Research Article

Discovering the flight autostabilizer of fruit flies by inducing aerial stumbles

Leif Ristroph, Attila J. Bergou, Gunnar Ristroph, Katherine Coumes, Gordon J. Berman, John Guckenheimer, Z. Jane Wang, and Itai Cohen
PNAS March 16, 2010 107 (11) 4820-4824; https://doi.org/10.1073/pnas.1000615107

  1. Communicated by Jacob N. Israelachvili, University of California, Santa Barbara, CA, January 22, 2010 (received for review September 11, 2009)

Article Figures & SI

Figures

  • Fig. 1.
    Fig. 1.

    Three-dimensional reconstruction of a recovery maneuver. Three orthogonal high-speed cameras capture 35 frames per wingbeat, and the still images shown on the side panels are spaced by about four wingbeats. The corresponding three-dimensional wing and body configurations extracted from the images are displayed on a computer-generated model of the fruit fly (body length 2.5 mm). As the fly descends from left to right, we apply a magnetic field (Red Looped Arrow) for one wingbeat that torques the ferromagnetic pin (Bronze Rod) glued to its back and reorients the insect’s flight heading. The insect responds to the flight perturbation by making a corrective turn that lasts several wingbeats.

  • Fig. 2.
    Fig. 2.

    Accuracy of the corrective response. (Inset) For each trial, the error Δψerr (final minus initial yaw) and maximum induced deflection Δψmax are measured from the yaw dynamics. In the main figure, the error is plotted against the deflection for 23 experiments. The dashed blue horizontal line is the predicted perfect correction from a linear control model, and the solid blue line is the result of a nonlinear model. See text for details of both models.

  • Fig. 3.
    Fig. 3.

    Body and wing motions for a case of accurate correction. (A) Top-view images of the insect before the perturbation, during the induced rightward rotation, during the corrective turn leftward, and after accurate recovery. The yaw angle, or heading, is shown as a red arrow, and the wings are moving forward in each image. The differences in right and left wing area in the third image indicate differences in angles of attack that drive the corrective turn. (B) Yaw angle as a function of time measured in wingbeat periods, T = 4.5 ms. The red stripe indicates the 5 ms during which the perturbing torque, Next = 0.8 × 10-9 Nm, is applied. The yaw is experimentally measured (Open Circles), and a control model (Blue Curve) is fit to the experimental data. The parameters used for the fit are: I = 0.6 × 10-13 kg m2, β = 1.0 × 10-11 kg m2 s-1, Δt = 2.5 T, KP = 5.0 × 10-10 kg m2 s-2, KD = 4.1 × 10-12 kg m2 s-1. See text for description of the model (Eqs. 1–4). (C) The attack angle difference between wings averaged over each wingbeat, Δα, is plotted in black (mean and standard error of the mean). These data are compared to the torque predicted by the model (Blue Curve).

  • Fig. 4.
    Fig. 4.

    Physical and biological elements of the flight control model. (A) and (B) Aerodynamics of symmetric flapping flight during body rotation. Top-view images of the fly as it is rotated to its right by the perturbing torque show that the insect continues to beat symmetrically. The imposed rotation induces differences in wing velocity that generate unbalanced drag on the wings. (C) and (D) Active steering is driven by differences in wing angles of attack. To turn rightward, the insect assumes different pitch angles for the right and left wings that generate an unbalanced drag-based torque. (E) The haltere organs (S) sense body rotations, the neural controller (C) processes this information, and the flight motor (M) drives the wing motions that generate corrective aerodynamic torque (A). (F) Information flow diagram for the insect flight control model. The upper circuit describes the feedback loop used for correction, and the lower circuit shows the detailed control model. After an initial time delay, a term that is proportional to the sensed yaw-rate signal and a term that integrates this signal are added to determine the output torque exerted by the fly.

  • Fig. 5.
    Fig. 5.

    Recovery time, Δtrec, increases for stronger perturbations. Here, Δtrec is plotted for cases of accurate correction, and the model prediction is the dashed blue curve. The theoretical curve marks the total time to return to within 2° of the original yaw angle and is generated using the mean parameter values extracted from fits to trials of accurate recovery: I = 0.9 × 10-13 kg ·m2, β = 0.9 × 10-11 kg ·m2·s-1, Δt = 3.5 T, T = 0.0045 s, KP = 5.9 × 10-10 kg ·m2 ·s-2, KD = 5.3 × 10-12 kg ·m2 ·s-1.

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Discovering the flight autostabilizer of fruit flies by inducing aerial stumbles
Leif Ristroph, Attila J. Bergou, Gunnar Ristroph, Katherine Coumes, Gordon J. Berman, John Guckenheimer, Z. Jane Wang, Itai Cohen
Proceedings of the National Academy of Sciences Mar 2010, 107 (11) 4820-4824; DOI: 10.1073/pnas.1000615107
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Proceedings of the National Academy of Sciences: 107 (11)
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