{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T06:43:29Z","timestamp":1774766609280,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T00:00:00Z","timestamp":1709078400000},"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>Electromagnet arrays show significant potential in the untethered guidance of particles, devices, and eventually robots. However, complications in obtaining accurate models of electromagnetic fields pose challenges for precision control. Manipulation often requires the reduced-order modeling of physical systems, which may be computationally complex and may still not account for all possible system dynamics. Additionally, control schemes capable of being applied to electromagnet arrays of any configuration may significantly expand the usefulness of any control approach. In this study, we developed a data-driven approach to the magnetic control of a neodymium magnets (NdFeB magnetic sphere) using a simple, highly constrained magnetic actuation architecture. We developed and compared two regression-based schemes for controlling the NdFeB sphere in the workspace of a four-coil array of electromagnets. We obtained averaged submillimeter positional control (0.85 mm) of a NdFeB hard magnetic sphere in a 2D plane using a controller trained using a single-layer, five-input regression neural network with a single hidden layer.<\/jats:p>","DOI":"10.3390\/robotics13030039","type":"journal-article","created":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T06:14:22Z","timestamp":1709100862000},"page":"39","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Control Interface for Autonomous Positioning of Magnetically Actuated Spheres Using an Artificial Neural Network"],"prefix":"10.3390","volume":"13","author":[{"given":"Victor","family":"Huynh","sequence":"first","affiliation":[{"name":"Department of Bioengineering, George Mason University, Fairfax, VA 22030, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Basam","family":"Mutawak","sequence":"additional","affiliation":[{"name":"Department of Bioengineering, George Mason University, Fairfax, VA 22030, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Minh Quan","family":"Do","sequence":"additional","affiliation":[{"name":"Department of Bioengineering, George Mason University, Fairfax, VA 22030, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2538-929X","authenticated-orcid":false,"given":"Elizabeth A.","family":"Ankrah","sequence":"additional","affiliation":[{"name":"Department of Bioengineering, George Mason University, Fairfax, VA 22030, USA"},{"name":"Department of Informatics, University of California Irvine, Irvine, CA 92617, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-7250-5016","authenticated-orcid":false,"given":"Pouya","family":"Kassaeiyan","sequence":"additional","affiliation":[{"name":"Department of Bioengineering, George Mason University, Fairfax, VA 22030, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8564-2982","authenticated-orcid":false,"given":"Irving N.","family":"Weinberg","sequence":"additional","affiliation":[{"name":"Weinberg Medical Physics, Inc., North Bethesda, MD 20852, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4203-4140","authenticated-orcid":false,"given":"Nathalia","family":"Peixoto","sequence":"additional","affiliation":[{"name":"Department of Bioengineering, George Mason University, Fairfax, VA 22030, USA"},{"name":"Department of Electrical and Computer Engineering, George Mason University, Fairfax, VA 22030, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0923-8413","authenticated-orcid":false,"given":"Qi","family":"Wei","sequence":"additional","affiliation":[{"name":"Department of Bioengineering, George Mason University, Fairfax, VA 22030, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9459-3932","authenticated-orcid":false,"given":"Lamar O.","family":"Mair","sequence":"additional","affiliation":[{"name":"Weinberg Medical Physics, Inc., North Bethesda, MD 20852, USA"},{"name":"Image Guided Therapy Research Institute, North Bethesda, MD 20852, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1038\/s42256-020-00231-9","article-title":"Enabling the future of colonoscopy with intelligent and autonomous magnetic manipulation","volume":"2","author":"Martin","year":"2020","journal-title":"Nat. Mach. Intell."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kumar, P., Malik, S., Toyserkani, E., and Khamesee, M.B. (2022). Development of an electromagnetic micromanipulator levitation system for metal additive manufacturing applications. Micromachines, 13.","DOI":"10.3390\/mi13040585"},{"key":"ref_3","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. Horizons"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2000082","DOI":"10.1002\/aisy.202000082","article-title":"Magnetic actuation systems for miniature robots: A review","volume":"2","author":"Yang","year":"2020","journal-title":"Adv. Intell. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1705061","DOI":"10.1002\/adma.201705061","article-title":"Small-scale machines driven by external power sources","volume":"30","author":"Chen","year":"2018","journal-title":"Adv. Mater."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1109\/JPROC.2014.2385105","article-title":"Biomedical applications of untethered mobile milli\/microrobots","volume":"103","author":"Sitti","year":"2015","journal-title":"Proc. IEEE"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1346","DOI":"10.3390\/mi6091346","article-title":"Magnetic actuation based motion control for microrobots: An overview","volume":"6","author":"Xu","year":"2015","journal-title":"Micromachines"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1146\/annurev-control-032720-104318","article-title":"Motion control in magnetic microrobotics: From individual and multiple robots to swarms","volume":"4","author":"Yang","year":"2021","journal-title":"Annu. Rev. Control Robot. Auton. