Research ArticleBIOMIMETICS

Soft biohybrid morphing wings with feathers underactuated by wrist and finger motion

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Science Robotics  16 Jan 2020:
Vol. 5, Issue 38, eaay1246
DOI: 10.1126/scirobotics.aay1246
  • Fig. 1 Wrist and finger angles are the primary driver of avian wing morphing.

    (A) The four major bones in a pigeon (C. livia) wing are the humerus, radius, ulna, and manus. The 20 flight feathers (remiges) comprise 10 primary and 10 secondary feathers, which insert into the manus and ulna bones, respectively, and are embedded in the postpatagium tissue. We define the feather angle, θfeather, as the angle from the ulna to each feather. The ulna and carpometacarpus meet at the wrist with angle θwrist. The postpatagium consists of elastic ligament and smooth muscles that connect around the proximal base of each feather. Pigeon wing drawing adapted from Proctor and Lynch (44). (B) Within the manus, the carpometacarpus and distal phalanx of the second digit form the finger angle, θfinger. An additional pose showing the range of motion of the second digit is shown for illustration purposes in light pink based on earlier work (14). (C) The first principal component represents more than 75% of the 3D measured skeletal motion during animated wing flexion and extension [for measurement details, see (14)]. Adding the second principal component captures 97% of the 3D measured skeletal motion (radius, red; ulna, blue; manus, purple trace). (D) Pigeon wing feather angles correlate linearly with wrist angles and finger angles. Distal primary feather angles (wing tip) are more sensitive to wrist and finger angles than proximal secondary feather angles (wing root). Gray horizontal bars on the horizontal axis indicate the range over which PigeonBot’s biohybrid wing morphs. Solid lines indicate average angles and shaded regions indicate the standard deviation.

  • Fig. 2 PigeonBot: A soft biohybrid aerial robot consists of a propeller-driven instrumented body with an underactuated feathered morphing wing.

    (A) PigeonBot’s body includes a propeller-driven electric propulsion system, sensors (GPS, pitot tube, barometers, and three-axis accelerometers, gyroscopes, and magnetometers), radios, an autopilot with data logging (PixRacer R14), and a tail. (B) The body is constructed from a single piece of laser-cut foamboard that is folded and glued together. (C) The foam tail has a conventional configuration with an elevator for longitudinal control and a rudder for lateral control. (D) The system block diagram shows how each actuator is controlled. For our wing morphing flight experiments, the ground station commands a wing pose, neutral static rudder, and constant propulsion throttle, whereas the elevator is under closed-loop control to sustain the robot’s pitch. (E) The morphing wing was designed through iterative steps that were all successfully flight-tested. The successive steps were as follows: static pigeon wing planforms made out of foamboard (1); a fully extended planform with pigeon feathers glued to a foamboard skeleton (2); a simple one–degree of freedom foamboard “swing wing” with actuated wrists (3); primary feathers glued on a foamboard leading edge to form a feathered hand wing (4); primary and secondary feathers glued to an articulated one–degree of freedom foamboard skeleton forming the hand and arm (5); elastic bands added between each feather so that the feathers moved relative to each other rather than as discrete hand and arm panels (6). Last, we added an additional skeletal finger joint (7) to improve the range of planforms achieved by the biohybrid morphing wing (Fig. 4C).

  • Fig. 3 Biological principles inform detailed biohybrid morphing wing design.

    (A) We integrated all 10 primary and 10 secondary remiges in the biohybrid wing. Each feather is mounted via pin joints to a simplified artificial skeleton consisting of a static fused “radioulna” bone and directly actuated carpometacarpus and finger bones. By directly actuating θwrist and θfinger with servomotors, we underactuate all the feather angles (θfeathers). Cardstock (shown in light blue) covered portions of the wing normally covered by covert feathers in a bird wing. (B) Independent rubber bands link each feather pair to recreate the feather motion that we recorded in bird cadavers. (C) We fitted in vivo gliding pigeon wing data (23) to a database of existing low–Reynolds number airfoils (https://m-selig.ae.illinois.edu) to determine the most representative shape for the root section of the biohybrid wing. (D) Similarly, we fitted these data to a linear model to determine the dihedral angle for our biohybrid wing. (E) We attached all 20 remiges to mechanical pin joints via custom 3D-printed feather interfaces that mount the feather with adhesive heat shrink. We adjusted the orientation of the feather after assembly by heating the thermoplastic feather interfaces and posing the feather in the desired pose. (F) The completed biohybrid wing enables large wing shape changes harnessing the passive softness of overlapping pigeon feathers, which we flight-tested outdoors (G).

