Research ArticleBIOPHYSICS

Flies land upside down on a ceiling using rapid visually mediated rotational maneuvers

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Science Advances  23 Oct 2019:
Vol. 5, no. 10, eaax1877
DOI: 10.1126/sciadv.aax1877
  • Fig. 1 Experimental setup, kinematic definitions, and some examples of diverse inverted landing sequences.

    (A) Landing maneuvers of flies are captured by three high-speed cameras operating at 5000 frames/s with exposure of 1/25,600 s. The landing area (10 cm by 10 cm) is located at the center of the ceiling of the flight chamber (20 cm by 20 cm by 20 cm) and is covered by mesh patterns to enhance visual contrast. (B) Anatomical landmarks of the flies from the captured images are digitized, from which we determine the body and wing kinematics according to the coordinate systems and kinematic angles defined in (C). (C) Body rotation is defined with respect to the body-fixed frame Fb = {xb, yb, zb}, where angular velocity is represented by roll p, pitch q, and yaw r rates. Body translational velocity relative to the ceiling is calculated with respect to the yaw-aligned global frame F = {x, y, z}, which is obtained via rotating the global frame by the fly’s yaw angle. The translational velocity is represented by forward/aft Vx, lateral Vy, and vertical Vz components. Wing kinematics are described by three Euler angles: stroke ψ, deviation θ, and rotation ϕ. The inverted landing behaviors are exemplified by those with rapid rotational maneuvers primarily about (D) pitch or (E) roll axes, and (F) those with a large leg-assisted body swing. (i) Sketches of flight sequences are separated spatially to make each instance visible. The instant when flies start to extend forelegs is denoted by the horizontal black dash line. (ii) Sketches of flight sequences are shown in their actual relative spatial locations. (iii) The time traces of wingbeat frequency fw; body translational velocities Vx, Vy, and Vz; and body angular velocities p, q, and r. The time 0 represents the instant when a fly’s leg first touches the ceiling, which is also indicated by the asterisk in (i). Black dashed lines in the subplots of fw denote the average wingbeat frequency of the reference wing kinematics (173 Hz), measured during the upward-acceleration phase prior to the rotational maneuvers. The time instants starting to pitch or roll are identified separately as the instants when the pitch or roll rate reaches one-fourth of the corresponding peak rate. In comparison to (D) and (E), where flies maintain high upward velocities Vz (~0.8 m/s) and reach nearly ventral side up orientations by actively generating rapid pitch or roll maneuvers, the landing maneuver exemplified in (F) is characterized with large forward velocity Vx and negligible body rotational maneuver before forelegs touchdown. (Photo credit: Bo Cheng, Pennsylvania State University.)

  • Fig. 2 DoI of the flies’ body depended on the vertical and horizontal velocity components shortly before the feet touchdown in successful landing.

    For successful, groping, and failed landing cases, the DoI of flies’ body are plotted against the vertical (Vz) and horizontal (Vh) components of flies’ body linear velocity one wingbeat before the feet touchdown. Successful landing cases are marked in black, failed landing in red, and groping landing in light blue. The failed landing cases due to low body inversion and early body rotation are marked as “×” and “+,” respectively. (A) DoI versus Vz and (B) DoI versus Vh. The highest Vz observed among successful landings is approximately 0.7 m/s. DoI ranges from 0, representing no body inversion (or ventral side down), to 1, representing full body inversion (or ventral side up). DoI increases with Vz but decreases with Vh in successful landing cases. For successful landings, the linear regressions between DoI and Vz, and DoI and Vh are shown with the Pearson’s linear correlation coefficient ρ and P value; the 95% confidence intervals are also shown. In general, failed landing cases have lower DoI and higher Vz than the successful landing. Groping landing cases have relatively low DoI and low vertical velocity. The successful landing cases for low- and high-contrast landing areas are also differentiated.

  • Fig. 3 The rotational maneuvers are triggered with short delays when RREV exceeds a threshold.

    (A) When a fly approaches the ceiling with velocity Vz, it perceives looming stimuli with increasing RREV on its retina. When RREV exceeds a threshold, the rotational maneuvers are triggered after a time delay ΔT. (B) Time traces of the coefficients of variation (CV) (thick solid green) and mean values (thick dashed green, the green shaded areas represent ±1 SD) of the RREV (n = 10). The time traces from the individual landing maneuvers (thin dotted green) are aligned at the instants when (Bi) the body pitch or (Bii) the body roll motion starts, as indicated by the thick black dashed lines. Time 0 indicates the averaged time instant when one of the fly’s feet first touched the ceiling. The CV and mean values for the other estimated sensory cues are shown in figs. S4 and S5. To estimate the time delay ΔT, a time period when the CV of RREV reaches a low-value region is defined (between the two thin black dashed lines) (Supplementary Materials), the lower and upper bounds of which yield an upper bound (ΔTu=27 ms) and a lower bound (ΔTl = 7 ms) estimate of the time delay. The gray shaded areas represent the corresponding range of RREV threshold for triggering the rotational maneuver, which is between 19 and 32 rad/s, corresponding to time to collision between 53 and 31 ms, respectively.