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1146\/annurev-control-081219-082713","article-title":"Magnetic methods in robotics","volume":"3","author":"Abbott","year":"2020","journal-title":"Annu. Rev. Control Robot. Auton. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1109\/TCST.2011.2152842","article-title":"Steering a ferromagnetic particle by optimal magnetic feedback control","volume":"20","author":"Komaee","year":"2011","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1109\/TCST.2016.2539322","article-title":"Feedback control for transportation of magnetic fluids with minimal dispersion: A first step toward targeted magnetic drug delivery","volume":"25","author":"Komaee","year":"2016","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2205382","DOI":"10.1002\/advs.202205382","article-title":"Data-driven intelligent manipulation of particles in microfluidics","volume":"10","author":"Fang","year":"2023","journal-title":"Adv. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"13095","DOI":"10.1364\/OE.14.013095","article-title":"Automated trapping, assembly, and sorting with holographic optical tweezers","volume":"14","author":"Chapin","year":"2006","journal-title":"Opt. Express"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"118102","DOI":"10.1103\/PhysRevLett.94.118102","article-title":"Control of nanoparticles with arbitrary two-dimensional force fields","volume":"94","author":"Cohen","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"12764","DOI":"10.1038\/ncomms12764","article-title":"Controlling the motion of multiple objects on a Chladni plate","volume":"7","author":"Zhou","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1016\/j.jmmm.2010.08.024","article-title":"Planar steering of a single ferrofluid drop by optimal minimum power dynamic feedback control of four electromagnets at a distance","volume":"323","author":"Probst","year":"2011","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1109\/TRO.2018.2875393","article-title":"Design of an electromagnetic setup for independent three-dimensional control of pairs of identical and nonidentical microrobots","volume":"35","author":"Ongaro","year":"2018","journal-title":"IEEE Trans. Robot."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2200466","DOI":"10.1002\/aisy.202200466","article-title":"Advances in Finite Element Analysis of External Field-Driven Micro\/Nanorobots: A Review","volume":"5","author":"Liu","year":"2023","journal-title":"Adv. Intell. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1109\/60.103639","article-title":"Identification and control of a dc motor using back-propagation neural networks","volume":"6","author":"Weerasooriya","year":"1991","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_20","unstructured":"Kolo, B.A. (1998). Neural Networks in Magnetic Guidance, University of Virginia."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Yu, R., Charreyron, S.L., Boehler, Q., Weibel, C., Chautems, C., Poon, C.C., and Nelson, B.J. (August, January 31). Modeling electromagnetic navigation systems for medical applications using random forests and artificial neural networks. Proceedings of the 2020 IEEE International Conference on Robotics and Automation (ICRA), Paris, France.","DOI":"10.1109\/ICRA40945.2020.9197212"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Kazemzadeh Heris, P., and Khamesee, M.B. (2022). Design and fabrication of a magnetic actuator for torque and force control estimated by the ann\/sa algorithm. Micromachines, 13.","DOI":"10.3390\/mi13020327"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"631303","DOI":"10.3389\/frobt.2021.631303","article-title":"A recurrent neural-network-based real-time dynamic model for soft continuum manipulators","volume":"8","author":"Tariverdi","year":"2021","journal-title":"Front. Robot. AI"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1380","DOI":"10.1109\/TASE.2020.3006131","article-title":"3-D autonomous manipulation system of helical microswimmers with online compensation update","volume":"18","author":"Liu","year":"2020","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2200023","DOI":"10.1002\/aisy.202200023","article-title":"Smart Magnetic Microrobots Learn to Swim with Deep Reinforcement Learning","volume":"4","author":"Behrens","year":"2022","journal-title":"Adv. Intell. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3895","DOI":"10.1017\/S0263574722000662","article-title":"Position control of a wheel-based miniature magnetic robot using neuro-fuzzy network","volume":"40","author":"Salehi","year":"2022","journal-title":"Robotica"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Turan, M., Ornek, E.P., Ibrahimli, N., Giracoglu, C., Almalioglu, Y., Yanik, M.F., and Sitti, M. (2018, January 1\u20135). Unsupervised odometry and depth learning for endoscopic capsule robots. Proceedings of the 2018 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain.","DOI":"10.1109\/IROS.2018.8593623"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"eaav7725","DOI":"10.1126\/scirobotics.aav7725","article-title":"Intelligent magnetic manipulation for gastrointestinal ultrasound","volume":"4","author":"Norton","year":"2019","journal-title":"Sci. Robot."