022","journal-title":"Highlights Sci. Eng. Technol."},{"key":"ref_3","first-page":"36","article-title":"Risk analysis and safety pre-evaluation of scaffold erection and removal","volume":"13","author":"Huang","year":"2017","journal-title":"China Sci. Technol. Prod. Saf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.prostr.2020.01.037","article-title":"Typical damage in steel storage tanks in operation","volume":"22","author":"Zdravkov","year":"2019","journal-title":"Procedia Struct. Integr."},{"key":"ref_5","first-page":"11","article-title":"Cleaning and maintenance of naphtala tanks","volume":"30","author":"Li","year":"2013","journal-title":"Petrochem. Corros. Prot."},{"key":"ref_6","unstructured":"Sattar, T., Corsar, M., James, R., and Seghier, D. (2018, January 10\u201312). Robotics Transforming the Future. Proceedings of the 21st International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, Panama City, Panama."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s12206-021-1228-2","article-title":"The multi-objective optimization design for the magnetic adsorption unit of wall-climbing robot","volume":"36","author":"Zhao","year":"2022","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Chen, X., Wu, Y., Hao, H., Shi, H., and Huang, H. (2019). Tracked Wall-Climbing Robot for Calibration of Large Vertical Metal Tanks. Appl. Sci., 9.","DOI":"10.3390\/app9132671"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Abdulkader, R.E., Veerajagadheswar, P., Htet Lin, N., Kumaran, S., Vishaal, S.R., and Mohan, R.E. (2020). Sparrow: A Magnetic Climbing Robot for Autonomous Thickness Measurement in Ship Hull Maintenance. J. Mar. Sci. Eng., 8.","DOI":"10.3390\/jmse8060469"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6004","DOI":"10.1109\/TIM.2020.2969300","article-title":"A Mechanism and Method of Leak Detection for Pressure Vessel: Whether, When, and How","volume":"69","author":"Gao","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1007\/s10948-021-06094-4","article-title":"Magnetic Field Analysis and Structure Design of a New Magnetic Wheel for Wall-Climbing Robot","volume":"35","author":"Gao","year":"2021","journal-title":"J. Supercond. Nov. Magn."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Powelson, M.W., Demirjian, W.A., and Canfield, S.L. (2019, January 18\u201321). Integrating Dry Adhesives and Compliant Suspension for Track-Type Climbing Robots. Proceedings of the ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Anaheim, CA, USA.","DOI":"10.1115\/DETC2019-98012"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1007\/s42235-019-0112-6","article-title":"A Three-row Opposed Gripping Mechanism with Bioinspired Spiny Toes for Wall-climbing Robots","volume":"16","author":"Xie","year":"2019","journal-title":"J. Bionic Eng."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Shao, J., Li, X., Zong, C., Guo, W., Bai, Y., Dai, F., and Gao, X. (2012, January 5\u20138). A Wall-Climbing Robot with Gecko Features. Proceedings of the 2012 IEEE International Conference on Mechatronics and Automation, Chengdu, China.","DOI":"10.1109\/ICMA.2012.6283270"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Yoshida, Y., and Ma, S. (2011, January 7\u201311). A Wall-Climbing Robot without Any Active Suction Mechanisms. Proceedings of the 2011 IEEE International Conference on Robotics and Biomimetics, Phuket, Thailand.","DOI":"10.1109\/ROBIO.2011.6181587"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.robot.2018.03.008","article-title":"Experimental investigation on climbing robot using rotation-flow adsorption unit","volume":"105","author":"Zhou","year":"2018","journal-title":"Robot. Auton. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.mechatronics.2016.02.001","article-title":"Hybrid electrostatic and elastomer adhesion mechanism for wall climbing robot","volume":"35","author":"Koh","year":"2016","journal-title":"Mechatronics"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1016\/j.procs.2018.07.110","article-title":"Modeling and Experimental Analysis of Suction Pressure Generated by Active Suction Chamber Based Wall Climbing Robot with a Novel Bottom Restrictor","volume":"133","author":"Navaprakash","year":"2018","journal-title":"Procedia Comput. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"045002","DOI":"10.1115\/1.4045652","article-title":"Theoretical and Experimental Study and Design Method of Blade Height of a Rotational-Flow Suction Unit in a Wall-Climbing Robot","volume":"12","author":"Chen","year":"2020","journal-title":"J. Mech. Robot."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"031017","DOI":"10.1115\/1.4045672","article-title":"Design of Track-Type Climbing Robots Using Dry Adhesives and Compliant Suspension for Scalable Payloads","volume":"12","author":"Demirjian","year":"2020","journal-title":"J. Mech. Robot."