Feedback control of an achiral robotic microswimmer


Magnetic microswimmers are useful for navigating and performing tasks at small scales. To demonstrate effective control over such microswimmers, we implemented feedback control of the three-bead achiral microswimmers in both simulation and experiment. The achiral microswimmers with the ability to swim in bulk fluid are controlled wirelessly using magnetic fields generated from electromagnetic coils. The achirality of the microswimmers introduces unknown handedness resulting in un-certainty in swimming direction. We use a combination of rotating and static magnetic fields generated from an approximate Helmholtz coil system to overcome such uncertainty. There are also movement uncertainties due to environmental factors such as unsteady flow conditions. A kinematic model based feedback controller was created based on data fitting of experimental data. However, the controller was unable to yield satisfactory performance due to uncertainties from environmental factors; i.e., the time to reach target pose under adverse flow condition is too long. Following the implementation of an integral controller to control the microswimmers’ swimming velocity, the microswimmers were able to reach the target in roughly half the time. Through simulation and experiments, we show that the feedback control law can move an achiral microswimmer from any initial conditions to a target pose.

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  1. [1]

    Ferreira A, Agnus J, Chaillet N, Breguet J-M. A smart mi-crorobot on chip: Design, identification, and control. IEEE/ASME Transactions on Mechatronics, 2004, 9, 508–519.

    Article  Google Scholar 

  2. [2]

    Zhang H, Hutmacher DW, Chollet F, Poo A N, Burdet E. Microrobotics and MEMS-based fabrication techniques for scaffold-based tissue engineering. Macromolecular Bioscience, 2005, 5, 477–489.

    Article  Google Scholar 

  3. [3]

    Dogangil G, Ergeneman O, Abbott J J, Pané S, Hall H, Muntwyler S, Nelson B J. Toward targeted retinal drug de-livery with wireless magnetic microrobots. IEEE Interna-tional Conference on Intelligent Robots and Systems (IROS), Nice, France, 2008, 1921–1926.

    Google Scholar 

  4. [4]

    Fusco S, Chatzipirpiridis G, Sivaraman K M, Ergeneman O, Nelson B J, Pané S. Chitosan electrodeposition for micro-robotic drug delivery. Advanced Healthcare Materials, 2013, 2, 1037–1044.

    Article  Google Scholar 

  5. [5]

    Kim S, Qiu F, Kim S, Ghanbari A, Moon C, Zhang L, Nelson B J, Choi H. Fabrication and characterization of magnetic microrobots for three-dimensional cell culture and targeted transportation. Advanced Materials, 2013, 25, 5829.

    Article  Google Scholar 

  6. [6]

    Liu X, Kim K, Zhang Y, Sun Y. Nanonewton force sensing and control in microrobotic cell manipulation. International Journal of Robotics Research, 2009, 28, 1065–1076.

    Article  Google Scholar 

  7. [7]

    Martel S, Mathieu J-B, Felfoul O, Chanu A, Aboussouan E, Tamaz S, Pouponneau P, Yahia L, Beaudoin G, Soulez G. Automatic navigation of an untethered device in the artery of a living animal using a conventional clinical magnetic resonance imaging system. Applied Physics Letters, 2007, 90, 114105.

    Article  Google Scholar 

  8. [8]

    Grady M S, Howard M A III, Molloy J A, Ritter R C, Quate E G, Gillies G T. Nonlinear magnetic stereotaxis: Three-dimensional, in vivo remote magnetic manipulation of a small object in canine brain. Medical Physics, 1990, 17, 405–415.

    Article  Google Scholar 

  9. [9]

    Mathieu J-B, Beaudoin G, Martel S. Method of propulsion of a ferromagnetic core in the cardiovascular system through magnetic gradients generated by an MRI system. IEEE Transactions on Biomedical Engineering, 2006, 53, 292–299.

    Article  Google Scholar 

  10. [10]

    Abbott J, Peyer K, Lagomarsino M, Zhang L, Dong L, Kaliakatsos I, Nelson B. How should microrobots swim? The International Journal of Robotics Research, 2009, 28, 1434–1447.

    Article  Google Scholar 

  11. [11]

    Ogrin F Y, Petrov P G, Winlove C P. Ferromagnetic mi-croswimmers. Physical Review Letters, 2008, 100, 218102.

  12. [12]

    Yesin K B, Exner P, Vollmers K, Nelson B J. Design and control of in-vivo magnetic microrobots. Medical Image Computing and Computer-Assisted Intervention, 2005, 3749, 819–826.

