The current study presents the transition of large amplitude oscillations to a fixed hovering point in the context of bio-inspired flapping robots (BIFRs). The experimental arrangement allows two degrees of freedom for the BIFRs under study: body pitching and translation. The primary objective of this investigation is to compare the flight mechanics characteristics of two almost-identical BIFR configurations: a two-winged configuration and a four-winged one that exploits wing–wing interaction for aerodynamic effects. A motion capture system is utilized to track the two degrees of freedom of each BIFR. The study reveals that the four-winged BIFR exhibits passive transition of large amplitude oscillations to a fixed point beyond a certain frequency, whereas no such transition was observed for the two-winged BIFR at any frequency within the considered range. Realizing that the main difference between the two systems lies within the wing–wing interaction, this study thus underscores the significance of the wing–wing interaction for the transitional response upon the four-winged model. This response might be due to a phenomenon called vibrational stabilization. From the study, it can be implied that wing–wing interaction promotes the transitional response beyond a critical frequency.
ArmaniniSCaetanoJGeaDC (2016) Quasi-steady aerodynamic model of clap-and-fling flapping mav and validation using free-flight data. Bioinspiration and Biomimetics11(4): 046002.
2.
BaltaMDebDTahaH (2021) Flow visualization and force measurement of the clapping effect in bio-inspired flying robots. Bioinspiration and Biomimetics16(6), https://doi.org/10.1088/1748-3190/ac2b00
3.
BennettL (1977) Clap and fling aerodynamics: an experimental evaluation. Journal of Experimental Biology69(1): 261–272. https://doi.org/10.1242/jeb.69.1.261
BhattiMLeeSHanJ (2021) Dynamic stability and flight control of biomimetic flapping-wing micro air vehicle. Aerospace8(12): 362. https://doi.org/10.3390/aerospace8120362
BulloF (2002) Averaging and vibrational control of mechanical systems. SIAM Journal on Control and Optimization41(2): 542–562. https://doi.org/10.1137/s0363012999364176
9.
ChenZXieYZhangY, et al. (2024) Aerodynamics of a flapping wing with stroke deviation in forward flight. Physics of Fluids36(5): 051908. https://doi.org/10.1063/5.0209169
10.
DawsonSGrebogiCJeaY, et al. (1992) Antimonotonicity: inevitable reversals of period-doubling cascades. Physics Letters A162(3): 249–254. https://doi.org/10.1016/0375-9601(92)90442-o
11.
DebDHuangKFoudaM (2022) Effect of self-induced body vibrations on thrust generation in bio-inspired flying robots. AIAA. https://doi.org/10.2514/6.2022-0022
12.
DebDHuangKVermaA, et al. (2023) Thrust enhancement and degradation mechanisms due to self-induced vibrations in bio-inspired flying robots. Scientific Reports13(1): 18317. https://doi.org/10.1038/s41598-023-45360-4
13.
DhimanKAbhishekAKotharicM (2022) Flight dynamics and control of an unmanned helicopter with underslung double pendulum. Journal of Aircraft59(1): 137–153. https://doi.org/10.2514/1.c036390
EllingtonCLighthillM (1984) The aerodynamics of hovering insect flight. Iv. Aerodynamic mechanisms. Philosophical Transactions of the Royal Society of London. B, Biological Sciences305(1122): 79–113. https://doi.org/10.1098/rstb.1984.0052
16.
EllingtonCvan den BergCAeaW, et al. (1996) Leading-edge vortices in insect flight. Nature384(6610): 626–630. https://doi.org/10.1038/384626a0
17.
HassanATahaH (2018) Combined averaging–shooting approach for the analysis of flapping flight dynamics. Journal of Guidance, Control, and Dynamics41(2): 542–549. https://doi.org/10.2514/1.g002795
18.
HassanATahaH (2019) Differential-geometric-control formulation of flapping flight multi-body dynamics. Journal of Nonlinear Science29: 1379–1417. https://doi.org/10.1007/s00332-018-9520-8
19.
