Skip to main content

Advertisement

SpringerLink
Log in

Controlled swarm motion of self-propelled microswimmers for energy saving

  • Research Article
  • Published:
Journal of Micro-Bio Robotics Aims and scope Submit manuscript

Abstract

Swarm motion is an amazing collective behavior in nature for energy saving. Inspiring this natural phenomenon in microorganisms’ swimming, we have proposed a motion strategy for a swarm of microrobots to reduce their energy consumption during path tracking. The investigated microrobot is an artificial Self-Propelled Microswimmer (SPM) with high maneuverability at low Reynolds number flow (Re ≪ 1). In this study, we have demonstrated that forming a swarm behavior with minimum energy consumption requires the microswimmers to be close enough to each other, since at small distances the hydrodynamic interactions of microswimmers reduce their energy consumption. Moreover, we also showed that depending on the employed path-tracking control strategy, collective motion may lead to decrease or increase of the overall energy consumption. To save energy using swarm behavior, the microswimmers must be able to adapt their orientation according to the surrounding flow field which is induced by the other swimmers. Otherwise, the energy consumption due to the induced hydrodynamic forces and torques increases. Based on the conducted simulations, it has been shown that the proposed motion strategy minimizes the energy consumption of swarm microswimmers during path tracking.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Kernbach S, Kernbach O (2011) Collective energy homeostasis in a large-scale microrobotic swarm. Robot Auton Syst 59(12):1090–1101

    Article  Google Scholar 

  2. Wiens A, Nahon M (2012) Optimally efficient swimming in hyper-redundant mechanisms: control, design, and energy recovery. Bioinspir Biomim 7(4):046016

    Article  Google Scholar 

  3. Liu Y, Passino KM (2000) Swarm intelligence: literature overview. Department of Electrical Engineering, the Ohio State University

  4. Trenchard H, Perc M (2016) Energy saving mechanisms, collective behavior and the variation range hypothesis in biological systems: a review. Biosystems 147:40–66

    Article  Google Scholar 

  5. Choi J, Kim Y (2007) Fuel efficient three dimensional controller for leader-follower UAV formation flight. In 2007 international conference on control, automation and systems. IEEE

  6. Purcell EM (1977) Life at low Reynolds number. Am J Phys 45(1):3–11

    Article  Google Scholar 

  7. Burton LJ, Hatton RL, Choset H, Hosoi AE (2010) Two-link swimming using buoyant orientation. Phys Fluids 22(9):091703

    Article  Google Scholar 

  8. Dreyfus R, Baudry J, Stone HA (2005) Purcell’s “rotator”: mechanical rotation at low Reynolds number. Eur Phys J B 47(1):161–164

  9. Najafi A, Golestanian RJPRE (2004) Simple swimmer at low Reynolds number: three linked spheres. Phys Rev E 69(6):062901

    Article  Google Scholar 

  10. Avron J, Kenneth O, Oaknin DJ (2005) Pushmepullyou: an efficient micro-swimmer. New J Phys 7(1):234

    Article  Google Scholar 

  11. Nasouri B, Khot A, Elfring GJ (2017) Elastic two-sphere swimmer in stokes flow. Phys Rev Fluids 2(4):043101

    Article  Google Scholar 

  12. Datt C, Nasouri B, Elfring GJ (2018) Two-sphere swimmers in viscoelastic fluids. Phys Rev Fluids 3(12):123301

    Article  Google Scholar 

  13. Ledesma-Aguilar R, Löwen H, Yeomans JM (2012) A circle swimmer at low Reynolds number. Eur Phys J E 35(8):70

    Article  Google Scholar 

  14. Najafi A, Zargar R (2010) Two-sphere low-Reynolds-number propeller. Phys Rev E 81(6):067301

    Article  Google Scholar 

  15. Jalali MA, Alam M-R, Mousavi S (2014) Versatile low-Reynolds-number swimmer with three-dimensional maneuverability. Phys Rev E 90(5):053006

