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.
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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
- 2.
Wiens A, Nahon M (2012) Optimally efficient swimming in hyper-redundant mechanisms: control, design, and energy recovery. Bioinspir Biomim 7(4):046016
- 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
- 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
- 7.
Burton LJ, Hatton RL, Choset H, Hosoi AE (2010) Two-link swimming using buoyant orientation. Phys Fluids 22(9):091703
- 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
- 10.
Avron J, Kenneth O, Oaknin DJ (2005) Pushmepullyou: an efficient micro-swimmer. New J Phys 7(1):234
- 11.
Nasouri B, Khot A, Elfring GJ (2017) Elastic two-sphere swimmer in stokes flow. Phys Rev Fluids 2(4):043101
- 12.
Datt C, Nasouri B, Elfring GJ (2018) Two-sphere swimmers in viscoelastic fluids. Phys Rev Fluids 3(12):123301
- 13.
Ledesma-Aguilar R, Löwen H, Yeomans JM (2012) A circle swimmer at low Reynolds number. Eur Phys J E 35(8):70
- 14.
Najafi A, Zargar R (2010) Two-sphere low-Reynolds-number propeller. Phys Rev E 81(6):067301
- 15.
Jalali MA, Alam M-R, Mousavi S (2014) Versatile low-Reynolds-number swimmer with three-dimensional maneuverability. Phys Rev E 90(5):053006
- 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
- 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
- 21.
Bricard A et al (2015) Emergent vortices in populations of colloidal rollers. Nat Commun 6(1):1–8
- 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
- 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
- 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
- 26.
Pooley C, Alexander G, Yeomans JJ (2007) Hydrodynamic interaction between two swimmers at low Reynolds number. Phys Rev Lett 99(22):228103
- 27.
Alexander G, Pooley C, Yeomans JJ (2009) Hydrodynamics of linked sphere model swimmers. J Phys Condens Matter 21(20):204108
- 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
- 29.
Mirzakhanloo M, Jalali MA, Alam M-R (2018) Hydrodynamic choreographies of microswimmers. Sci Rep 8(1):3670
- 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
- 31.
Golestanian R, Ajdari A (2008) Analytic results for the three-sphere swimmer at low Reynolds number. Phys Rev E 77(3):036308
- 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
- 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
- 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
- 35.
Nasouri B, Vilfan A, Golestanian R (2019) Efficiency limits of the three-sphere swimmer. Phys Rev Fluids 4(7):073101
- 36.
Tam D, Hosoi AE (2007) Optimal stroke patterns for Purcell’s three-link swimmer. Phys Rev Lett 98(6):068105
- 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
- 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
- 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
- 43.
Alouges F, DeSimone A, Lefebvre A (2009) Optimal strokes for axisymmetric microswimmers. Eur Phys J E 28(3):279–284
- 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
- 46.
Lopez D, Lauga E (2014) Dynamics of swimming bacteria at complex interfaces. Phys Fluids 26(7):400–412
- 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
- 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
- 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
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Abdi, H., Nejat Pishkenari, H. Controlled swarm motion of self-propelled microswimmers for energy saving. J Micro-Bio Robot (2021). https://doi.org/10.1007/s12213-021-00142-x
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Keywords
- Collective swarm motion
- Self-propelled microswimmer
- Energy saving
- Multi-agent formation control
- Low Reynolds number