Swimming performance of a biomimetic compliant fish-like robot

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Digital particle image velocimetry and fluorescent dye visualization are used to characterize the performance of fish-like swimming robots. During nominal swimming, these robots produce a ‘V’-shaped double wake, with two reverse-Kármán streets in the far wake. The Reynolds number based on swimming speed and body length is approximately 7500, and the Strouhal number based on flapping frequency, flapping amplitude, and swimming speed is 0.86. It is found that swimming speed scales with the strength and geometry of a composite wake, which is constructed by freezing each vortex at the location of its centroid at the time of shedding. Specifically, we find that swimming speed scales linearly with vortex circulation. Also, swimming speed scales linearly with flapping frequency and the width of the composite wake. The thrust produced by the swimming robot is estimated using a simple vortex dynamics model, and we find satisfactory agreement between this estimate and measurements made during static load tests.

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  1. 1.

    The listed minimum and maximum flapping frequencies that bound each regime correspond to frequencies tested in the PIV experiments. The precise frequencies that bound the regimes were not determined.

  2. 2.

    Recall, ‘wake width’ is defined as the lateral distance between vortex centroids, across the composite wake.


  1. Anderson J, Streitlien K, Barrett D, Triantafyllou M (1998) Oscillating foils of high propulsive efficiency. J Fluid Mech 360:41–72

  2. Anderson JM, Chhabra NK (2002) Maneuvering and stability performance of a robotic tuna. Integr Comp Biol 42:118–126

  3. Bandyopadhyay P, Donnelly MJ, Nedderman WH, Castano JM (1997) A dual flapping foil maneuvering device for low-speed rigid bodies. In: Third international symposium performance enhancement for marine vehicles. Newport, RI

  4. Bandyopadhyay PR (2005) Trends in biorobotic autonomous undersea vehicles. IEEE J Ocean Eng 30(1):109–139

  5. Borazjani I, Sotiropoulos F (2008) Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J Exp Biol 211:1541–1558

  6. Buchholz J, Smits A (2006) On the evolution of the wake structure produced by a low-aspect-ratio pitching panel. J Fluid Mech 546:433–443

  7. Childress S (1981) Mechanics of swimming and flying. Cambridge University Press, Cambridge

  8. Epps BP, Techet AH (2007) Impulse generated during unsteady maneuvering of swimming fish. Exp Fluids 43:691–700

  9. Fish FE, Lauder GV (2006) Passive and active flow control by swimming fishes and mammals. Annu Rev Fluid Mech 38:193–224

  10. Garner LJ, Wilson LN, Lagoudas DC, Rediniotis OK (2000) Development of a shape memory alloy actuated biomimetic vehicle. Smart Mater Struct 9:673–683

  11. Karniadakis GE, Triantafyllou GS (1989) Frequency selection and asymptotic states in laminar wakes. J Fluid Mech 199:441–469

  12. Lauder GV, Anderson EJ, Tangorra J, Madden PGA (2007) Fish biorobotics: kinematics and hydrodynamics of self-propulsion. J Exp Biol 210:2767–2780

  13. Liao JC, Beal DN, Lauder GV, Triantafyllou MS (2003) Fish exploiting vortices decrease muscle activity. Science 302(5650):1566–1569

  14. Licht S, Polidoro V, Flores M, Hover FS, Triantafyllou MS (2004) Design and projected performance of a flapping foil auv. IEEE J Ocean Eng 29(3):786–794

  15. Lighthill MJ (1960) Note on swimming of slender fish. J Fluid Mech 9:305–317

  16. Lighthill MJ (1975) Mathematical biofluiddynamics. Society for Industrial and Applied Mathematics, Philadelphia

  17. Müller UK, Stamhuis EJ, Videler JJ (2002) Riding the waves: the role of the body wave in undulatory fish swimming. Integr Comp Biol 42(5):981–987

  18. Nauen JC, Lauder GV (2002) Hydrodynamics of caudal fin locomotion by chub mackerel scomber japonicus (scombridae). J Exp Biol 205:1709–1724