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Seriani, S., Scalera, L., Caruso, M., Gasparetto, A., and Gallina, P. (2019). Upside-Down Robots: Modeling and Experimental Validation of Magnetic-Adhesion Mobile Systems. Robotics, 8.","DOI":"10.3390\/robotics8020041"},{"key":"ref_22","unstructured":"Wen, J. (2011). Design and Characteristics of Tank Wall Crawling Robot. [Ph.D. Thesis, Shanghai Jiao Tong University]."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Eto, H., and Asada, H.H. (August, January 31). Development of a Wheeled Wall-Climbing Robot with a Shape-Adaptive Magnetic Adhesion Mechanism. Proceedings of the 2020 IEEE International Conference on Robotics and Automation (ICRA), Paris, France.","DOI":"10.1109\/ICRA40945.2020.9196919"},{"key":"ref_24","first-page":"21","article-title":"Design of robot adsorption mechanism for rust removal and wall-climbing on oil tank inner wall","volume":"36","author":"Xiao","year":"2019","journal-title":"Mach. Des."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"035001","DOI":"10.1115\/1.4045655","article-title":"A Novel Style Design of a Permanent-Magnetic Adsorption Mechanism for a Wall-Climbing Robot","volume":"12","author":"Fan","year":"2020","journal-title":"J. Mech. Robot."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.jmapro.2017.04.002","article-title":"A real-time weld line detection for derusting wall-climbing robot using dual cameras","volume":"27","author":"Wang","year":"2017","journal-title":"J. Manuf. Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1016\/j.procs.2018.07.065","article-title":"Design of Dual Purpose Cleaning Robot","volume":"133","author":"Vishaal","year":"2018","journal-title":"Procedia Comput. Sci."},{"key":"ref_28","first-page":"69","article-title":"Research on the Walking Control of the Pipeline Automatic Welding Trolley","volume":"44","author":"Zhang","year":"2016","journal-title":"Weld. Technol."},{"key":"ref_29","first-page":"788","article-title":"Image detection and classification of bridge cracks based on wall-climbing robot","volume":"46","author":"Chen","year":"2016","journal-title":"J. Univ. Sci. Technol. China"},{"key":"ref_30","first-page":"94","article-title":"Research on vertical welding technology of EH36 Marine high strength steel based on wall-climbing robot","volume":"12","author":"Cao","year":"2020","journal-title":"Precis. Form. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2867","DOI":"10.1007\/s12206-018-0542-9","article-title":"Self-adjusted adsorption strategy for an aircraft skin inspection robot","volume":"32","author":"Gu","year":"2018","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.mechmachtheory.2018.02.010","article-title":"AnyClimb-II: Dry-adhesive linkage-type climbing robot for uneven vertical surfaces","volume":"124","author":"Liu","year":"2018","journal-title":"Mech. Mach. Theory"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.oceaneng.2017.01.003","article-title":"Design and performance analysis of a tracked wall-climbing robot for ship inspection in shipbuilding","volume":"131","author":"Huang","year":"2017","journal-title":"Ocean. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"103907","DOI":"10.1016\/j.robot.2021.103907","article-title":"A magnetic crawler wall-climbing robot with capacity of high payload on the convex surface","volume":"148","author":"Hu","year":"2022","journal-title":"Robot. Auton. Syst."},{"key":"ref_35","first-page":"1","article-title":"Modeling and Trajectory Tracking Control for Magnetic Wheeled Mobile Robots Based on Improved Dual-Heuristic Dynamic Programming","volume":"99","author":"Dian","year":"2020","journal-title":"IEEE Trans. Ind. Informatics"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1109\/87.911382","article-title":"Tracking control of unicycle-modeled mobile robots using a saturation feedback controller","volume":"9","author":"Lee","year":"2001","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_37","unstructured":"Kanayama, Y., Kimura, Y., Miyazaki, F., and Noguchi, T. (1990, January 13\u201318). A stable tracking control method for an autonomous mobile robot. Proceedings of the IEEE International Conference on Robotics and Automation, Cincinnati, OH, USA."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1109\/70.880812","article-title":"Adaptive tracking control of nonholonomic mobile robot","volume":"16","author":"Kukao","year":"2000","journal-title":"IEEE Trans Robot. Autom."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1002\/(SICI)1097-4563(199703)14:3<149::AID-ROB1>3.0.CO;2-R","article-title":"Control of a nonholonomic mobile robot: Backstepping kinematics into dynamics","volume":"14","author":"Fierro","year":"1997","journal-title":"J. Robot Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/255\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:07:57Z","timestamp":1760119677000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/255"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,17]]},"references-count":39,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["sym15020255"],"URL":"https:\/\/doi.org\/10.3390\/sym15020255","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,17]]}}}