Takeoff of an All-Polymer Micro-Aerial Flying Robot
Data files
Sep 08, 2026 version files 18.18 MB
-
Code_S1.m
7.83 KB
-
Data_S1.xlsx
1.69 MB
-
Data_S2.zip
16.47 MB
-
README.md
13.12 KB
Abstract
Flying insects are agile and can withstand impacts and compression due to their low inertia and resilient wings, exoskeletons, and muscles. These capabilities inspire the development of micro-aerial vehicles (MAVs) for surveillance, disaster response, and environmental monitoring in confined or hazardous spaces. However, MAVs, especially sub-gram flapping-wing platforms, remain fragile because they rely on rigid components in their wings, transmissions, or actuators. We report a resilient all-polymer flying robot weighing 185 milligrams, powered by an electrostrictive bending actuator that directly drives cone-shaped compliant wings without a transmission. The actuator achieves a power density of 1,600 watt per kilogram and a bending angle of 136 degrees at 110 hertz, enabling the flying robot to achieve a lift-to-weight ratio of 3.0 and a lift-to-power ratio of 8.3 millinewton per watt at 30 hertz. The robot demonstrates unaided takeoff with an average ascending speed of 40 centimeters per second. Thanks to its compliant and transmission-free structure, the robot can resume flight after being hit by a flyswatter or flattened by heavy loads. The robot design features mechanical simplicity and resilience, promising a paradigm for sub-gram flight in harsh environments.
Dataset DOI: 10.5061/dryad.q2bvq8421
Description of the data and file structure
Data S1 contains the data necessary to reproduce the figures (except Figure S14-S15).
Code S1 is the matlab script described in the Supplementary Methods.
Data S2 corresponds to Figure S14-S15.
Note: For each data file/sheet related to a figure, this README describes the figure, provides x and y units, and includes the figure legend, where applicable.
Files and variables
File: Code_S1.m
Description: Code S1 is the MATLAB script described in the Supplementary Methods, for a graphical calculation method for the kinetic energy of the electrostrictive actuator.
File: Data_S1.xlsx
Description: Data S1 contains the data necessary to reproduce the figures (except Figure S14-S15).
Sheet name Fig. 2C. Static bending angles of the actuators made with terpolymer films fabricated under different conditions.
x unit: voltage applied in kV.
y unit: bending angles in degree (°).
DMF: casting solvent is N,N-dimethylformamide
DMF-A: casting solvent is N,N-dimethylformamide, followed with annealing
Melt-recrystallization-A: casting solvent is N,N-dimethylformamide, followed by melting and recrystallization, then annealing
MEK-A: casting solent is methyl ethyl ketone, followed by annealing
Sheet name Fig. 2D. Static blocked force of the actuators made with terpolymer films fabricated under different conditions.
x unit: voltage applied in kV.
y unit: blocked force in mN.
Legend is the same as Fig. 2C.
Sheet name Fig. 3B. The dynamic bending angles, α, of the actuator under different applied voltages and frequencies.
x unit: frequency of applied voltage in Hz.
y unit: bending angles in degrees (°).
Legend: amplitude of applied voltage in kV.
Sheet name Fig. 3C. The representative dynamic displacement at 4 kV and 110 Hz at the location that is 1.6 mm from the fixed section of the actuator measured by a laser sensor. Negative displacement represents bending upwards.
x unit: time in ms.
y unit: displacement in mm.
The testing condition is 4kV and 110Hz.
Sheet name Fig. 3D. The Fourier transform of the time-domain displacement in Fig. 3C revealing the actuator’s oscillation frequency components.
x unit: frequency in Hz.
y unit: amplitude in mm.
The testing condition is 4kV and 110Hz.
Sheet name Fig. 3E. Blocked force of the flapping actuator under different applied voltages and operating frequencies. The average and standard deviation of the blocked force (sample size N = 36) are shown with the circle and error bar, respectively.
x unit: frequency in Hz.
y unit: blocked force in mN.
Legend: amplitude of applied voltage in kV.
Sheet name Fig. 3F. Kinetic energy density of the flapping actuator under different applied voltages and operating frequencies.
x unit: frequency in Hz.
y unit: maximum kinetic energy in mJ.
Legends: amplitude of applied voltage in kV.
Sheet name Fig. 3G. A comparison of the energy and power density of the electrostrictive flapping actuator with those of representative soft actuators reported for MAVs.
x unit: energy density of actuators in J/kg.
y unit: power density of actuators in W/kg.
