{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T15:55:01Z","timestamp":1765209301017,"version":"3.46.0"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T00:00:00Z","timestamp":1765152000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>Energy efficiency represents a fundamental aspect of sustainable industrial automation, where minimizing energy expenditure supports both environmental and economic goals. This work presents the modeling and comparative analysis of the energy consumption of three planar robotic manipulators performing pick-and-place operations: a serial RRR configuration (RRR-D2) and two alternative PRR architectures (PRR90 and PRR45) featuring linear prismatic guides. For each manipulator, kinematic and dynamic models are derived, and actuator electro-mechanical effects are incorporated to obtain realistic energy evaluations. The analysis is carried out over four representative trajectories and two design variables, enabling a consistent comparison in terms of both total and recoverable energy through regenerative braking. Results show that geometric and actuation parameters significantly influence energy performance and that specific PRR configurations can achieve comparable motion capabilities to the RRR structure with reduced energy demand. The proposed framework supports energy-aware robot selection and design, contributing to the development of efficient and sustainable planar manipulators for repetitive industrial operations.<\/jats:p>","DOI":"10.3390\/robotics14120185","type":"journal-article","created":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T14:52:24Z","timestamp":1765205544000},"page":"185","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modeling and Energy Expenditure Comparison of RRR and PRR Planar Robotic Manipulators for Pick-and-Place Operations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4457-1994","authenticated-orcid":false,"given":"Chiara","family":"Nezzi","sequence":"first","affiliation":[{"name":"Faculty of Engineering, Free University of Bozen-Bolzano, Via Bruno Buozzi Stra\u00dfe 1, 39100 Bozen-Bolzano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3349-2406","authenticated-orcid":false,"given":"Veit","family":"Gufler","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Free University of Bozen-Bolzano, Via Bruno Buozzi Stra\u00dfe 1, 39100 Bozen-Bolzano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7429-0974","authenticated-orcid":false,"given":"Renato","family":"Vidoni","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Free University of Bozen-Bolzano, Via Bruno Buozzi Stra\u00dfe 1, 39100 Bozen-Bolzano, Italy"},{"name":"Polytechnic Department of Engineering and Architecture, University of Udine, Via delle Scienze 206, 33100 Udine, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Renna, P., and Materi, S. (2021). A Literature Review of Energy Efficiency and Sustainability in Manufacturing Systems. Appl. Sci., 11.","DOI":"10.3390\/app11167366"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"28446","DOI":"10.1007\/s11356-023-25281-5","article-title":"Goals of sustainable infrastructure, industry, and innovation: A review and future agenda for research","volume":"30","author":"Singh","year":"2023","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_3","unstructured":"United Nations (2025, October 20). 2030 Agenda for Sustainable Development-Sustainable Development Goals. Available online: https:\/\/sdgs.un.org\/goals."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Muru, J., and Rass\u00f5lkin, A. (2025). A scoping review of energy consumption in industrial robotics. Machines, 13.","DOI":"10.3390\/machines13070542"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"124862","DOI":"10.1016\/j.jclepro.2020.124862","article-title":"A data-driven method for optimizing the energy consumption of industrial robots","volume":"285","author":"Zhang","year":"2021","journal-title":"J. Clean. Prod."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"119763","DOI":"10.1016\/j.enconman.2025.119763","article-title":"Energy efficiency improvement for decarbonization in manufacturing industry: A review","volume":"338","author":"Naumann","year":"2025","journal-title":"Energy Convers. Manag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1007\/978-3-030-23132-3_46","article-title":"Energy expenditure minimization for a delta-2 robot through a mixed approach","volume":"Volume 53","author":"Carabin","year":"2020","journal-title":"Multibody Dynamics 2019"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3692","DOI":"10.1016\/j.jclepro.2015.06.060","article-title":"Energy management in industry: A systematic review of previous findings and an integrative conceptual framework","volume":"112","author":"Nehler","year":"2016","journal-title":"J. Clean. Prod."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","unstructured":"Balderas Hill, R., Briot, S., Chriette, A., and Martinet, P. (2020). Minimizing the Energy Consumption of a Delta Robot by Exploiting the Natural Dynamics. ROMANSY 23\u2013Robot Design, Dynamics and Control (CISM IFToMM Symposium), Springer International Publishing.","DOI":"10.1007\/978-3-030-58380-4_26"},{"key":"ref_11","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_12","doi-asserted-by":"crossref","first-page":"2799","DOI":"10.1109\/TMECH.2024.3452509","article-title":"A survey of optimization-based task and motion planning: From classical to learning approaches","volume":"30","author":"Zhao","year":"2024","journal-title":"IEEE\/ASME Trans. Mechatronics"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.procir.2014.06.043","article-title":"Energy efficient trajectories for an industrial ABB robot","volume":"15","author":"Paes","year":"2014","journal-title":"Procedia CIRP"},{"key":"ref_14","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_15","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1016\/j.procir.2015.02.174","article-title":"Minimization