  • Fig. 4 Wrist and finger angles dynamically drive the motion of 20 feathers under aerodynamical loading.

    (A) We measured the biohybrid morphing wing kinematics in a wind tunnel at the same mean speed and angle of attack measured in outdoor flights (11.7 m s−1 and 4.4°; Materials and Methods). Under these quasi-static conditions in which the wing flexes and extends θwrist at 0.4 Hz for 42 cycles, while cycling θfinger at 0.01 Hz, θfeather is approximately a linear function of θwrist and θfinger (RMSE: 0.87°). (B) Fitted coefficients of the corroborated linear feather angle model show how distal feathers are more sensitive to θwrist and θfinger, B than proximal feathers. (C) The combinations of wrist and finger angle afford a wide configuration space of wing area, span, and aspect ratio under aerodynamic loading. (D) The response of the biohybrid wing to full flexion-extension commands at varying frequencies demonstrates a system bandwidth up to 5 Hz due to servo limitations.

  • Fig. 5 The quasi-static linear transfer functions, between wrist and finger input to feather angle output, approximate the measured dynamic response under aerodynamic loading well.

    (A and B) The measured wrist, θwrist, and finger, θfinger, angle kinematics resulting from step commanding the wrist and finger servos to extend and flex, respectively, the wing at maximal speed. The deviation from a step response in the wrist and finger kinematics is due to the biohybrid morphing wing’s (including servo motors) elastic, damping, and inertia properties under aerodynamic loading. The wrist and finger extension response is characteristic of an overdamped system, whereas the flexion response is characteristic of an underdamped system. (C) Visual inspection of the measured dynamic response of each flight feather to combined wrist (A) and finger (B) actuation suggests that the input and output kinematics are directly correlated. In (A) to (C), solid lines indicate average angles and shaded regions indicate the standard deviation. (D) The range of feather motion over a full extension and flexion cycle (Δθfeather) is largest for distal feathers, with ΔθP10 ≈ 70°. The small standard deviation (error bars) in feather motion range shows the high repeatability of the feather underactuation mechanism. (E) The quasi-static linear feather-angle transfer function (Fig. 4A) reproduces the measured feather kinematics of the slow morphing wing well (mean RMSE: 0.87°, morphing θwrist at 0.4 Hz for 42 flexion and extension cycles; see Fig. 4 for details). The same quasi-static transfer function predicts the measured feather kinematics similarly well (mean RMSE: 1.31°) when the biohybrid wing morphs dynamically at maximal speed [(A) to (C); 10 flexion and extension cycles]. The y axis of the feather angle error (E) was magnified 10× compared with the plot of feather motion range (D) to aid visual comparison.

  • Fig. 6 Aerodynamic simulations predict coupled roll and adverse yaw due to asymmetric morphing.

    (A) We approximate PigeonBot’s geometry using quantized wing geometries for aerodynamic simulations with the potential flow code AVL (31). (B) Moment coefficient results are reported in the reference frame shown, with positive roll and yaw indicating a right-hand turn. Simulating combinations of left (θsweep, left) and right (θsweep, left) wing morphing in steps of 5° shows coupled roll (C) and yaw (D) moment coefficients generated by the resulting 169 wing planforms. Positive roll moment coefficients with negative yaw moment coefficients indicate adverse yaw. (E) Ratio of yaw-to-roll moment coefficients shows peak adverse yaw ratios for slightly asymmetric tucked wings. The robot can minimize adverse yaw by harnessing extended wings that are only slightly asymmetric, combining symmetric extended wrist angles with asymmetric finger angles (symmetric wing configurations are not shown to avoid dividing by zero).

  • Fig. 7 Asymmetric morphing wing flight tests reveal initial coupled roll and adverse yaw dynamics.