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1055\/a-1306-7590","article-title":"Establishing key research questions for the implementation of artificial intelligence in colonoscopy: A modified Delphi method","volume":"53","author":"Ahmad","year":"2021","journal-title":"Endoscopy"},{"key":"ref_30","first-page":"1","article-title":"Dynamic magnetic field generation with high accuracy modeling applied to magnetic robots","volume":"57","author":"Fan","year":"2021","journal-title":"IEEE Trans. Magn."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1109\/TMRB.2022.3214426","article-title":"Control of Magnetic Surgical Robots With Model-Based Simulators and Reinforcement Learning","volume":"4","author":"Barnoy","year":"2022","journal-title":"IEEE Trans. Med. Robot. Bionics"},{"key":"ref_32","unstructured":"Liu, D. (2021). The Application of Machine Learning for Designing and Controlling Electromagnetic Fields. [Ph.D. Thesis, University of Wisconsin\u2013Madison]."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"11435","DOI":"10.1038\/s41598-022-15638-0","article-title":"Recurrent neural network based high-precision position compensation control of magnetic levitation system","volume":"12","author":"Huang","year":"2022","journal-title":"Sci. Rep."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1109\/TRO.2020.3047053","article-title":"Modeling electromagnetic navigation systems","volume":"37","author":"Charreyron","year":"2021","journal-title":"IEEE Trans. Robot."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2280","DOI":"10.1016\/j.patcog.2014.01.005","article-title":"Automatic generation and detection of highly reliable fiducial markers under occlusion","volume":"47","year":"2014","journal-title":"Pattern Recognit."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1109\/72.97934","article-title":"A general regression neural network","volume":"2","author":"Specht","year":"1991","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_37","first-page":"2825","article-title":"Scikit-learn: Machine Learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_38","unstructured":"(Deep Learning Toolbox, 2022). Deep Learning Toolbox, Version: 9.4 (R2022b)."},{"key":"ref_39","unstructured":"Mor\u00e9, J.J. (2006). Numerical Analysis, Proceedings of the Biennial Conference, Dundee, UK, June 28\u2013July 1 1977, Springer."},{"key":"ref_40","unstructured":"Guennebaud, G., Jacob, B., Avery, P., Bachrach, A., Barthelemy, S., Becker, C., Benjamin, D., Berger, C., Berres, A., and Blanco, J.L. (2019, January 15). Eigen v3. Available online: http:\/\/eigen.tuxfamily.org."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1893","DOI":"10.1016\/j.matt.2020.08.034","article-title":"Intelligent microfluidics: The convergence of machine learning and microfluidics in materials science and biomedicine","volume":"3","author":"Galan","year":"2020","journal-title":"Matter"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1002\/wnan.1311","article-title":"Open challenges in magnetic drug targeting","volume":"7","author":"Shapiro","year":"2015","journal-title":"Wiley Interdiscip. Rev. Nanomed. Nanobiotechnol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1611","DOI":"10.2217\/nnm.12.133","article-title":"Microfabricated magnetic structures for future medicine: From sensors to cell actuators","volume":"7","author":"Vitol","year":"2012","journal-title":"Nanomedicine"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"736730","DOI":"10.3389\/fnins.2021.736730","article-title":"Study on magnetic control systems of micro-robots","volume":"15","author":"Shao","year":"2021","journal-title":"Front. Neurosci."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1109\/TBME.2020.3009693","article-title":"Magnetic control of a flexible needle in neurosurgery","volume":"68","author":"Hong","year":"2020","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1038\/s41575-020-0290-z","article-title":"Next-generation robotics in gastrointestinal surgery","volume":"17","author":"Kinross","year":"2020","journal-title":"Nat. Rev. Gastroenterol. Hepatol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1038\/s41585-020-0375-z","article-title":"Autonomous surgery in the era of robotic urology: Friend or foe of the future surgeon?","volume":"17","author":"Connor","year":"2020","journal-title":"Nat. Rev. Urol."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"6617309","DOI":"10.1155\/2021\/6617309","article-title":"Control of Magnetic Manipulator Using Reinforcement Learning Based on Incrementally Adapted Local Linear Models","volume":"2021","author":"Brablc","year":"2021","journal-title":"Complexity"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1038\/s42256-023-00779-2","article-title":"Autonomous 3D positional control of a magnetic microrobot using reinforcement learning","volume":"6","author":"Abbasi","year":"2024","journal-title":"Nat. Mach. Intell."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"7699","DOI":"10.1109\/TCYB.2022.3199213","article-title":"Deep Reinforcement Learning Framework-Based Flow Rate Rejection Control of Soft Magnetic Miniature Robots","volume":"53","author":"Cai","year":"2022","journal-title":"IEEE Trans. Cybern."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/13\/3\/39\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:06:16Z","timestamp":1760105176000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/13\/3\/39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,28]]},"references-count":50,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["robotics13030039"],"URL":"https:\/\/doi.org\/10.3390\/robotics13030039","relation":{},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,28]]}}}