Legends: different types of actuators and the corresponding references.
Sheet name Fig. 4C. The time-domain relationship between the flapping angle α of the electrostrictive actuator and the folding cone angle β of the compliant wings at 4 kV and 30 Hz. The dash line indicates the time-boundary between the recovery stroke and the power stroke.
x unit: time in ms.
y unit: bending angles in degrees (°).
Legend: α for actuators and β for compliant wings.
Sheet name Fig. 4D. Lift force of the APFR under different applied voltages and frequencies. The dash line indicates the weight of the robot.
x unit: frequency in Hz.
y unit: lift force in mN.
Legend: amplitude of applied voltage in kV.
There is an empty cell in the column of 3kV and 40Hz, because the lift force for 3kV and 38Hz is already a negative value. This indicates that the net lift force upward is no longer valid when the operating frequency deviates too much from the optimal value. Therefore, there is no necessity to test the combination of 3kV and 40Hz, and the cell is left empty.
Sheet name Fig. 4E. Real-time lift force measurement under the driving condition of 4 kV and 30 Hz.
x unit: time in ms.
y unit: lift force in mN.
Sheet name Fig. 4F. The representative dynamic displacement and durability test at 4 kV and 30 Hz at a location on the electrostrictive actuator that is 1.6 mm from the root of the actuator beam. Negative displacement represents bending upwards.
x unit: time in ms.
y unit: displacement in mm.
Legend: before and after 18,000 cycles.
There are empty cells at the end of the third and fourth columns, because the figure intends to show the data within a fixed time period (500ms). During this period, the total number of samples may differ slightly depending on the delay of the oscilloscope. In this case, the data for "after 18,000 cycles" is one sample less than the data for "before 18,000 cycles", which is the reason for the empty cells here.
Sheet name Fig. 5D. The time-elevation relationships of the unaided flight scenarios.
x unit: time in ms.
y unit: vertical displacement in mm.
Sheet name Fig. 5E. The time-elevation relationships of the impact flight scenarios.
x unit: time in ms.
y unit: vertical displacement in mm.
Sheet name Fig. 5F. The time-elevation relationships of the compression flight scenarios.
x unit: time in ms.
y unit: vertical displacement in mm.
Sheet name Fig. S2A. Fourier Transform Infrared Spectroscopy (FTIR) of the four terpolymer films in Table S1. The peaks at 605/614, 772 and 800 cm-1 in an FTIR spectrum are assigned to the switchable dipoles (short trans sequences) within the terpolymer film that are responsible for the film’s electrostrictive actuations. The film samples all have a thickness of 30 µm.
x unit: wavenumber in cm-1.
y unit: absorbance in a.u. (Arbitrary Unit).
DMF: casting solvent is N,N-dimethylformamide
DMF-A: casting solvent is N,N-dimethylformamide, followed with annealing
Melt-recrystallization-A: casting solvent is N,N-dimethylformamide, followed by melting and recrystallization, then annealing
MEK-A: casting solent is methyl ethyl ketone, followed by annealing
Sheet name Fig. S2B. Stress-strain curves of the DMF-A film.
x unit: strain in percent.
y unit: Stress in MPa.
The sample legend is DMF-A (casting solvent is N,N-dimethylformamide, followed with annealing).
Sheet name Fig. S6A. Comparison of the power density and lift-to-weight ratio of the electrostrictive flapping actuator with representative soft actuators reported for MAVs.
x unit: power density in W/kg.
y unit: lift-to-weight ratios in dimensionless.
Legends: different types of actuators and the corresponding references.
Sheet name Fig. S6B. The average displacement of a point on the actuator, at a location 1.6 mm from the root of the actuator beam, measured by a laser sensor every 6,600 cycles at 4 kV and 110 Hz. The slight increase can be attributed to plastic deformation that accumulates during the test. After that the material tends to breakdown due to defects or aging.
x unit: cycle number (dimensionless).
y unit: displacement in mm.
Legend: downward and upward.
Sheet name Fig. S6C. The displacement of a point on the actuator, at a location 1.6 mm from the root of the actuator beam, measured by a laser sensor every 6,600 cycles at 4 kV and 110 Hz. Minor fluctuations in the time-domain displacement peaks can be attributed to the peripheral oscillation of the auxiliary structure to which the actuator is fixed.
x unit: time in ms.
y unit: displacement in mm.
