{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T13:21:23Z","timestamp":1788268883370,"version":"build-2803163510"},"reference-count":47,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12304260"],"award-info":[{"award-number":["12304260"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12327806"],"award-info":[{"award-number":["12327806"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["12304260"],"award-info":[{"award-number":["12304260"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"award":["12327806"],"award-info":[{"award-number":["12327806"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008990","name":"Key R&D Project of Zhejiang Province","doi-asserted-by":"publisher","award":["2025C01162"],"award-info":[{"award-number":["2025C01162"]}],"id":[{"id":"10.13039\/501100008990","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>Magnetically actuated soft robots enable untethered operation in confined and complex environments; however, achieving controllable directional locomotion in structurally symmetric systems remains a fundamental challenge due to intrinsic force cancellation under uniform fields. Here, we present a modular strategy that integrates assembled programmable magnetization with energy-biased symmetry-breaking joints to overcome this limitation. By embedding hard-magnetic NdFeB microparticles into an Ecoflex matrix, discrete magnetic units with programmable magnetization are fabricated and assembled into higher-order architectures. We show that asymmetric film constraints prescribe joint polarity and bias strain-energy distribution during actuation, producing distinct deformation modes (folding versus bending) under identical magnetic inputs. This energy asymmetry breaks the balanced response of symmetric structures, enabling net directional motion under spatially uniform magnetic fields. Based on this principle, a segmented crawler achieves a maximum speed of 5.42 mm s\u22121 under a half-wave magnetic field, while a quadruped robot realizes programmable multi-directional locomotion (\u00b1X, \u00b1Y) via dual-field coupling, reaching a maximum speed of 3.125 mm s\u22121. These results demonstrate that modular magnetization and joint-mediated energy bias can cooperatively generate controllable directional locomotion through mechanically encoded symmetry breaking. This work provides a scalable design framework for programmable magnetic soft robots under spatially uniform magnetic fields.<\/jats:p>","DOI":"10.3390\/mi17080927","type":"journal-article","created":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T17:26:52Z","timestamp":1785778012000},"page":"927","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Programmable Magnetic Soft Robots via Assembled Magnetization and Joint-Mediated Symmetry Breaking"],"prefix":"10.3390","volume":"17","author":[{"given":"Rufei","family":"Cui","sequence":"first","affiliation":[{"name":"College of Materials and Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"given":"Boqi","family":"Ding","sequence":"additional","affiliation":[{"name":"College of Materials and Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Xiaoyu","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Materials and Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"}]},{"given":"Jiangxing","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Physics, Hangzhou Normal University, Hangzhou 311121, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Yongjun","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Materials and Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Xinyu","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Materials and Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"software","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"}]},{"given":"Yaxin","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Materials and Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Renxian","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Materials and Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Kun","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Materials and Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"investigation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Fengyi","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Materials and Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"software","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8622-0175","authenticated-orcid":false,"given":"Zhe","family":"Kong","sequence":"additional","affiliation":[{"name":"Division of Microelectronic Materials and Devices, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2104347","DOI":"10.1002\/advs.202104347","article-title":"A Shift from Efficiency to Adaptability: Recent Progress in Biomimetic Interactive Soft Robotics in Wet Environments","volume":"9","author":"Fang","year":"2022","journal-title":"Adv. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1186\/s10033-022-00707-2","article-title":"A Review of Smart Materials for the Boost of Soft Actuators, Soft Sensors, and Robotics Applications","volume":"35","author":"Hao","year":"2022","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1089\/soro.2022.0206","article-title":"Engineering Magnetic Soft and Reconfigurable Robots","volume":"11","author":"Ning","year":"2024","journal-title":"Soft Robot."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Singh, A., Ansari, M., Dey, A., Laux, P., Samal, S., Malgaretti, P., Mohapatra, S., Busse, M., Suar, M., and Tisato, V. (2025). Bioinspired Soft Machines: Engineering Nature\u2019s Grace into Future Innovations. J. Funct. Biomater., 16.","DOI":"10.20944\/preprints202502.2028.v1"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Liu, K., Chen, W., Yang, W., Jiao, Z., and Yu, Y. (2023). Review of the Research Progress in Soft Robots. Appl. Sci., 13.","DOI":"10.3390\/app13010120"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1800477","DOI":"10.1002\/admt.201800477","article-title":"Soft-Matter Engineering for Soft Robotics","volume":"4","author":"Majidi","year":"2019","journal-title":"Adv. Mater. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"101423","DOI":"10.1016\/j.apmt.2022.101423","article-title":"Liquid Metal Droplets Enabled Soft Robots","volume":"27","author":"Zheng","year":"2022","journal-title":"Appl. Mater. Today"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2301862","DOI":"10.1002\/admt.202301862","article-title":"Recent Advances in Bioinspired Soft Robots: Fabrication, Actuation, Tracking, and Applications","volume":"9","author":"Ye","year":"2024","journal-title":"Adv. Mater. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2300311","DOI":"10.1002\/aisy.202300311","article-title":"A Review of Soft Microrobots: Material, Fabrication, and Actuation","volume":"5","author":"Ye","year":"2023","journal-title":"Adv. Intell. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1038\/s41578-018-0022-y","article-title":"Biomedical Applications of Soft Robotics","volume":"3","author":"Cianchetti","year":"2018","journal-title":"Nat. Rev. Mater."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1089\/soro.2018.0019","article-title":"A Magnetically Controlled Soft Microrobot Steering a Guidewire in a Three-Dimensional Phantom Vascular Network","volume":"6","author":"Jeon","year":"2019","journal-title":"Soft Robot."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"8247","DOI":"10.1021\/acsnano.0c01705","article-title":"Cancer Cells Microsurgery via Asymmetric Bent Surface Au\/Ag\/Ni Microrobotic Scalpels Through a Transversal Rotating Magnetic Field","volume":"14","author":"Pumera","year":"2020","journal-title":"ACS Nano"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1178","DOI":"10.1016\/j.jmapro.2020.03.059","article-title":"Additive Manufacturing of Multi-Material Soft Robot for On-Demand Drug Delivery Applications","volume":"56","author":"Joyee","year":"2020","journal-title":"J. Manuf. Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"eabb5696","DOI":"10.1126\/sciadv.abb5696","article-title":"A Magnetically Actuated Microrobot for Targeted Neural Cell Delivery and Selective Connection of Neural Networks","volume":"6","author":"Kim","year":"2020","journal-title":"Sci. Adv."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4230","DOI":"10.1109\/TRO.2023.3299530","article-title":"Crawling Soft Robot Exploiting Wheel-Legs and Multimodal Locomotion for High Terrestrial Maneuverability","volume":"39","author":"Ai","year":"2023","journal-title":"IEEE Trans. Robot."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1186\/s40638-017-0076-0","article-title":"Characterizing Dynamic Behaviors of Three-Particle Paramagnetic Microswimmer near a Solid Surface","volume":"4","author":"Wang","year":"2017","journal-title":"Robot. Biomim."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4999","DOI":"10.1021\/acs.chemrev.0c01234","article-title":"Magnetically Driven Micro and Nanorobots","volume":"121","author":"Zhou","year":"2021","journal-title":"Chem. Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1039\/C9MH00714H","article-title":"Recent Advances in Manipulation of Micro- and Nano-Objects with Magnetic Fields at Small Scales","volume":"7","author":"Cao","year":"2020","journal-title":"Mater. Horiz."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"e11415","DOI":"10.1016\/j.heliyon.2022.e11415","article-title":"Shape Programmable Magnetic Pixel Soft Robot","volume":"8","author":"Zhao","year":"2022","journal-title":"Heliyon"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"14895","DOI":"10.1021\/acsnano.2c05783","article-title":"Multistimuli-Responsive Hydroplaning Superhydrophobic Microrobots with Programmable Motion and Multifunctional Applications","volume":"16","author":"Wang","year":"2022","journal-title":"ACS Nano"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"112399","DOI":"10.1016\/j.matdes.2023.112399","article-title":"A Magnetically Actuated Soft Robot and Its Motion Regulation","volume":"235","author":"Xue","year":"2023","journal-title":"Mater. Des."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2420045","DOI":"10.1002\/adma.202420045","article-title":"Magnetically Switchable Adhesive Millirobots for Universal Manipulation in Both Air and Water","volume":"37","author":"Zhang","year":"2025","journal-title":"Adv. Mater."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5317","DOI":"10.1021\/acs.chemrev.1c00481","article-title":"Magnetic Soft Materials and Robots","volume":"122","author":"Kim","year":"2022","journal-title":"Chem. Rev."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"171160","DOI":"10.1016\/j.jmmm.2023.171160","article-title":"Design, Actuation, and Functionalization of Untethered Soft Magnetic Robots with Life-Like Motions: A Review","volume":"586","author":"Miao","year":"2023","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_25","first-page":"103532","article-title":"Modeling and Design of Three-Dimensional Voxel Printed Lattice Metamaterials","volume":"69","author":"Dong","year":"2023","journal-title":"Addit. Manuf."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2110997","DOI":"10.1002\/adfm.202110997","article-title":"Reprogrammable Soft Robot Actuation by Synergistic Magnetic and Light Fields","volume":"32","author":"Han","year":"2022","journal-title":"Adv. Funct. Mater."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"eabm7834","DOI":"10.1126\/sciadv.abm7834","article-title":"Soft Robotic Origami Crawler","volume":"8","author":"Ze","year":"2022","journal-title":"Sci. Adv."