of the energy consumption in motion planning for single-robot tasks","volume":"29","author":"Pellegrinelli","year":"2015","journal-title":"Procedia CIRP"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Bj\u00f6rkenstam, S., Gleeson, D., Bohlin, R., Carlson, J.S., and Lennartson, B. (2013, January 17\u201320). Energy Efficient and Collision Free Motion of Industrial Robots using Optimal Control. Proceedings of the IEEE Conference on Automation Science and Engineering (CASE), Madison, WI, USA.","DOI":"10.1109\/CoASE.2013.6654025"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1062","DOI":"10.1109\/TIE.2015.2481360","article-title":"Distributed-torque-based independent joint tracking control of a redundantly actuated parallel robot with two higher kinematic pairs","volume":"63","author":"Cheng","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1016\/j.promfg.2018.06.122","article-title":"Energy-efficient trajectory planning for an industrial robot using a multi-objective optimisation approach","volume":"25","author":"Liu","year":"2018","journal-title":"Procedia Manuf."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/j.rcim.2018.12.020","article-title":"Optimization of the energy consumption of industrial robots for automatic code generation","volume":"57","author":"Gadaleta","year":"2019","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"102046","DOI":"10.1016\/j.rcim.2020.102046","article-title":"Extensive experimental investigation for the optimization of the energy consumption of a high payload industrial robot with open research dataset","volume":"68","author":"Gadaleta","year":"2021","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1080\/19397038.2020.1805040","article-title":"Energy consumption parameter analysis of industrial robots using design of experiment methodology","volume":"14","author":"Luong","year":"2021","journal-title":"Int. J. Sustain. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Baggetta, M., Berselli, G., Razzoli, R., and Zucchinetti, M. (2022). Energy efficient trajectory planning in robotic cells via virtual prototyping tools. International Joint Conference on Mechanics, Design Engineering & Advanced Manufacturing, Springer International Publishing.","DOI":"10.1007\/978-3-031-15928-2_54"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1687814018773852","DOI":"10.1177\/1687814018773852","article-title":"Energy consumption modeling of industrial robot based on simulated power data and parameter identification","volume":"10","author":"Liu","year":"2018","journal-title":"Adv. Mech. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1007\/978-3-031-91179-8_66","article-title":"Energy expenditure comparison of planar robotic manipulators for pick-and-place operations","volume":"Volume 180","author":"Nezzi","year":"2025","journal-title":"Proceedings of I4SDG Workshop 2025-IFToMM for Sustainable Development Goals"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Carabin, G., Wehrle, E., and Vidoni, R. (2017). A review on energy-saving optimization methods for robotic and automatic systems. Robotics, 6.","DOI":"10.3390\/robotics6040039"},{"key":"ref_26","first-page":"268","article-title":"Energy saving in redundant robotic cells: Optimal trajectory planning","volume":"Volume 66","author":"Boscariol","year":"2018","journal-title":"Mechanism Design for Robotics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2677","DOI":"10.1007\/s00170-024-13496-w","article-title":"Dynamic modelling and energy-efficiency optimization in a 3-DOF parallel robot","volume":"132","author":"Fabris","year":"2024","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"051004","DOI":"10.1115\/1.4053158","article-title":"Performing energy-efficient pick-and-place motions for high-speed robots by using variable stiffness springs","volume":"14","author":"Briot","year":"2022","journal-title":"J. Mech. Robot."},{"key":"ref_29","first-page":"4235","article-title":"Minimizing Energy Consumption of Elastic Robots in Repetitive Tasks","volume":"53","author":"Cherubini","year":"2023","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1234","DOI":"10.1109\/LRA.2023.3290518","article-title":"Optimization of Mono- and Bi-Articular Parallel Elastic Elements for a Robotic Arm Performing a Pick-and-Place Task","volume":"8","author":"Marchal","year":"2023","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Siciliano, B., Sciavicco, L., Villani, L., and Oriolo, G. (2010). Robotics: Modelling, Planning and Control, Springer.","DOI":"10.1007\/978-1-84628-642-1"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Nezzi, C., De Marchi, M., Vidoni, R., and Rauch, E. (2025). A Multi-Purpose Simulation Layer for Digital Twin Applications in Mechatronic Systems. Machines, 13.","DOI":"10.3390\/machines13080671"},{"key":"ref_33","unstructured":"igus (Automation Division) (2025, October 18). 2-Axis Delta Robot. Available online: https:\/\/rbtx.com\/en-US\/components\/robots\/2-axis-delta-robot-pre-assembled-with-control-unit-working-space-diameter-700-mm?srsltid=AfmBOorVLWXIS3VIgvxpDuMry8rk7hx_BbrYUmBwH3rYLHCf5ewqiqdH."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"102045","DOI":"10.1016\/j.rcim.2020.102045","article-title":"An energy-efficient approach for 3D printing with a Linear Delta Robot equipped with optimal springs","volume":"67","author":"Carabin","year":"2021","journal-title":"Robot. Comput. Integr. Manuf."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/14\/12\/185\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T15:16:13Z","timestamp":1765206973000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/14\/12\/185"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,8]]},"references-count":34,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["robotics14120185"],"URL":"https:\/\/doi.org\/10.3390\/robotics14120185","relation":{},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,8]]}}}