{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T21:54:40Z","timestamp":1780696480123,"version":"3.54.1"},"reference-count":23,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T00:00:00Z","timestamp":1759104000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Scientific research projects of colleges and universities in Hebei Province","award":["QN2024063"],"award-info":[{"award-number":["QN2024063"]}]},{"name":"The Best Supported Postdoctoral Scientific Research Projects in Hebei Province","award":["B2023005005"],"award-info":[{"award-number":["B2023005005"]}]}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Robotics"],"abstract":"<jats:p>Robot energy consumption is a prominent challenge in intelligent manufacturing and construction. Reducing energy consumption during robot trajectory execution is an urgent issue requiring immediate attention. In view of the shortcomings of traditional trajectory optimization methods, this paper proposes a multi-objective trajectory optimization method that combines energy consumption mapping with the NSGA-II, aiming to reduce robots\u2019 trajectory energy consumption and optimize execution efficiency. By establishing a dynamic energy consumption model, energy consumption mapping is employed to constrain energy consumption within the robot\u2019s workspace, thereby providing guidance for the optimization process. Simultaneously, with energy consumption minimization and time consumption as optimization objectives, the NSGA-II is utilized to obtain the Pareto-optimal solution set through non-dominated sorting and congestion distance calculation. Energy consumption mapping serves as a dynamic feedback mechanism during the optimization process, guiding the distribution of trajectory points towards low-energy-consumption regions, accelerating algorithm convergence, and enhancing the quality of the solution set. The experimental results demonstrate that the proposed method can significantly reduce robots\u2019 trajectory energy consumption and achieve an effective balance between energy consumption and time consumption. Compared with the conventional NSGA-II normalized weighted function method in similar task scenarios, the robot can save 14.87% and 10.47% of its energy consumption, respectively. Compared with traditional methods, this method exhibits superior energy-saving performance and adaptability in complex task environments, providing a novel solution for the efficient trajectory planning of robots.<\/jats:p>","DOI":"10.3390\/robotics14100138","type":"journal-article","created":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T10:49:34Z","timestamp":1759142974000},"page":"138","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Research on Energy Consumption Optimization Strategies of Robot Joints Based on NSGA-II and Energy Consumption Mapping"],"prefix":"10.3390","volume":"14","author":[{"given":"Dong","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xin","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ming","family":"Han","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,29]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","unstructured":"Bugmann, G., Siegel, M., and Burcin, R. (2011, January 13\u201315). A role for robotics in sustainable development?. Proceedings of the IEEE Africon \u201911, Victoria Falls, Zambia.","DOI":"10.1109\/AFRCON.2011.6072154"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1142\/S2301385025500372","article-title":"Trajectory Planning for Autonomous Formation of Wheeled Mobile Robots via Modified Artificial Potential Field and Improved PSO Algorithm","volume":"12","author":"Bouaziz","year":"2024","journal-title":"Unmanned Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/j.mechatronics.2013.01.013","article-title":"A method for reducing the energy consumption of pick-and-place industrial robots","volume":"23","author":"Pellicciari","year":"2013","journal-title":"Mechatronics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1016\/j.procir.2014.10.055","article-title":"Minimizing energy consumption for robot arm movement","volume":"25","author":"Mohammed","year":"2014","journal-title":"Procedia CIRP"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1080\/15397734.2022.2106241","article-title":"Energy optimal point-to-point motion profile optimization","volume":"52","author":"Vanbecelaere","year":"2024","journal-title":"Mech. Based Des. Struct. Mach."},{"key":"ref_7","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_8","doi-asserted-by":"crossref","first-page":"7247093","DOI":"10.1155\/2018\/7247093","article-title":"Minimum Energy Trajectory Optimization for Driving Systems of Palletizing Robot Joints","volume":"2018","author":"He","year":"2018","journal-title":"Math. Probl. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Qie, X., Kang, C., Zong, G., and Chen, S. (2022). Trajectory Planning and Simulation Study of Redundant Robotic Arm for Upper Limb Rehabilitation Based on Back Propagation Neural Network and Genetic Algorithm. Sensors, 22.","DOI":"10.3390\/s22114071"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1142\/S2301385024500018","article-title":"New robust backstepping attitude control approach applied to quanser 3 DOF hover quadrotor in the case of actuators faults","volume":"12","author":"Benghezal","year":"2024","journal-title":"Unmanned Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1016\/j.energy.2017.02.174","article-title":"Multi-objective optimization methods and application in energy saving","volume":"125","author":"Cui","year":"2017","journal-title":"Energy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1007\/s10846-018-0922-5","article-title":"Self-Tuning Time-Energy Optimization for the Trajectory Planning of a Wheeled Mobile Robot","volume":"95","author":"Serralheiro","year":"2019","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"15217","DOI":"10.1007\/s10462-023-10526-z","article-title":"A comprehensive survey on NSGA-II for multi-objective optimization and applications","volume":"56","author":"Ma","year":"2023","journal-title":"Artif. Intell. Rev."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Holzmann, P., Pfefferkorn, M., Peters, J., and Findeisen, R. (2024, January 25\u201328). Learning Energy-Efficient Trajectory Planning for Robotic Manipulators Using Bayesian Optimization. Proceedings of the 2024 European Control Conference, Stockholm, Sweden.","DOI":"10.23919\/ECC64448.2024.10590756"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1007\/s00170-014-6737-z","article-title":"Reducing the energy consumption of industrial robots in manufacturing systems","volume":"78","author":"Paryanto","year":"2015","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1002\/rob.21927","article-title":"Off-road ground robot path energy cost prediction through probabilistic spatial map","volume":"37","author":"Quann","year":"2020","journal-title":"J. Field Robot."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1108\/AA-07-2020-0099","article-title":"Planning and optimization of robotic pick-and-place operations in highly constrained industrial environments","volume":"41","author":"Tipary","year":"2021","journal-title":"Assem. Autom."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4029","DOI":"10.1007\/s00500-023-07923-5","article-title":"Jerk-bounded trajectory planning for rotary flexible joint manipulator: An experimental approach","volume":"27","author":"Bilal","year":"2023","journal-title":"Soft Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.procir.2024.01.041","article-title":"The Impacts of Industrial Safety on Environmental Sustainability in Human-Robot-Collaboration within Industry 5.0","volume":"122","author":"Bonello","year":"2024","journal-title":"Procedia CIRP"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"271","DOI":"10.3724\/SP.J.1218.2010.00271","article-title":"Multi-objective Optimization on Dynamic Performance for a Planar Parallel Mechanism with NSGA-II Algorithm","volume":"32","author":"Kong","year":"2010","journal-title":"Robot"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1429","DOI":"10.1016\/j.jbusres.2015.01.027","article-title":"Improving productivity using a multi-objective optimization of robotic trajectory planning","volume":"68","author":"Rubio","year":"2015","journal-title":"J. Bus. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"031001","DOI":"10.1115\/1.4026031","article-title":"Global performance index system for kinematic optimization of robotic mechanism","volume":"136","author":"Zhang","year":"2014","journal-title":"J. Mech. Des."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"104725","DOI":"10.1016\/j.mechmachtheory.2022.104725","article-title":"Review of the performance optimization of parallel manipulators","volume":"170","author":"Yang","year":"2022","journal-title":"Mech. Mach. 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