  • Fig. 4 The rotational maneuver patterns are correlated with multiple sensory cues perceived during inverted landing.

    (Ai) The fly’s upward motion Vz results in RREV, and the fly’s fore/aft motion Vx results in the ceiling rotating backward/forward on the fly’s retina (ωy about the Y axis). (Bi) Similarly, the fly’s lateral motion Vy results in the ceiling rotating laterally (in an opposite direction) on the fly’s retina (ωx about the X axis). Among the successful landing trials, there exist strong correlations between peak pitch or roll rate and multiple sensory cues at different preceding time instants; the time traces of the corresponding correlation coefficients and the P value are shown for visual cues (Aii) ωy, RREV and (Bii) ωx, and mechanosensory cues (Aiii) Vx and Vz, and (Biii) Vy. As an example, fig. S8 shows the linear regressions between the peak pitch (or roll) rate with the visual cues at a particular preceding time instant (20 ms before the peak). The solid and dashed lines represent the Pearson’s linear correlation coefficients and P value, respectively. The shaded areas indicate the region where P ≤ 0.005. The peak pitch rate is positively correlated with RREV and Vz, and negatively correlated with ωy and Vx. The peak roll rate is positively correlated with ωx and Vy. All the time traces from different landing trials are aligned at the instant of peak pitch or roll rate, which is indicated by vertical black dashed lines. Time 0 indicates the averaged time instant when one of the fly’s feet first touch the ceiling. The complete correlation results between the pitch (or roll) rate and the estimated sensory cues are shown in figs. S6 and S7 and table S2.

  • Fig. 5 The rotational maneuvers are generated by the modulation of wing kinematic patterns.

    (Ai) To generate nose-up pitch rotation, a fly tilts its stroke plane backward and shifts its mean wing spanwise rotation angle backward. (Bi) To generate roll rotation, a fly elevates the outer wing and lowers the inner wing, thereby tilting its stroke plane laterally toward the inner wing. Changes in the instantaneous wing kinematic patterns for generating pitch (Aii) and roll (Bii) within a time-normalized wingbeat cycle: stroke ψ, rotation ϕ, and deviation θ angles. The thick and thin solid lines represent the averaged and individual wing kinematics. The shaded areas represent ±1 SD. The dashed black lines represent the reference wing kinematics (see fig. S9). The linear regressions between stroke-averaged pitch/roll rates and the changes of wing kinematics are shown with the Pearson’s linear correlation coefficient ρ and P value. The stroke-averaged pitch rate is strongly correlated with bilateral symmetric change in stroke plane tilt and wing spanwise rotation. The stroke-averaged roll rate is strongly correlated with bilateral asymmetric change in wing deviation (i.e., the lateral tilt of stroke plane).

  • Fig. 6 Summary of visually mediated inverted landing.

    A fly landing on a ceiling starts with an initial (i) upward acceleration, followed by (ii) rapid rotational maneuvers and (iii) leg extension, and ends with a (iv) leg-assisted body swing with forelegs firmly attached on the ceiling. In successful landing, the rapid rotational maneuvers orient the fly to a proper inversion according its linear velocity. The rotational maneuvers are triggered when RREV exceeds a threshold and are likely mediated by multiple visual (ωx, ωy, and RREV) and/or mechanosensory (Vx, Vy, and Vz) cues. The complex behavioral modules observed, particularly the highly variable rotational maneuver, suggest that inverted landing likely involves multiple neural pathways, in addition to those reported earlier for leg extension in vertical landing.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/10/eaax1877/DC1

    Supplementary Materials and Methods

    Fig. S1. Relationship between the visual cues and the fly’s body translational kinematics.

    Fig. S2. Sketches of flight sequences of two failed landing attempts and the corresponding kinematics.

    Fig. S3. Time traces of body kinematics of landing maneuvers dominated by pitch and roll.

    Fig. S4. The pitch rotation in inverted landings is triggered when RREV exceeds a threshold.

    Fig. S5. The roll rotation in inverted landings is triggered when RREV exceeds a threshold.