Legends: before and after 66,000 cycles.
Sheet name Fig. S6D. The lift force of the APFR measured every 10,000 cycles under a 3.5 kV and 30 Hz operation for lifetime evaluation.
x unit: cycle number (dimensionless).
y unit: lift force in mN.
Sheet name Fig. S7B. Variety of compliant wing parameters and the corresponding lift force generated by the APFR when equipped with these wings at 4 kV.
x unit: frequency in Hz.
y unit: lift force in mN.
Legends: all 9 combinations of wing fabrication parameters θ1 θ2 θ3 and h1 h2 h3.
Sheet name Fig. S7C. The voltage and current waveforms of the APFR driven at 4 kV and 30 Hz.
x unit: time in ms.
y unit: voltage in kV and current in mA.
Sheet name Fig. S7D. The power consumption of the electrostrictive actuator driven at 110 Hz and that of the APFR driven at 30 Hz, with respect to different applied voltages. The average and standard deviation of the power consumption (sample size N = 10) are shown with the bar height and error bar, respectively.
x unit: frequency in Hz.
y unit: power consumption in W.
Legend: amplitude of applied voltage in kV.
Sheet name Fig. S8D. Lift force measurement after compression along each respective axis.
x unit: bending axis (x, y, and z).
y unit: lift force in mN.
Legends: before and after the compression.
Sheet name Fig. S9A. The current waveform during the process when the actuator was interfered by a wooden stick’s poking. The shaded area indicates the time period during which the interference occurred, and the dotted lines denote stable (non-pulse) charging and discharging currents.
x unit: time in s.
y unit: current in mA.
The testing condition is 3.5kV and 25Hz.
Sheet name Fig. S9B. The current waveform during the process when the compliant wing was interfered by a wooden stick’s poking. The shaded area indicates the time period during which the interference occurred, and the dotted lines denote stable (non-pulse) charging and discharging currents.
x unit: time in s.
y unit: current in mA.
The testing condition is 3.5kV and 25Hz.
Sheet name Fig. S10A. Free-decay time-displacement curve of the actuator for obtaining the first-order damping ratio ζ1. The displacement is measured at a location that is 1.6 mm from the root of the actuator beam. Negative displacement represents upward bending.
x unit: time in ms.
y unit: displacement in mm.
The testing condition is 4kV and 110Hz.
Sheet name Fig. S10B. Path of the edge of the actuator at 4 kV and 110 Hz obtained from images of the high-speed camera video, with representative images shown in Fig. 3A.
x unit: x coordinate in mm.
y unit: y coordinate in mm.
Legends: path of the edge, and root of the beam.
Sheet name Fig. S13A. Vertical displacement-time history of the highest structural position on the wing during the recovery stroke.
x unit: time in s.
y unit: displacement in m.
Sheet name Fig. S13B. Vertical displacement-time history of the highest structural position on the wing during the power stroke.
x unit: time in s.
y unit: displacement in m.
Sheet name Fig. S13C. Lift-time history of the wing during the recovery stroke.
x unit: time in s.
y unit: lift force in N/m.
Sheet name Fig. S13D. Lift-time history of the wing during the power stroke.
x unit: time in s.
y unit: lift force in N/m.
Variables
- Described in the files section.
File: Data_S2.zip
Description: Data S2 corresponds to Figure S14-S15.
Fig. S14. Velocity contour plots at four representative instants of the wing. (A) The highest position (beginning to go downward, β = 101.3°). (B) Position when the maximum vertical downward velocity of the wing is obtained (β = 101.3°). (C) The lowest position (beginning to go upward, β = 83.2°). (D) Position when the maximum vertical upward velocity of the wing is obtained (β = 83.2°).
Color bar: velocity in m/s.
Fig. S15. Pressure contour plots at four representative instants of the wings. (A) The highest position (beginning to go downward, β = 101.3°). (B) Position when the maximum vertical downward velocity of the wing is obtained (β = 101.3°). (C) The lowest position (beginning to go upward, β = 83.2°). (D) Position when the maximum vertical upward velocity of the wing is obtained (β = 83.2°).
Color bar: pressure in Pa.
Code/software
Matlab is required to run Code S1. Tecplot or ParaView (freely available) is required to open Data S2.
Access information
Other publicly accessible locations of the data:
- N/A
Data was derived from the following sources:
- N/A