  19. Newman JN (1973) The force on a slender fish-like body. J Fluid Mech 58:689–702

  20. Raffel M, Willert C, Kompenhans J (2002) Particle image velocimetry: a practical guide. Springer, New York

  21. Sfakiotakis M, Lane DM, Davies JBC (1999) Review of fish swimming modes for aquatic locomotion. IEEE J Ocean Eng 24(2):237–252

  22. Streitlien K, Triantafyllou GS (1998) On thrust estimates for flapping foils. J Fluids Struct 12:47–55

  23. Techet AH, Hover FS, Triantafyllou MS (2003) Separation and turbulence control in biomimetic flows. Flow Turbul Combust 71:105–118

  24. Triantafyllou G, Triantafyllou M, Chryssostomidis C (1986) On the formation of vortex streets behind stationary cylinders. J Fluid Mech 170:461–477

  25. Triantafyllou G, Triantafyllou M, Grosenbaugh M (1993) Optimal thrust development in oscillating foils with application to fish propulsion. J Fluids Struct 7:205–224

  26. Triantafyllou M, Triantafyllou G (1995) An efficient swimming machine. Sci Am 272(3):64–70

  27. Triantafyllou M, Triantafyllou G, Gopalkrishnan R (1991) Wake mechanics for thrust generation in oscillating foils. Phys Fluids A 3:2835–2837

  28. Triantafyllou MS, Triantafyllou GS, Yue DKP (2000) Hydrodynamics of fish-like swimming. Annu Rev Fluid Mech 32:33–53

  29. Tytell ED, Lauder GV (2004) The hydrodynamics of eel swimming i. wake structure. J Exp Biol 207:1825–1841

  30. Valdivia y Alvarado P (2007) Design of biomimetic compliant devices for locomotion in liquid environments. PhD thesis, Institute of Technology, Massachusetts

  31. Valdivia y Alvarado P, Youcef-Toumi K (2003) Modeling and design methodology for an efficient underwater propulsion system. In: Proceedings of IASTED international conference on robotics and applications. Salzburg, Austria

  32. Valdivia y Alvarado P, Youcef-Toumi K (2005) Performance of machines with flexible bodies designed for biomimetic locomotion in liquid environments. In: IEEE international conference on robotics and automation. Barcelona, Spain

  33. ValdiviayAlvarado P, Youcef-Toumi K (2006) Design of machines with compliant bodies for biomimetic locomotion in liquid environments. ASME J Dyn Syst Meas Control 128:3–13

  34. Valdivia y Alvarado P, Youcef-Toumi K (2008) On the design of compliant biomimetic fish-like devices. in press

  35. Videler J (1993) Fish swimming. Chapman and Hall, London

  36. vonKármán T, Burgers JM (1935) Arodynamic theory, vol II: general aerodynamic theory—perfect fluids. Springer, Berlin

  37. Wardle CS, Videler JJ, Altringham JD (1995) Tuning in to fish swimming waves: body form, swimming mode, and muscle function. J Exp Biol 198:1629–1636

  38. Wolfgang M, Anderson J, Grosenbaugh M, Yue D, Triantafyllou M (1999) Near-body flow dynamics in swimming fish. J Exp Biol 202:2303–2327

  39. Wu TY (1971) Hydromechanics of swimming propulsion. part 1. swimming of a two-dimensional flexible plate at varible forward speeds in an inviscid fluid. J Fluid Mech 46(part 2):337–355

  40. Yu J, Tan M, Wang S, Chen E (2004) Development of a biomimetics robotic fish and its control algorithm. IEEE Trans Syst Man Cybern Part B: Cybern 34(4):1798–1810

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Correspondence to Alexandra H. Techet.

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Appendix: Tabulated experimental results

Appendix: Tabulated experimental results

See Tables 1 and 2.

Table 1 Table of measured quantities
Table 2 Table of computed performance parameters

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Epps, B.P., Valdivia y Alvarado, P., Youcef-Toumi, K. et al. Swimming performance of a biomimetic compliant fish-like robot. Exp Fluids 47, 927 (2009).

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  • Vortex
  • Particle Image Velocimetry
  • Swimming Speed
  • Strouhal Number
  • Vortex Loop