    Fig. S6. Correlations between visual or mechanosensory cues to the pitch rate of the rotational maneuvers.

    Fig. S7. Correlations between visual or mechanosensory cues to the roll rate of the rotational maneuvers.

    Fig. S8. Linear regressions between peak pitch (or roll) rate and sensory cues at an example time instant of 20 ms before the time instant of the peak pitch (or roll) rate.

    Fig. S9. The wing kinematics that generate upward acceleration prior to rotational maneuvers are defined as the reference wing kinematics.

    Table S1. Categorized landing trials.

    Table S2. The Pearson’s linear correlation coefficient and P value between body rotation variables and multiple sensory cues at an example time instant of 20 ms before peak of rotation rate.

    Table S3. The Pearson’s linear correlation coefficient and P value between body kinematic variables and the changes of wing kinematic variables.

    Movie S1. High-speed video recordings of an example pitch-dominated landing (PD) shown in Fig. 1D.

    Movie S2. High-speed video recordings of an example roll-dominated landing (RD) shown in Fig. 1E.

    Movie S3. High-speed video recordings of an example longitudinal-body-swing-dominated landing (SLon) shown in Fig. 1F.

    Movie S4. High-speed video recordings of an example lateral-body-swing-dominated landing (SLat).

    Movie S5. High-speed video recordings of an example pitch-roll combined landing (PR).

    Movie S6. High-speed video recordings of an example landing with ceiling groping (CG).

    Movie S7. High-speed video recordings of an example failed landing due to early body rotation (FER) shown in Fig. S2A.

    Movie S8. High-speed video recordings of an example failed landing due to low body inversion with delayed leg extension (FDE) shown in Fig. S2B.

    Movie S9. High-speed video recordings of an example failed landing due to low body inversion with minor body rotation (FMR).

    References (51, 52)

  • Supplementary Materials

    The PDF file includes:

    • Supplementary Materials and Methods
    • Fig. S1. Relationship between the visual cues and the fly’s body translational kinematics.
    • Fig. S2. Sketches of flight sequences of two failed landing attempts and the corresponding kinematics.
    • Fig. S3. Time traces of body kinematics of landing maneuvers dominated by pitch and roll.
    • Fig. S4. The pitch rotation in inverted landings is triggered when RREV exceeds a threshold.
    • Fig. S5. The roll rotation in inverted landings is triggered when RREV exceeds a threshold.
    • Fig. S6. Correlations between visual or mechanosensory cues to the pitch rate of the rotational maneuvers.
    • Fig. S7. Correlations between visual or mechanosensory cues to the roll rate of the rotational maneuvers.
    • Fig. S8. Linear regressions between peak pitch (or roll) rate and sensory cues at an example time instant of 20 ms before the time instant of the peak pitch (or roll) rate.
    • Fig. S9. The wing kinematics that generate upward acceleration prior to rotational maneuvers are defined as the reference wing kinematics.
    • Table S1. Categorized landing trials.
    • Legends for tables S2 and S3
    • Legends for movies S1 to S9
    • References (51, 52)

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Table S2 (Microsoft Excel format). The Pearson’s linear correlation coefficient and P value between body rotation variables and multiple sensory cues at an example time instant of 20 ms before peak of rotation rate.
    • Table S3 (Microsoft Excel format). The Pearson’s linear correlation coefficient and P value between body kinematic variables and the changes of wing kinematic variables.
    • Movie S1 (.mp4 format). High-speed video recordings of an example pitch-dominated landing (PD) shown in Fig. 1D.
    • Movie S2 (.mp4 format). High-speed video recordings of an example roll-dominated landing (RD) shown in Fig. 1E.
    • Movie S3 (.mp4 format). High-speed video recordings of an example longitudinal-body-swing-dominated landing (SLon) shown in Fig. 1F.
    • Movie S4 (.mp4 format). High-speed video recordings of an example lateral-body-swing-dominated landing (SLat).
    • Movie S5 (.mp4 format). High-speed video recordings of an example pitch-roll combined landing (PR).
    • Movie S6 (.mp4 format). High-speed video recordings of an example landing with ceiling groping (CG).
    • Movie S7 (.mp4 format). High-speed video recordings of an example failed landing due to early body rotation (FER) shown in fig. S2A.
    • Movie S8 (.mp4 format). High-speed video recordings of an example failed landing due to low body inversion with delayed leg extension (FDE) shown in fig. S2B.
    • Movie S9 (.mp4 format). High-speed video recordings of an example failed landing due to low body inversion with minor body rotation (FMR).

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