    Google Scholar 

  13. [13]

    Avron J E, Kenneth O, Oaknin D H. Pushmepullyou: An efficient micro-swimmer. New Journal of Physics, 2005, 7, 234–234.

    Article  Google Scholar 

  14. [14]

    Najafi A, Golestanian R. Simple swimmer at low Reynolds number: Three linked spheres. Physical Review E, 2004, 69, 062901.

  15. [15]

    Clearfield A. Current opinion in solid state & materials science. Current Science, 1996, 1, 268.

    Google Scholar 

  16. [16]

    Singh R, Lillard J W Jr. Nanoparticle-based targeted drug delivery. Experimental and Molecular Pathology, 2009, 86, 215–223.

    Article  Google Scholar 

  17. [17]

    Tan M L, Choong P F, Dass C R. Recent developments in liposomes, microparticles and nanoparticles for protein and peptide drug delivery. Peptides, 2010, 31, 184–193.

    Article  Google Scholar 

  18. [18]

    Bae Y H, Park K. Targeted drug delivery to tumors: Myths, reality and possibility. Journal of Controlled Release, 2011, 153, 198–205.

    Article  Google Scholar 

  19. [19]

    Cheang U K, Kim M J. Self-assembly of robotic micro- and nanoswimmers using magnetic nanoparticles. Journal of Nanoparticle Research, 2015, 17, 145.

    Article  Google Scholar 

  20. [20]

    Ghosh A, Paria D, Rangarajan G, Ghosh A. Velocity fluc-tuations in helical propulsion: How small can a propeller be. Journal of Physical Chemistry Letters, 2013, 5, 62–68.

    Article  Google Scholar 

  21. [21]

    Sun C, Lee J S, Zhang M. Magnetic nanoparticles in MR imaging and drug delivery. Advanced Drug Delivery Re-views, 2008, 60, 1252–1265.

    Article  Google Scholar 

  22. [22]

    Dobson, J. Magnetic nanoparticles for drug delivery. Drug Development Research, 2006, 67, 55–60.

    Article  Google Scholar 

  23. [23]

    Purcell E M. Life at low Reynolds number. American Journal of Physics, 1977, 45, 3–11.

    Article  Google Scholar 

  24. [24]

    Zhang L, Abbott J J, Dong L, Kratochvil B E, Bell D, Nelson B J. Artificial bacterial flagella: Fabrication and magnetic control. Applied Physics Letters, 2009, 94, 064107.

  25. [25]

    Zhang L, Ruh E, Grützmacher D, Dong L, Bell D J, Nelson B J, Schönenberger C. Anomalous coiling of SiGe/Si and SiGe/Si/Cr helical nanobelts. Nano Letters, 2006, 6, 1311–1317.

    Article  Google Scholar 

  26. [26]

    Tottori S, Zhang L, Qiu F, Krawczyk KK, Franco-Obregón A, Nelson B J. Magnetic helical micromachines: Fabrication, controlled swimming, and cargo transport. Advanced Materials, 2012, 24, 811–816.

    Article  Google Scholar 

  27. [27]

    Ghosh A, Fischer P. Controlled propulsion of artificial magnetic nanostructured propellers. Nano Letters, 2009, 9, 2243–2245.

    Article  Google Scholar 

  28. [28]

    Cheang U K, Roy D, Lee J H, Kim M J. Fabrication and magnetic control of bacteria-inspired robotic microswim-mers. Applied Physics Letters, 2010, 97, 213704

  29. [29]

    Temel F Z, Yesilyurt S. Magnetically actuated micro swimming of bio-inspired robots in mini channels. IEEE International Conference on Mechatronics (ICM), Istanbul, Turkey, 2011, 342–347.

    Google Scholar 

  30. [30]

    Gao W, Feng X, Pei A, Kane C R, Tam R, Hennessy C, Wang J. Bioinspired helical microswimmers based on vas-cular plants. Nano Letters, 2013, 14, 305–310.

    Article  Google Scholar 

  31. [31]

    Dreyfus R, Baudry J, Roper M L, Fermigier M, Stone H A. Microscopic artificial swimmers. Nature, 2005, 437, 862–865.

    Article  Google Scholar 

  32. [32]

    Gao W, Kagan D, Pak O S, Clawson C, Campuzano S, Chuluun-Erdene E, Shipton E, Fullerton E E, Zhang L, Lauga E, Wang J. Cargo — towing fuel — free magnetic nanoswimmers for targeted drug delivery. Small, 2012, 8, 460–467.

