Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Dexterous magnetic manipulation of conductive non-magnetic objects

Nature volume 598, pages 439–443 (2021)Cite this article

Subjects

Abstract

Dexterous magnetic manipulation of ferromagnetic objects is well established, with three to six degrees of freedom possible depending on object geometry1. There are objects for which non-contact dexterous manipulation is desirable that do not contain an appreciable amount of ferromagnetic material but do contain electrically conductive material. Time-varying magnetic fields generate eddy currents in conductive materials2,3,4, with resulting forces and torques due to the interaction of the eddy currents with the magnetic field. This phenomenon has previously been used to induce drag to reduce the motion of objects as they pass through a static field5,6,7,8, or to apply force on an object in a single direction using a dynamic field9,10,11, but has not been used to perform the type of dexterous manipulation of conductive objects that has been demonstrated with ferromagnetic objects. Here we show that manipulation, with six degrees of freedom, of conductive objects is possible by using multiple rotating magnetic dipole fields. Using dimensional analysis12, combined with multiphysics numerical simulations and experimental verification, we characterize the forces and torques generated on a conductive sphere in a rotating magnetic dipole field. With the resulting model, we perform dexterous manipulation in simulations and physical experiments.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Induced forces and torques on a conductive sphere in three canonical positions relative to a rotating magnetic dipole.
Fig. 2: Typical numerical and experimental results for force-torque characterization.
Fig. 3: Dexterous manipulation of a copper sphere in simulated microgravity.

Data availability

All data generated and scripts for analyses during this study are included in the published article and can be found using the following link: https://osf.io/uk3rx/.

References

  1. Abbott, J. J., Diller, E. & Petruska, A. J. Magnetic methods in robotics. Annu. Rev. Control Robot. Auton. Syst. 3, 57–90 (2020).

    Article  Google Scholar 

  2. Hertz, H. Miscellaneous Papers Chapter 2 [transl. Jones, D. E. & Schott, G. A.] (Macmillan, 1896).

  3. Griffiths, D. J. Introduction to Electrodynamics 4th edition (Cambridge Univ. Press, 2017).

  4. Nagel, J. R. Induced eddy currents in simple conductive geometries: mathematical formalism describes the excitation of electrical eddy currents in a time-varying magnetic field. IEEE Antennas Propag. Mag. 3, 81–88 (2018).

    Article  ADS  Google Scholar 

  5. Youngquist, R. C., Nurge, M. A., Starr, S. O., Leve, F. A. & Peck, M. A. A slowly rotating hollow sphere in a magnetic field: first steps to de-spin a space object. Am. J. Phys. 84, 181–191 (2016).

    Article  ADS  Google Scholar 

  6. Nurge, M. A., Youngquist, R. C. & Starr, S. O. A thick-walled sphere rotating in a uniform magnetic field: the next step to de-spin a space object. Am. J. Phys. 85, 596–610 (2017).

    Article  ADS  Google Scholar 

  7. Nurge, M. A., Youngquist, R. C. & Starr, S. O. Drag and lift forces between a rotating conductive sphere and a cylinderical magnet. Am. J. Phys. 86, 443–452 (2018).

    Article  ADS  Google Scholar 

  8. Sharma, K. K. et al. Space debris reduction using eddy currents. In 2018 Atmospheric Flight Mechanics Conf., 3161 (American Institute of Aeronautics and Astronautics, 2018).

  9. Reinhardt, B. Z. & Peck, M. A. New electromagnetic actuator for on-orbit inspection. J. Spacecraft Rockets 53, 241–248 (2016).

    Article  ADS  Google Scholar 

  10. Liu, X., Lu, Y., Zhou, Y. & Yin, Y. Prospects of using a permanent mangetic end effector to despin and detumble an uncooperative target. Adv. Space Res. 61, 2147–2158 (2018).

    Article  ADS  Google Scholar 

  11. Smith, Y. R., Nagel, J. R. & Rajamani, R. K. Eddy current seperation for recovery of non-ferrous metallic particles: a comprehensive review. Miner. Eng. 133, 149–159 (2019).

    Article  CAS  Google Scholar 

  12. Buckingham, E. On physically similar systems; illustrations of the use of dimensional equations. Phys. Rev. 4, 345 (1914).

    Article  ADS  Google Scholar 

  13. Shan, M., Guo, J. & Gill, E. Review and comparison of active space debris capturing and removal methods. Prog. Aerosp. Sci. 80, 18–32 (2016).

    Article  Google Scholar 

  14. Mark, C. P. & Kamath, S. Review of active space debris removal methods. Space Policy 47, 194–206 (2019).

    Article  Google Scholar 

  15. Kessler, D. J., Johnson, N. L., Liou J. C. & Matney, M. The Kessler syndrome: implications to future space operations. Adv. Astronaut. Sci. 137, AAS 10-016 (2010).

  16. Opiela, J. N. A study of the material density distribution of space debris. Adv. Space Res. 43, 1058–1064 (2009).

    Article  ADS  CAS  Google Scholar 

  17. Pelrine, R. et al. Diamagnetically levitated robots: an approach to massively parallel robotic systems with unusual motion properties. IEEE Int. Conf. Robotics and Automation, 739–744 (2012).

  18. Mirica, K. A., Ilievski, F., Ellerbee, A. K., Shevkoplyas, S. S. & Whitesides, G. M. Using magnetic levitation for three dimensional self-assembly. Adv. Mater. 23, 4134–4140 (2011).

