Source-linked AI summary
Towards insect-like distributed proprioception in actuators and appendages for flapping-wing insect-scale aerial robots
Alexander Hedrick, Arvind Gupta, Kaushik Jayaram
TL;DR
Insect-scale flapping robots often depend on off-board sensing, motivating embedded proprioception compatible with severe size, weight, and power constraints. This paper integrates PVDF sensors into an actuator and pitching flexure, achieving accurate stroke and pitch tracking and demonstrating collision detection and self-excited flapping.
Problem
Off-board sensing commonly supports insect-scale flapping robots, while autonomous operation requires onboard sensing architectures compatible with severe size, weight, and power constraints.
Method
The paper embeds thin PVDF films in a piezoelectric bending actuator and passive wing-pitching flexure, using a composite-beam model and laminate-compatible fabrication.
Results
The sensors accurately tracked stroke with 0.44° RMSE and pitch with 2.44° RMSE over the 110–190 Hz operating range, supporting collision detection and self-excited flapping demonstrations.
Takeaways & Limitations
Embedded proprioceptive sensors provide active and passive wingbeat measurements for demonstrated collision detection and asynchronous actuation in insect-scale flapping mechanisms.
Takeaways & Limitations
The authors identify uncertainty about whether asynchronous muscles make insects robust to wing damage, adaptive, or both, leaving this biological hypothesis for future study.
Abstract
from arXiv · showhide
Modern flapping-wing insect-scale air vehicles display agility similar to that of their insect counterparts; however, these impressive maneuvers are only possible with off-board sensors like optical tracking cameras. In this manuscript, we introduce two embedded proprioceptive sensors for insect-scale aerial robots: thin film piezoelectric polymers integrated directly into a driving actuator and a pitching hinge which track stroke and pitch angle, respectively. We fabricate the aforementioned size-agnostic mechanically intelligent structures (sensor-actuator, sensor-flexure) using laminate stack fabrication methods. Chirp experiments with our sensors integrated into an insect-size flapping-wing robot show accurate tracking of stroke (RMSE = 0.44 deg) and pitch (RMSE = 2.44 deg) angles in the relevant frequency range. As the first step towards demonstrating the utility of these sensors for enabling numerous onboard autonomy applications, including closed-loop wingbeat control and sensor fusion with existing insect-scale sensor suites for more accurate proprioception and localization, we show one application for each sensor. The proprioceptive hinge enables collision detection, reducing the chance of permanent damage if the robot's wing collides with an object. The proprioceptive actuator enables asynchronous flapping, which is hypothesized to increase adaptability and efficiency in insects and robots alike. A microrobot equipped with our proprioceptive actuator allows us to test these hypotheses with potential for improving flapping aerial robot performance. We foresee proprioceptive sensors having an important role in progressing both the fields of insect-scale aerial robots and robo-physics due to the bio-inspired nature and high integration level of our sensors.
I. INTRODUCTION
Insect-scale flapping robots increasingly achieve capable flight but typically depend on off-board sensing, motivating integrated proprioception that fits severe size, weight, and power constraints. This work introduces embedded PVDF sensors for stroke and pitch and demonstrates accurate tracking plus collision detection and asynchronous flapping applications.
- Off-board motion capture and infrastructure commonly provide state estimation and control for capable insect-scale flapping vehicles.
- Within-wingbeat events and local wing dynamics cannot be directly measured by conventional body-mounted sensors or reliably inferred from actuator commands alone.
- Thin PVDF films are embedded in a piezoelectric actuator to measure stroke and a passive pitching flexure to measure pitch.
- A composite-beam model and laminate-stack fabrication process provide a common sensing framework across the actuator and flexure geometries.
II. SENSOR: ARCHITECTURE, MODEL, FABRICATION
The sensing architecture targets two local wingbeat states: actuator-driven stroke and passively generated pitch. The integrated testbed evaluates these measurements during dynamic flapping.
- The platform integrates strain sensing at locations that encode actuator-driven wing stroke and passively generated wing pitch.
- The resulting sensor–actuator and sensor–flexure structures are evaluated as an integrated testbed under dynamic flapping conditions.
A. Flapping mechanism and sensing locations
The flapping mechanism converts piezoelectric actuator motion into wing stroke while compliant leading-edge flexures permit passive wing pitch. PVDF sensors are placed to measure these active and passive components separately.
- A piezoelectric bimorph drives two four-bar transmissions through a slider–crank mechanism that converts amplified actuator-tip displacement into wing stroke ϕ.
- Compliant leading-edge flexures permit passive wing pitching ψ under transmission, inertial, stiffness, and aerodynamic effects.
- The transmission and slider–crank are fabricated as one structure to reduce assembly variation and enable rapid wing replacement during testing.
- A PVDF film on the actuator measures stroke indirectly through actuator curvature and linear transmission kinematics.
- A second PVDF film on the pitching flexure directly measures pitch during passive wing rotation.
B. Sensor design and operational model
The sensors use PVDF composite-beam mechanics to convert bending strain into charge and voltage. The model incorporates layer geometry and material properties, while a charge amplifier provides the measured output.
- PVDF generates electric charge under mechanical strain, and bonding it away from the neutral axis enables bending-angle sensing.
- Generated charge is modeled from PVDF geometry, material properties, and average film strain.
- The composite-beam model treats each sensor as backing and PVDF layers and computes strain from beam displacement relative to the neutral bending axis.
- A charge amplifier converts accumulated sensor charge into an analog voltage for measurement.
- Equation 6 relates measured voltage to sensor tip displacement through input charge, VHREF = 1.25 V, and tunable gain Kca.
C. Proprioceptive actuator manufacturing
The proprioceptive actuator combines piezoelectric bending layers, a carbon-fiber center layer, and an electrically isolated PVDF sensing layer. A two-stage laminate-stack process protects the PVDF during high-temperature structural curing.
- C. Proprioceptive actuator manufacturing: The sensor–actuator uses outer PZT-5H layers for bending actuation, a carbon-fiber center layer, and a surface-bonded PVDF layer for strain sensing.The PVDF is placed away from the composite neutral axis to maximize bending strain.
- C. Proprioceptive actuator manufacturing: The two-stage laminate-stack process avoids exposing PVDF to structural curing temperatures above its approximately 100°C Curie temperature.The structural actuator layers are cured above 175°C for more than two hours.
- C. Proprioceptive actuator manufacturing: The completed actuator has five electrical connections: three for driving and two for reading the embedded sensor.A mini-breakout board provides access to these signals, and the actuator is press-fit and mechanically secured to the airframe.
D. Proprioceptive wing manufacturing
The proprioceptive wing integrates a PVDF sensing layer into the compliant leading-edge flexure that permits passive pitching. Wing rotation strains the film, allowing the flexure to encode pitch motion.
- D. Proprioceptive wing manufacturing: The sensor–flexure is integrated into the leading-edge wing structure that permits passive pitching.Its structural stack includes Mylar, high-temperature acrylic adhesive, a carbon-fiber laminate, and PVDF.
- D. Proprioceptive wing manufacturing: A thin PVDF layer bonded across the compliant pitching region strains during wing rotation and senses passive pitch.The carbon-fiber 0° direction aligns with the leading edge, while the 45° layer aligns with the wing spars.
III. SENSOR PERFORMANCE CHARACTERIZATION
The embedded actuator and flexure sensors were characterized against high-speed-camera ground truth across the relevant 60–200 Hz flapping range. Their amplitude tracking was quantified for stroke and pitch, with consistent phase lag that can be accounted for in control design.
- III. SENSOR PERFORMANCE CHARACTERIZATION: The experimental setup drives the robot through amplified voltage inputs while charge-amplified sensor outputs and high-speed-camera motion are recorded for synchronized ground-truth comparison.The same setup is used to track wing motion, with external amplifier boards that could be miniaturized for onboard use.
- III. SENSOR PERFORMANCE CHARACTERIZATION: 0.44° RMSE was achieved for stroke-amplitude tracking, with a sensor-output gain of 25.5 deg/V.The error compares sensor amplitude with ground-truth amplitude.
- III. SENSOR PERFORMANCE CHARACTERIZATION: 2.44° amplitude RMSE was measured for pitch in the relevant range between the approximately 110 Hz stroke resonance and approximately 190 Hz pitch resonance.Across the entire tested frequency range, amplitude RMSE was 4.04°; averaged across all trials it was 8.20°.
- III. SENSOR PERFORMANCE CHARACTERIZATION: The stroke and pitch sensors showed consistent phase lag, with phase RMSE values of 9.69° and 14.41°, respectively.The authors state that the consistent lag can be accounted for when designing a controller.
IV. APPLICATIONS
The characterization enables two proof-of-concept applications of locally embedded sensing: detecting contact-induced pitch deviations and providing stroke feedback for self-excited flapping.
- IV. APPLICATIONS: The flexure sensor reports contact-induced deviations from nominal pitch dynamics, while the actuator sensor supplies stroke feedback for delayed-stretch-activation-inspired self-excited flapping.These demonstrations illustrate locally embedded sensing rather than completed autonomous flight control.
- IV. APPLICATIONS: The demonstrations do not yet constitute closed-loop flight control, quantitative collision classification, or measurements of energetic or disturbance-rejection benefits.Those evaluations are identified as future directions.
A. Wing collisions produce measurable pitch deviations
Wing collisions create measurable deviations in the proprioceptive pitch signal, distinguishing collision trials from no-collision trials and a pure 100 Hz input.
- A. Wing collisions produce measurable pitch deviations: 3.23° RMSE separates collision FFTs from a pure sine wave, versus 0.53° without collisions over 0–500 Hz.Collision signals show lower amplitude at 100 Hz and much higher amplitude at 200 Hz than the pure sine wave.
- A. Wing collisions produce measurable pitch deviations: 15.81° time-data RMSE occurs with collisions, compared with 3.34° without collisions against the pure sine wave.
- A. Wing collisions produce measurable pitch deviations: A controller could compare collision-signal RMSE against a threshold such as 1° and change behavior when the threshold is exceeded.
- A. Wing collisions produce measurable pitch deviations: The experiment places a solid bar above the wing so that collisions occur on every flap under a 100 Hz pure sine-wave actuator input.The system is allowed to reach steady state, with points labeled before, during, and after collision within each wingbeat.
B. Embedded stroke feedback enables self-excited flapping
The robot uses proprioceptive actuator feedback to implement self-excited asynchronous flapping, drawing on delayed stretch activation as a model for insect muscle dynamics.
- B. Embedded stroke feedback enables self-excited flapping: Asynchronous insects use self-excited wingbeats at frequencies higher than nervous-system signals, unlike synchronous insects whose signals match wingbeat frequency.
- B. Embedded stroke feedback enables self-excited flapping: Delayed stretch activation increases muscle stress after a time delay following strain and is modeled with differential equations.The dSA filter acts as a second-order low-pass filter on stroke velocity.
- B. Embedded stroke feedback enables self-excited flapping: A prior dynamically scaled flapping system demonstrated adaptive effects and collision detection, but its actuator-velocity tracking method cannot scale down to insect size.
- B. Embedded stroke feedback enables self-excited flapping: The robot successfully transitions from synchronous to asynchronous flapping using proprioceptive actuator feedback to estimate stroke angle.Stroke angle, frequency, and amplitude are determined from the sensor signal, with frequency and amplitude obtained using a Hilbert transform.
V. CONCLUSION AND FUTURE WORK
The paper demonstrates highly integrated proprioceptive sensing for active stroke and passive pitch, with applications in collision detection and asynchronous actuation. Future work extends these capabilities toward autonomous insect-scale robots, robophysical studies, and broader periodic-bending systems.
- The integrated sensors accurately track wing stroke and pitch while enabling collision detection and asynchronous actuation.Thin PVDF films are embedded in a bending actuator and pitching flexure to measure active and passive wingbeat components, respectively.
- The proprioceptive actuator supports a transition from synchronous to asynchronous flapping as the synchronous-force fraction Kr decreases to 0.The emergent frequency becomes slightly higher than system resonance, with frequency and amplitude controlled by dSA coefficients r3, κ, and µ.
- The sensing elements weigh approximately 0.1–1 mg, compared with approximately 0.1–1 g for prior proprioceptive sensors.The laminate fabrication technique supports miniaturization and can scale to larger flapping systems and legged robots.
- PVDF in the pitching hinge could later support angle-of-attack control by electrically changing the hinge’s neutral angle.The authors propose improved PVDF actuator designs for controlling robot attitude and studying biological stabilization mechanisms.
- Future work will use the platform to study whether asynchronous muscles contribute to maintaining flight performance after wing damage.The authors identify uncertainty about whether asynchronous muscles are robust to wing damage, adaptive, or both.