    (A) We tested open-loop dynamics due to asymmetric wing morphing using three experimental permutations: coupled wrist/finger asymmetry (blue) with left finger and wrist extended, right wrist and finger tucked; wrist asymmetry only (green) with both fingers intermediate, left wrist extended, right wrist tucked; and finger asymmetry only (red) with both wrists extended, left finger extended, right finger tucked. Lock icons indicate that left and right joints are the same angle. (B) The measurement results are reported in the reference frame shown, with positive roll and yaw indicating a right-hand turn. (C) Using our wing kinematics model (Eq. 7 based on Fig. 5, A and B), we estimated the time-resolved wing position for the step response commands for the three wing asymmetry cases shown in (A). Solid lines indicate the average and shaded regions indicate the standard deviation. (D) Roll, pitch, and yaw responses of the robot to the three wing asymmetry cases in (A) reveal a dominant roll response coupled with adverse yaw initially for the wrist asymmetry cases. The finger asymmetry case has no appreciable adverse yaw. Once the robot has rolled sufficiently into the turn, the adverse yaw angle changes direction, yawing into the turn instead (n = 12; 6 right + 6 left asymmetry trials pooled). Rotation rates are reported in full rotations per second. (E) A 3D reconstruction of a representative trial from each wing asymmetry variation in (A); the 3D flight paths are plotted in 0.1-s increments and projected on the (x,y), (x,z), and (y,z) plane for comparison.

  • Fig. 8 Asymmetric morphing wing flight tests reveal that finger motion alone can control steady-state turns.

    We measured open-loop dynamics of nine permutations of wing asymmetry cases, including extended/intermediate variations (A), intermediate/tucked variations (D), and extended/tucked variations (G) (Fig. 7) with coupled wrist/finger (blue), wrist asymmetry only (green), and finger asymmetry only (red) (B, E, and H). Projected top-down flight traces show that PigeonBot can control turns based on minor finger flexion asymmetry alone [red traces in (G), (H), and (I)]. (C, F, and I) Once past the initial response, most responses to wing asymmetry result in an equilibrium roll angle and turn curvature. Solid lines indicate the average and shaded regions indicate the standard deviation.

  • Table 1 The first principal component explains at least 75% of the variation in wing shape during gliding in pigeons.

    Together, the first two principal components (PCs) represent at least 97% of the variation. This implies that a two–degree of freedom mechanism replicates almost all measured wing motion and that a single–degree of freedom mechanism represents the majority of the motion.

    IndividualPC1PC2PC3PC4PC5
    Pigeon 174.5%22.5%1.64%0.48%0.38%
    Pigeon 292.2%4.94%1.62%0.55%0.34%
    Pigeon 386.4%9.85%2.37%0.63%0.23%
  • Movie 1. Morphing wing response to increasing flexion/extension cycling frequency under aerodynamic loading.

    A subset of the cycling frequencies tested (0.4, 1.0, 2.0, 5.1, and 8.9 Hz) shows that the PigeonBot wing responds well to control inputs up to ~5 Hz.

  • Movie 2. Morphing wing response to flexion and extension step commands of wrist and finger angle under aerodynamic loading.

    The wing and feather kinematics during wing flexion behave like an underdamped system, whereas during wing extension, they behave like an overdamped system.

  • Movie 3. PigeonBot untethered flight responses to wing asymmetry.

    With PigeonBot flying straight and level, we commanded wing asymmetries while locking the rudder neutral and measured the resulting kinematics. Feathered wing asymmetry causes primarily roll with adverse yaw.

  • robotics.sciencemag.org/cgi/content/full/5/38/eaay1246/DC1

    Supplementary Text

    Fig. S1. Rubber band force versus length properties.

    Fig. S2. Templates used for rubber band selection and tuning.

    Table S1. PigeonBot feathers were 90% from the same individual; the wind tunnel model feathers were 100% from the same individual.

    Table S2. Rubber bands used to connect PigeonBot feathers.

    Table S3. Rubber bands used to connect wind tunnel model feathers.

    Table S4. Bill of materials for constructing PigeonBot.

    References (45, 46)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • Fig. S1. Rubber band force versus length properties.
    • Fig. S2. Templates used for rubber band selection and tuning.
    • Table S1. PigeonBot feathers were 90% from the same individual; the wind tunnel model feathers were 100% from the same individual.
    • Table S2. Rubber bands used to connect PigeonBot feathers.
    • Table S3. Rubber bands used to connect wind tunnel model feathers.
    • Table S4. Bill of materials for constructing PigeonBot.
    • References (45, 46)

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