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"eabn8932","DOI":"10.1126\/sciadv.abn8932","article-title":"Untethered Small-Scale Magnetic Soft Robot with Programmable Magnetization and Integrated Multifunctional Modules","volume":"8","author":"Dong","year":"2022","journal-title":"Sci. Adv."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1038\/nature25443","article-title":"Small-Scale Soft-Bodied Robot with Multimodal Locomotion","volume":"554","author":"Hu","year":"2018","journal-title":"Nature"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2688","DOI":"10.1109\/TMECH.2020.2988718","article-title":"Magnetic Soft Robot with the Triangular Head\u2013Tail Morphology Inspired by Lateral Undulation","volume":"25","author":"Manamanchaiyaporn","year":"2020","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Venkiteswaran, V.K., Samaniego, L.F.P., Sikorski, J., and Misra, S. (2019, January 20\u201324). Bio-Inspired Terrestrial Motion of Magnetic Soft Millirobots. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Montreal, QC, Canada.","DOI":"10.1109\/LRA.2019.2898040"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"eabe8436","DOI":"10.1126\/sciadv.abe8436","article-title":"Magnetic Soft Micromachines Made of Linked Microactuator Networks","volume":"7","author":"Hu","year":"2021","journal-title":"Sci. Adv."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"eaav4494","DOI":"10.1126\/scirobotics.aav4494","article-title":"Millimeter-Scale Flexible Robots with Programmable Three-Dimensional Magnetization and Motions","volume":"4","author":"Xu","year":"2019","journal-title":"Sci. Robot."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"101306","DOI":"10.1016\/j.apmt.2021.101306","article-title":"Magneto-\/Electro-Responsive Polymers toward Manufacturing, Characterization, and Biomedical\/Soft Robotic Applications","volume":"26","author":"Yarali","year":"2021","journal-title":"Appl. Mater. Today"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1038\/s41586-018-0185-0","article-title":"Printing Ferromagnetic Domains for Untethered Fast-Transforming Soft Materials","volume":"558","author":"Kim","year":"2018","journal-title":"Nature"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"eabc6414","DOI":"10.1126\/sciadv.abc6414","article-title":"Reprogrammable Shape Morphing of Magnetic Soft Machines","volume":"6","author":"Alapan","year":"2020","journal-title":"Sci. Adv."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1021\/accountsmr.3c00227","article-title":"Magnetic Soft Matter toward Programmable and Multifunctional Miniature Machines","volume":"5","author":"Xia","year":"2024","journal-title":"Acc. Mater. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"106169","DOI":"10.1016\/j.nanoen.2021.106169","article-title":"Reconfigurable Magnetic Soft Robots with Multimodal Locomotion","volume":"87","author":"Ju","year":"2021","journal-title":"Nano Energy"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"835","DOI":"10.1109\/LRA.2017.2657879","article-title":"Reliable Grasping of Three-Dimensional Untethered Mobile Magnetic Microgripper for Autonomous Pick-and-Place","volume":"2","author":"Zhang","year":"2017","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"eabf0112","DOI":"10.1126\/scirobotics.abf0112","article-title":"Voxelated Three-Dimensional Miniature Magnetic Soft Machines via Multimaterial Heterogeneous Assembly","volume":"6","author":"Zhang","year":"2021","journal-title":"Sci. Robot."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"43802","DOI":"10.1021\/acsami.2c13108","article-title":"Aligned Magnetic Nanocomposites for Modularized and Recyclable Soft Microrobots","volume":"14","author":"Shui","year":"2022","journal-title":"ACS Appl. Mater. Interfaces"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2466","DOI":"10.1039\/D3SM00090G","article-title":"Assembly and Manipulation of Responsive and Flexible Colloidal Structures by Magnetic and Capillary Interactions","volume":"19","author":"Basu","year":"2023","journal-title":"Soft Matter"},{"key":"ref_43","first-page":"19814","article-title":"Spatially Confined Assembly and Immobilization of Hierarchical Nanoparticle Architectures inside Microdroplets in Magnetic Fields","volume":"18","author":"Basu","year":"2024","journal-title":"ACS Nano"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2415690","DOI":"10.1002\/adfm.202415690","article-title":"Annelids-Inspired Modular Design of Multi-Modal Deformation for Magnetic Soft Robots","volume":"35","author":"Nong","year":"2025","journal-title":"Adv. Funct. Mater."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2301895","DOI":"10.1002\/advs.202301895","article-title":"Kirigami Makes a Soft Magnetic Sheet Crawl","volume":"10","author":"Duhr","year":"2023","journal-title":"Adv. Sci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2500157","DOI":"10.1002\/aisy.202500157","article-title":"Symmetry Breaking Metamaterial Sleeve Actuators","volume":"7","author":"Milana","year":"2025","journal-title":"Adv. Intell. Syst."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"10486","DOI":"10.1109\/LRA.2022.3194318","article-title":"Versatile Motion Generation of Magnetic Origami Spring Robots in the Uniform Magnetic Field","volume":"7","author":"Yuan","year":"2022","journal-title":"IEEE Robot. Autom. Lett."}],"container-title":["Micromachines"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-666X\/17\/8\/927\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T12:50:10Z","timestamp":1788267010000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-666X\/17\/8\/927"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,1]]},"references-count":47,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["mi17080927"],"URL":"https:\/\/doi.org\/10.3390\/mi17080927","relation":{},"ISSN":["2072-666X"],"issn-type":[{"value":"2072-666X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,1]]}}}