    Article  CAS  Google Scholar 

  19. Petruska, A. J. & Abbott, J. J. Omnimagnet: an omnidirectional electromagnet for controlled dipole-field generation. IEEE Trans. Magn. 50, 8400410 (2014).

    Article  Google Scholar 

  20. Wright, S. E., Mahoney, A. W., Popek, K. M. & Abbott, J. J. The spherical-actuator-magnet manipulator: a permanent-magnet robotic end-effector. IEEE Trans. Robot. 33, 1013–2924 (2017).

    Article  Google Scholar 

  21. Petruska, A. J. & Abbott, J. J. Optimal permanent-magnet geometries for dipole field approximation. IEEE Trans. Magn. 49, 811–819 (2013).

    Article  ADS  Google Scholar 

  22. Lynch, K. M. & Park, F. C. Modern Robotics: Mechanics, Planning, and Control (Cambridge Univ. Press, 2017).

  23. Diller, E., Giltinan, J., Lum, G. Z., Ye, Z. & Sitti, M. Six-degree-of-freedom magnetic actuation for wireless microrobotics. Int. J. Robot. Res. 35, 114–128 (2016).

    Article  Google Scholar 

  24. Kummer, M. P. et al. OctoMag: an electromagnetic system for 5-DOF wireless micromanipulation. IEEE Trans. Robot. 26, 1006–1017 (2010).

    Article  Google Scholar 

  25. Petruska, A. J. & Nelson, B. J. Minimum bounds on the number of electromagnets required for remote magnetic manipulation. IEEE Trans. Robot. 31, 714–722 (2015).

    Article  Google Scholar 

  26. Ryan, P. & Diller, E. Magnetic actuation for full dexterity microrobotic control using rotating permanent magnets. IEEE Trans. Robot. 33, 1398–1409 (2017).

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Science Foundation under grants 1841845 and 1846341.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Utah, Salt Lake City, UT, USA

    Lan N. Pham & Jake J. Abbott

  2. School of Computing, University of Utah, Salt Lake City, UT, USA

    Griffin F. Tabor, Ashkan Pourkand & Tucker Hermans

  3. Lawrence Livermore National Laboratory, Livermore, CA, USA

    Jacob L. B. Aman

  4. NVIDIA, Seattle, WA, USA

    Tucker Hermans

Authors
  1. Lan N. Pham
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Griffin F. Tabor
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ashkan Pourkand
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jacob L. B. Aman
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tucker Hermans
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jake J. Abbott
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.J.A. and T.H. proposed the research. All authors participated in the planning of the article. L.N.P. and J.J.A. performed the dimensional analysis and designed the experiments to characterize force-torque. L.N.P. and J.L.B.A. performed the numerical simulations to characterize force-torque. G.F.T. and T.H. designed the numerical microgravity manipulation simulator and control scheme, and integrated the controller into the experimental manipulation system. L.N.P., G.F.T. and A.P. designed and performed the manipulation experiments. L.N.P., G.F.T. and J.J.A drafted the manuscript. All other authors performed a critical revision.

Corresponding author

Correspondence to Jake J. Abbott.

Ethics declarations

Competing interests

J.J.A. has patents and patents pending on electromagnet and permanent-magnet devices designed to generate rotating magnetic dipole fields. The other authors declare no competing interests.

Additional information

Peer review information Nature thanks Eric Diller and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This document comprises the complete supplementary information associated with the article, organized in eight sections, ordered as the respective topics are introduced in the article: 1. Dimensional analysis. 2. Characterization of force and torque. 3. Model derivation. 4. Experimental verification of force and torque. 5. Comparison of numerical and experimental results. 6. Manipulation numerical simulations. 7 Manipulation experiments. 8. Discussion.

Supplementary Video 1

Numerical simulation of dexterous manipulation of a copper sphere in microgravity, with 3-DOF position control along the edges of a cube and uncontrolled orientation, using six dipole-field sources surrounding the sphere. The black line is the path taken, and an orthonormal frame depicts the sphere’s orientation. Highlighting indicates which single dipole-field source is activated at any given instant.

Supplementary Video 2

Numerical simulation of dexterous manipulation of a copper sphere in microgravity, with 3-DOF position control along the edges of a cube and 3-DOF constant-orientation control, using six dipole-field sources surrounding the sphere. The black line is the path taken, and an orthonormal frame depicts the sphere’s orientation. Highlighting indicates which single dipole-field source is activated at any given instant.

Supplementary Video 3

Dexterous manipulation of a copper sphere floating in a raft on the surface of water, with 2-DOF position control along the edges of a square in the horizontal plane and uncontrolled orientation about the vertical axis, using four electromagnetic dipole-field sources located below the sphere. The yellow line is the path taken, and a red arrow depicts the sphere’s orientation, which is logged over time. Highlighting indicates which single dipole-field source is activated at any given instant, with a blue arrow depicting the axis of rotation of the rotating magnetic dipole.

Supplementary Video 4

Dexterous manipulation of a copper sphere floating in a raft on the surface of water, with 2-DOF position control along the edges of a square in the horizontal plane and 1-DOF orientation control about the vertical axis, using four electromagnetic dipole-field sources located below the sphere. The yellow line is the path taken, and a red arrow depicts the sphere’s orientation, which is logged over time. Highlighting indicates which single dipole-field source is activated at any given instant, with a blue arrow depicting the axis of rotation of the rotating magnetic dipole.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pham, L.N., Tabor, G.F., Pourkand, A. et al. Dexterous magnetic manipulation of conductive non-magnetic objects. Nature 598, 439–443 (2021). https://doi.org/10.1038/s41586-021-03966-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-021-03966-6

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing