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A tailless aerial robotic flapper reveals that flies use torque coupling in rapid banked turns

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Science  14 Sep 2018:
Vol. 361, Issue 6407, pp. 1089-1094
DOI: 10.1126/science.aat0350
  • Fig. 1 An insect-inspired free-flying robotic platform is controlled through its two pairs of independently flapping wings.

    (A) Description of the robot’s components. (B to D) High-speed camera frames capturing the robot in hover (B), forward flight (C), and sideways flight (D), from movies S1 to S3, respectively. (E to G) Details of the robot design: (E) the wing root adjustment mechanism for yaw torque control, (F) the dihedral control mechanism for pitch torque control, and (G) the flapping mechanism (of the left wing pair), used for thrust and roll torque control. (H to J) Wing actuation and aerodynamic forces and torques during yaw control (H), pitch control (I), and roll control (J). Magenta arrows show actuation action, gray arrows show the nominal wingbeat-average aerodynamic thrust vectors, and red arrows show wingbeat-average thrust and torques after control actuation.

  • Fig. 2 The robot mimics rapid banked turns observed in escaping fruit flies.

    (A and C) Time sequences (top view) of a roll-dominated maneuver (pitch rate/roll rate ratio q/p = 0.52) and a pitch-dominated maneuver (q/p = 1.67), respectively. The start of the open-loop (OL) phase is marked with a green circle. (B and D) Time sequences (top view) of the equivalent fruit fly evasive maneuvers with the stimulus (green arrowhead) coming from the left and the front, respectively. (E to I) Detailed analysis of a roll-dominated maneuver (q/p = 0.54). (E) Time sequence with constant time interval of 0.125 s; trajectory projections are shown by dotted lines. Wings are color-coded according to thrust command magnitude, as shown in the color bar. [(F) to (I)] Time histories of roll command (F), roll acceleration and flapping frequency of the right wing pair (G), pitch command (H), and pitch acceleration and dihedral angle (I). In (A) to (E), blue and magenta arrows represent velocity and acceleration vectors, respectively; vectors (arrow lengths) are relative to the black scale bars in (A) and (E) for the robot and in (B) for flies. The OL phase in (F) to (I) is highlighted by gray background.

  • Fig. 3 The turn angle during the banked turn can be controlled by varying the ratio of pitch to roll torque commands.

    Results are color-coded [see key in (A)] according to the q/p ratio of the maneuver; thin lines are individual trials and thick lines are series averages. (A) Top view of trajectories, aligned at the start of the OL phase (t = 0 s) where the robot is shown. (B to D) Time histories of angular rates during the maneuvers. The OL phase is highlighted by gray background. (E) Angular rate vector in the horizontal body plane, relative to the forward-directed black arrow. (F and G) Turn angle and turn rate versus q/p, respectively, for individual tests (squares) and mean ± SD per condition (error bars).

  • Fig. 4 The passive yaw accelerations during the recovery phase of banked turns originate from the coupling between the roll and pitch torque generation mechanisms and translational body motions.

    (A and B) Correlation coefficient between the yaw acceleration and the roll (solid) and pitch (dashed) accelerations at various pitch-to-roll rate ratios q/p for rapid banked turns produced by the robot (A) and for evasive maneuvers produced by fruit flies (B). (C) Correlation coefficients for the same evasive maneuvers of fruit flies, after correcting for the flapping countertorque and including the translational body velocities. (D and E) Measured (black) and modeled (red) yaw accelerations during the banked turn of the robot: (D) roll-dominated banked turn (q/p = 0.50), (E) pitch-dominated banked turn (q/p = 1.34). Line style of individual model components follows the legend below (E). (F to H) The three passive yaw torque–producing mechanisms at t = 0.4 s in (D) and (E) are flapping countertorque (F), torque due to forward motion with uneven left and right flapping frequencies (G), and torque due to sideways motion with nonzero dihedral angle (H). Color coding of the flapping frequency and the positive directions of all the coordinates are shown below (H). DL and DR are the wingbeat-average drag forces of the left and right wing pair, respectively, as defined by eq. S9.