    Article  Google Scholar 

  16. Saadat M et al (2019) The Experimental Realization of an Artificial Low-Reynolds-Number Swimmer with Three-Dimensional Maneuverability. In 2019 American Control Conference (ACC). IEEE

  17. Rizvi MS, Farutin A, Misbah C (2018) Three-bead steering microswimmers. Phys Rev E 97(2):023102

    Article  Google Scholar 

  18. Esfandbod A, Pishkenari HN, Meghdari A (2018) Dynamic modelling and control of a sphere-based micro robot with adjustable arm. In 2018 international conference on manipulation, automation and robotics at small scales (MARSS). IEEE

  19. Khalesi R, Pishkenari HN, Vossoughi G (2020) Independent control of multiple magnetic microrobots: design, dynamic modelling, and control. J Micro-Bio Robot:1–10

  20. Lin Z, Gao C, Chen M, Lin X, He Q (2018) Collective motion and dynamic self-assembly of colloid motors. Curr Opin Colloid Interface Sci 35:51–58

    Article  Google Scholar 

  21. Bricard A et al (2015) Emergent vortices in populations of colloidal rollers. Nat Commun 6(1):1–8

    Article  Google Scholar 

  22. Dunkel J, Heidenreich S, Drescher K, Wensink HH, Bär M, Goldstein RE (2013) Fluid dynamics of bacterial turbulence. Phys Rev Lett 110(22):228102

    Article  Google Scholar 

  23. Wensink HH, Dunkel J, Heidenreich S, Drescher K, Goldstein RE, Lowen H, Yeomans JM (2012) Meso-scale turbulence in living fluids. Proc Natl Acad Sci 109(36):14308–14313

    Article  Google Scholar 

  24. Gompper G et al (2016) Microswimmers–from single particle motion to collective behavior. Springer

  25. Jalali MA, Khoshnood A, Alam M-R (2015) Microswimmer-induced chaotic mixing. J Fluid Mech 779:669–683

    Article  MathSciNet  Google Scholar 

  26. Pooley C, Alexander G, Yeomans JJ (2007) Hydrodynamic interaction between two swimmers at low Reynolds number. Phys Rev Lett 99(22):228103

    Article  Google Scholar 

  27. Alexander G, Pooley C, Yeomans JJ (2009) Hydrodynamics of linked sphere model swimmers. J Phys Condens Matter 21(20):204108

    Article  Google Scholar 

  28. Farzin M, Ronasi K, Najafi A (2012) General aspects of hydrodynamic interactions between three-sphere low-Reynolds-number swimmers. Phys Rev E 85(6):061914

    Article  Google Scholar 

  29. Mirzakhanloo M, Jalali MA, Alam M-R (2018) Hydrodynamic choreographies of microswimmers. Sci Rep 8(1):3670

    Article  Google Scholar 

  30. Chowdhury S, Jing W, Cappelleri DJ (2015) Controlling multiple microrobots: recent progress and future challenges. J Micro-Bio Robot 10(1–4):1–11

    Article  Google Scholar 

  31. Golestanian R, Ajdari A (2008) Analytic results for the three-sphere swimmer at low Reynolds number. Phys Rev E 77(3):036308

    Article  Google Scholar 

  32. Lighthill M (1952) On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun Pure Appl Math 5(2):109–118

    Article  MathSciNet  Google Scholar 

  33. Pande J, Smith A-S (2015) Forces and shapes as determinants of micro-swimming: effect on synchronisation and the utilisation of drag. Soft Matter 11(12):2364–2371

    Article  Google Scholar 

  34. Rizvi MS, Farutin A, Misbah C (2018) Size and shape affect swimming of a triangular bead-spring microswimmer. Phys Rev E 98(4):043104