    Article  Google Scholar 

  33. [33]

    Steager E B, Sakar M S, Kumar V, Pappas G J, Kim M J. Electrokinetic and optical control of bacterial microrobots. Journal of Micromechanics and Microengineering, 2011, 21, 035001.

  34. [34]

    Kim D H, Cheang U K, Kohidai L, Byun D, Kim M J. Artificial magnetotactic motion control of Tetrahymena pyriformis using ferromagnetic nanoparticles: A tool for fabrication of microbiorobots. Applied Physics Letters, 2010, 97, 173702.

  35. [35]

    Leoni M, Kotar J, Bassetti B, Cicuta P, Lagomarsino M C. A basic swimmer at low Reynolds number. Soft Matter, 2009, 5, 472–476.

    Article  Google Scholar 

  36. [36]

    Manesh K B, Cardona M, Yuan R, Clark M, Kagan D, Balasubramanian S, Wang J. Template-assisted fabrication of salt-independent catalytic tubular microengines. ACS Nano, 2010, 4, 1799–1804.

    Article  Google Scholar 

  37. [37]

    Gao W, D’Agostino M, Garcia-Gradilla V, Orozco J, Wang J. Multi-ful driven janus micromotors. Small, 2013, 9, 467–471.

    Article  Google Scholar 

  38. [38]

    Hong Y, Blackman N M, Kopp N D, Sen A, Velegol D. Chemotaxis of nonbiological colloidal rods. Physical Re-view Letters, 2007, 99, 178103.

  39. [39]

    Mori N, Kuribayashi K, Takeuchi S. Artificial flagellates: Analysis of advancing motions of biflagellate micro-objects. Applied Physics Letters, 2010, 96, 083701.

  40. [40]

    Volpe G, Buttinoni I, Vogt D, Kümmerer H-J, Bechinger C. Microswimmers in patterned environments. Soft Matter, 2011, 7, 8810–8815.

    Article  Google Scholar 

  41. [41]

    Cheang U K, Milutinovic D, Choi J, Kim M J. Towards model-based control of achiral microswimmers. ASME Dynamic Systems and Control Conference, TX, USA, 2014.

    Google Scholar 

  42. [42]

    Cheang U K, Meshkati F, Kim D, Kim M J, Fu H C. Minimal geometric requirements for micropropulsion via magnetic rotation. Physical Review E, 2014, 90, 033007.

  43. [43]

    Cheang U K, Kim H, Milutinovic D, Choi J, Rogowski L, Kim M J. Feedback control of three-bead achiral robotic microswimmers. IEEE International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), 2015, 518–523.

    Google Scholar 

  44. [44]

    Happel J, Brenner H. Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media, Springer, 1965.

    Google Scholar 

  45. [45]

    Atherton T J, Kerbyson D J. Size invariant circle detection. Image and Vision Computing, 1999, 17, 795–803.

    Article  Google Scholar 

  46. [46]

    Sun Y, Duthaler S, Nelson B J. Autofocusing in computer microscopy: Selecting the optimal focus algorithm. Mi-croscopy Research and Technique, 2004, 65, 139–149.

    Article  Google Scholar 

  47. [47]

    Griffiths D J. Introduction to Electrodynamics, Prentice Hall, Upper Saddle River, NJ, USA, 1999.

    Google Scholar 

  48. [48]

    Cheang U K, Lee K, Julius A A, Kim M J. Multiple-robot drug delivery strategy through coordinated teams of microswimmers. Applied Physics Letters, 2014, 105, 083705.

  49. [49]

    Aicardi M, Casalino G, Bicchi A, Balestrino A. Closed loop steering of unicycle like vehicles via Lyapunov techniques. IEEE Robotics & Automation Magazine, 1995, 2, 27–35.

    Article  Google Scholar 

  50. [50]

    Kim P S S, Becker A, Ou Y, Julius A A, Kim M J. Imparting magnetic dipole heterogeneity to internalized iron oxide nanoparticles for microorganism swarm control. Journal of Nanoparticle Research, 2015, 17, 1–15.

    Article  Google Scholar 

  51. [51]

    Slotine J J E, Li W. Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ, USA, 1991.

    Google Scholar 

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Correspondence to Min Jun Kim.

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Cheang, U.K., Kim, H., Milutinović, D. et al. Feedback control of an achiral robotic microswimmer. J Bionic Eng 14, 245–259 (2017).

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  • microrobotics
  • magnetic control
  • low Reynold number
  • chirality
  • feedback control