Journal of Micro-Bio Robotics

, Volume 12, Issue 1–4, pp 9–19 | Cite as

Two-agent formation control of magnetic microrobots in two dimensions

  • Mohammad Salehizadeh
  • Eric DillerEmail author
Research Article


This paper presents a new method to control multiple micro-scale magnetic agents operating in close proximity to each other for applications in microrobotics. Controlling multiple magnetic microrobots close to each other is difficult due to magnetic interactions between the agents, and here we seek to control those interactions for the creation of desired multi-agent formations. We use the fact that all magnetic agents orient to the global input magnetic field to modulate the local attraction-repulsion forces between nearby agents. Here we study these controlled interaction magnetic forces for two cases: i) agents with free 3D magnetization, and ii) agents with constrained magnetization to horizontal motion plane. Accordingly, we devise two controllers to regulate the inter-agent spacing, heading and position of the set, for motion in two dimensions. Simulation and experimental demonstrations on two agents in this paper show the feasibility of the idea and its potential for the completion of complex tasks using teams of microrobots. Average tracking error of less than 39 micrometers and 1.45 degrees is accomplished for the regulation of the inter-agent space and the pair heading angle, respectively, for identical spherical-shape agents with nominal radius less than of 250 micrometers operating within several body-lengths of each other.


Microrobot Multi-agent control Underactuated system Magnetic actuation Motion planning 



This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through the Discovery Grants Program 2014-04703.

Supplementary material

12213_2017_95_MOESM1_ESM.pdf (282 kb)
(PDF 282 KB)
12213_2017_95_MOESM2_ESM.mp4 (1 mb)
(MP4 1.01 MB)
12213_2017_95_MOESM3_ESM.mp4 (15.9 mb)
(MP4 15.9 MB)


  1. 1.
    Nelson BJ, Kaliakatsos IK, Abbott JJ (2010) Microrobots for minimally invasive medicine. Ann Rev Biomed Eng 12:55–85CrossRefGoogle Scholar
  2. 2.
    Steager EB, Sakar MS, Magee C, Kennedy M, Cowley A, Kumar V (2013) Automated biomanipulation of single cells using magnetic microrobots. Int J Robot Res 32(3):346–359CrossRefGoogle Scholar
  3. 3.
    Whitesides GM, Grzybowski B (2002) Self-assembly at all scales. Science 295(5564):2418–2421CrossRefGoogle Scholar
  4. 4.
    Sitti M, Ceylan H, Wenqi H, Giltinan J, Turan M, Yim S, Diller E (2015) Biomedical applications of untethered mobile milli/microrobots. Proc IEEE 103(2):205–224CrossRefGoogle Scholar
  5. 5.
    Diller E, Sitti M (2014) Three-dimensional programmable assembly by untethered magnetic robotic micro-grippers. Adv Funct Mater 24(28):4397–4404CrossRefGoogle Scholar
  6. 6.
    Wenqi H, Fan Q, Ohta AT (2014) Interactive actuation of multiple opto-thermocapillary flow-addressed bubble microrobots. Robot Biomimet 1(1):1–6CrossRefGoogle Scholar
  7. 7.
    Arcese L, Fruchard M, Ferreira A (2013) Adaptive controller and observer for a magnetic microrobot. IEEE Trans Robot 29(4):1060–1067CrossRefGoogle Scholar
  8. 8.
    Abbott JJ, Lagomarsino MC, Li Z, Dong L, Nelson BJ (2009) How should microrobots swim? Int J Robot Res 28(11–12):1434–1447CrossRefGoogle Scholar
  9. 9.
    Chowdhury S, Jing W, Cappelleri DJ (2015) Controlling multiple microrobots: recent progress and future challenges. J Micro-Bio Robot 10(1-4):1–11CrossRefGoogle Scholar
  10. 10.
    Diller E, Giltinan J, Sitti M (2013) Independent control of multiple magnetic microrobots in three dimensions. Int J Robot Res 32(5):614–631CrossRefGoogle Scholar
  11. 11.
    Ng JM, Fuerstman MJ, Grzybowski BA, Stone HA, Whitesides GM (2003) Self-assembly of gears at a fluid/air interface. J Amer Chem Soc 125(26):7948–7958CrossRefGoogle Scholar
  12. 12.
    Grzybowski BA, Stone HA, Whitesides GM (2000) Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid–air interface. Nature 405(6790):1033–1036CrossRefGoogle Scholar
  13. 13.
    Snezhko A, Aranson IS (2011) Magnetic manipulation of self-assembled colloidal asters. Nat Mater 10(9):698–703CrossRefGoogle Scholar
  14. 14.
    Martel S, Mohammadi M, Felfoul O, Zhao L, Pouponneau P (2009) Flagellated magnetotactic bacteria as controlled mri-trackable propulsion and steering systems for medical nanorobots operating in the human microvasculature. Int J Robot Res 28(4):571–582CrossRefGoogle Scholar
  15. 15.
    Cappelleri D, Efthymiou D, Goswami A, Vitoroulis N, Zavlanos M (2014) Towards mobile microrobot swarms for additive micromanufacturing. Int J Adv Robot Syst:11Google Scholar
  16. 16.
    Becker A, Yan O, Kim P, Kim MJ, Julius A (2013) Feedback control of many magnetized: tetrahymena pyriformis cells by exploiting phase inhomogeneity. In: IEEE International conference on intelligent robots and systems, pp 3317–3323Google Scholar
  17. 17.
    Mellal L, Folio D, Belharet K, Ferreira A (2016) Optimal control of multiple magnetic microbeads navigating in microfluidic channels. In: 2016 IEEE International conference on robotics and automation (ICRA)Google Scholar
  18. 18.
    Diller E, Pawashe C, Floyd S, Sitti M (2011) Assembly and disassembly of magnetic mobile micro-robots towards deterministic 2-D reconfigurable micro-systems. Int J Robot Res 30(14):1667–1680CrossRefGoogle Scholar
  19. 19.
    Miyashita S, Diller E, Sitti M (2013) Two-dimensional magnetic micro-module reconfigurations based on inter-modular interactions. Int J Robot Res 32(5):591–613CrossRefGoogle Scholar
  20. 20.
    Salehizadeh M, Diller E (2016) Two-agent formation control of magnetic microrobots. In: International conference on manipulation, automation and robotics at small scales (MARSS). IEEE, pp 1–6Google Scholar
  21. 21.
    Villani DD, Yung KW, Landecker PB (1998) An analytic solution for the force between two magnetic dipoles. Magn Electr Sep 9:39–52CrossRefGoogle Scholar
  22. 22.
    Gao L, McCarthy TJ (2006) Contact angle hysteresis explained. Langmuir 22(14):6234–6237CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringUniversity of TorontoTorontoCanada

Personalised recommendations