Supplementary Materials

  • A tailless aerial robotic flapper reveals that flies use torque coupling in rapid banked turns

    Matěj Karásek, Florian T. Muijres, Christophe De Wagter, Bart D. W. Remes, Guido C. H. E. de Croon

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

    Download Supplement
    • Materials and Methods
    • Supplementary Text
    • Figs. S1 to S26
    • Tables S1 to S6
    • Captions for Movies S1 to S10
    • References

    Images, Video, and Other Media

    Movie S1
    High-speed video recording (1000 fps) of the robot prototype in hovering flight, whereby the autopilot maintains stable flight of the inherently unstable flight platform. The movie shows the maneuver twice, first in real-time and then slowed down 33 times.
    Movie S2
    High-speed video recording (1000 fps) capturing the robot prototype during the pitch maneuver described in the section 'Rapid transitions from hover to fast forward/sideways flight and back' (18). During the maneuver, the robot transitioned from hover to forward flight by rapidly pitching forward, and then pitched back again to return to a hover condition. The movie shows the maneuver twice, first in real-time and then slowed down 33 times.
    Movie S3
    High-speed video recording (1000 fps) capturing the robot prototype during the roll maneuver described in the section 'Rapid transitions from hover to fast forward/sideways flight and back' (18). During the maneuver, the robot transitioned from hover to sideways flight by rapidly rolling sideways, and then roll back again to return to a hover condition. The movie shows the maneuver twice, first in real-time and then slowed down 33 times.
    Movie S4
    High-speed video recording (240 fps) capturing the robot prototype rapidly accelerating from hover to fast forward flight, as part of the reproducibility test experiments (18). During the maneuver, the robot transitioned from hover to a set forward body pitch angle. The movie shows the maneuver three times: twice in real-time, and once slowed down 16 times.
    Movie S5
    High-speed video recording (240 fps) capturing the robot prototype making 360° roll flip maneuver, as described in the section 'Rapid 360° roll and pitch up flips: barrel rolls and loopings' (18). The movie shows the maneuver three times, twice in real-time and once slowed down 16 times.
    Movie S6
    High-speed video recording (240 fps) capturing the robot prototype making 360° pitch flip maneuver, as described in the section 'Rapid 360° roll and pitch up flips: barrel rolls and loopings' (18). The movie shows the maneuver three times, twice in real-time and once slowed down 16 times.
    Movie S7
    High-speed video recording (240 fps) of the robot prototype making a fly inspired rapid banked turn, as described in the section 'Rapid banked turns inspired by the evasive maneuvers of fruit flies' (18). The movie shows the maneuver three times, twice in real-time and once slowed down 16 times.
    Movie S8
    Animation of the comparison between the fly-inspired rapid banked turn (Fig. 2A, movie slowed down 16 times) and the original maneuver by the fruit fly (Fig. 2B, movie slowed down 150 times) (3). The difference in size between the robot and fruit fly is indicated by the scale bars in the video, representing the wing span of the robot and fly. The wing motion of the robot is for illustration purposes only; the flapping frequency was estimated using the on-board recorded commands.
    Movie S9
    Animation of the comparison between the fly-inspired rapid banked turn (Fig. 2C, movie slowed down 16 times) and the original maneuver by the fruit fly (Fig. 2D, movie slowed down 150 times) (3). The difference in size between the robot and fruit fly is indicated by the scale bars in the video, representing the wing span of the robot and fly. The wing motion of the robot is for illustration purposes only; the flapping frequency was estimated using the on-board recorded commands.
    Movie S10
    Animation of the fly-inspired rapid banked turn of Fig. 2E (q/p = 0.54), as described in the section 'Rapid banked turns inspired by the evasive maneuvers of fruit flies' (18). The animation was upsampled to 120 fps and replayed at 20 fps, and thus movie playback is slowed down 6 times. The three-dimensional trajectory is shown by the magenta dotted line, and the trajectory projections are shown as black dotted lines. Wings are color-coded with percentage motor command, see color bar. The flight phase, time t, speed U, and roll, pitch and yaw angle throughout the maneuver are provided in the top left of the movies. The wing motion of the robot is for illustration purposes only; the flapping frequency was estimated using the on-board recorded commands.

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