HongKS (2002) An open-loop control for underactuated manipulators using oscillatory inputs: steering capability of an unactuated joint. IEEE Transactions on Control Systems Technology10(3): 469–480. https://doi.org/10.1109/87.998037
20.
HopfE (1942) Abzweigung einer periodischen lösung von einer stationären lösung eines differentialsystems. Berichte der Mathematisch-Physikalischen Klasse der Sächsischen Akademie der Wissenschaften Leipzig94: 1–22.
21.
JadhavSLuaKTayW (2019) Effect of clap-and-fling mechanism on force generation in flapping wing micro aerial vehicles. Bioinspiration and Biomimetics14(3): 036006. https://doi.org/10.1088/1748-3190/ab0477
MaggiaMEisaSTahaH (2020) On higher-order averaging of time-periodic systems: reconciliation of two averaging techniques. Nonlinear Dynamics99: 813–836. https://doi.org/10.1007/s11071-019-05085-4
24.
MeerkovS (1980) Principle of vibrational control: theory and applications. IEEE Transactions on Automatic Control25(4): 755–762. https://doi.org/10.1109/tac.1980.1102426
25.
PhanHAuTParkH (2016) Clap-and-fling mechanism in a hovering insect-like two-winged flapping-wing micro air vehicle. Royal Society Open Science3(12): 160746. https://doi.org/10.1098/rsos.160746
26.
RamananarivoSGodoy-DianaRThiriaB (2011) Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance. Proceedings of the National Academy of Sciences108(15): 5964–5969. https://doi.org/10.1073/pnas.1017910108
27.
SaneS (2003) The aerodynamics of insect flight. Journal of Experimental Biology206(23): 4191–4208. https://doi.org/10.1242/jeb.00663
TahaH (2013) Mechanics of Flapping Flight: Analytical Formulations of Unsteady Aerodynamics, Kinematic Optimization, Flight Dynamics, and Control. Virginia Polytechnic Institute and State University. Phd Thesis.
TahaHHajjMNayfehA (2014) Longitudinal flight dynamics of hovering mavs/insects. Journal of Guidance, Control, and Dynamics37(3): 970–979. https://doi.org/10.2514/1.62323
32.
TahaHTahmasianSCeaW (2015) The need for higher-order averaging in the stability analysis of hovering, flapping-wing flight. Bioinspiration and Biomimetics10(1): 016002.
33.
TahaHWoolseyCHajjM (2016) Geometric control approach to longitudinal stability of flapping flight. Journal of Guidance, Control, and Dynamics39(2): 214–226. https://doi.org/10.2514/1.g001280
34.
TahaHKianiMNavarroJ (2018) Experimental demonstration of the vibrational stabilization phenomenon in bio-inspired flying robots. IEEE Robotics and Automation Letters3(2): 643–647. https://doi.org/10.1109/LRA.2017.2778759
35.
TahaHKianiMTeaH (2020) Vibrational control: a hidden stabilization mechanism in insect flight. Science Robotics5(46): eabb1502.
36.
TahmasianSWoolseyC (2015) A control design method for underactuated mechanical systems using high-frequency inputs. Journal of Dynamic Systems, Measurement, and Control137(7): 071004. https://doi.org/10.1115/1.4029627
37.
TaylorGNuddsRThomasA (2003) Flying and swimming animals cruise at a strouhal number tuned for high power efficiency. Nature425(6959): 707–711. https://doi.org/10.1038/nature02000
38.
VelaPBurdickJ (2003) Control of underactuated mechanical systems with drift using higher-order averaging theory, In: 42nd IEEE International Conference on Decision and Control (IEEE Cat. No. 03CH37475), Maui, HI, USA, 09-12 December 2003, pp. 3111–3117.
39.
ZhengHXieFJiT, et al. (2020) Multifidelity kinematic parameter optimization of a flapping airfoil. Physical Review E101(1): 013107. https://doi.org/10.1103/PhysRevE.101.013107