    Article  Google Scholar 

  35. Nasouri B, Vilfan A, Golestanian R (2019) Efficiency limits of the three-sphere swimmer. Phys Rev Fluids 4(7):073101

    Article  Google Scholar 

  36. Tam D, Hosoi AE (2007) Optimal stroke patterns for Purcell’s three-link swimmer. Phys Rev Lett 98(6):068105

    Article  Google Scholar 

  37. Wiezel O, Or Y (2016) Using optimal control to obtain maximum displacement gait for purcell's three-link swimmer. In 2016 IEEE 55th Conference on Decision and Control (CDC). IEEE

  38. Wang Q (2019) Optimal strokes of low Reynolds number linked-sphere swimmers. Appl Sci 9(19):4023

    Article  Google Scholar 

  39. Abdi H, Pishkenari HN (2019) Optimal control of a high maneuverable micro-swimmer in low Reynolds number flow to reduce energy consumption. In 2019 7th international conference on robotics and mechatronics (ICRoM). IEEE

  40. Alouges F, DeSimone A, Heltai L (2011) Numerical strategies for stroke optimization of axisymmetric microswimmers. Math ModelsMethods Appl Scis 21(02):361–387

    Article  MathSciNet  Google Scholar 

  41. Alouges F et al (2010) Optimally swimming Stokesian robots. arXiv preprint arXiv:1007.4920

  42. Alouges F, DeSimone A, Lefebvre A (2008) Optimal strokes for low Reynolds number swimmers: an example. J Nonlinear Sci 18(3):277–302

    Article  MathSciNet  Google Scholar 

  43. Alouges F, DeSimone A, Lefebvre A (2009) Optimal strokes for axisymmetric microswimmers. Eur Phys J E 28(3):279–284

    Article  Google Scholar 

  44. Happel J, Brenner H (2012) Low Reynolds number hydrodynamics: with special applications to particulate media. Vol. 1. Springer Science & Business Media

  45. Chwang AT, Wu TY-T (1975) Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows. J Fluid Mech 67(4):787–815

    Article  MathSciNet  Google Scholar 

  46. Lopez D, Lauga E (2014) Dynamics of swimming bacteria at complex interfaces. Phys Fluids 26(7):400–412

    Article  Google Scholar 

  47. Hoshiar AK et al (2020) Swarm of magnetic nanoparticles steering in multi-bifurcation vessels under fluid flow. J Micro-Bio Robot:1–9

  48. Mirzakhanloo M, Alam M-R (2018) Concealed Swarm of Micro-swimmers. arXiv preprint arXiv:1811.10101

  49. Howell TA, Osting B, Abbott JJ (2018) Sorting rotating micromachines by variations in their magnetic properties. Phys Rev Appl 9(5):054021

    Article  Google Scholar 

  50. Khodygo V, Swain MT, Mughal A (2019) Homogeneous and heterogeneous populations of active rods in two-dimensional channels. Phys Rev E 99(2):022602

    Article  Google Scholar 

  51. Etemadi S, Alasty A, Vossoughi G (2007) Stability analysis of robotic swarm with limited field of view. In ASME 2007 international mechanical engineering congress and exposition. American Society of Mechanical Engineers.

  52. Gazi V, Passino KM (2002) Stability analysis of swarms. In Proceedings of the 2002 American Control Conference (IEEE Cat. No. CH37301). IEEE

  53. Shi H, Wang L, Chu T (2004) Swarming behavior of multi-agent systems. J Control Theory Appl 2(4):313–318

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nano Robotics Laboratory, Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Hossein Abdi & Hossein Nejat Pishkenari

Authors
  1. Hossein Abdi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hossein Nejat Pishkenari
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Not applicable.

Corresponding author

Correspondence to Hossein Nejat Pishkenari.

Ethics declarations

Conflicts of interest/Competing interests

Not applicable.

Code availability

Not applicable.

Additional information

Publisher’s Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abdi, H., Nejat Pishkenari, H. Controlled swarm motion of self-propelled microswimmers for energy saving. J Micro-Bio Robot 17, 23–33 (2021). https://doi.org/10.1007/s12213-021-00142-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12213-021-00142-x

Keywords

Search

Navigation