Towards insect-like distributed proprioception in actuators and appendages for flapping-wing insect-scale aerial robots

Alexander Hedrick; Arvind Gupta; Kaushik Jayaram

cs.ROAug 22, 2026

Towards insect-like distributed proprioception in actuators and appendages for flapping-wing insect-scale aerial robots

Authors: Alexander Hedrick, Arvind Gupta, Kaushik Jayaram

Organizations: Animal Inspired Movement and Robotics Laboratory, Paul M. Rady Department of Mechanical Engineering, University of Colorado Boulder · Insect Inspired Intelligence Laboratory, Department of Bioengineering, Imperial College London

Abstract

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.

Figures & tables

Fig. 1: (a) The flapping-wing insect-scale air vehicle with integrated proprioceptive actuator and hinge labeled. (b) Side-view of the stackup for each sensor. (c) Three applications for these sensors: wing collision detection, asynchronous flapping, and closed-loop stroke control. Collision detection is demonstrated in Section IV-A while asynchronous flapping, a form of closed-loop stroke control, is demonstrated in Section IV-B .

Fig. 2: (a) Color-coded CAD model of platform with with stroke ( $\phi$ ) and pitch ( $\psi$ ) angles labeled. (b) Proprioceptive actuator. (c) Color-coded stackup for the proprioceptive actuator showing individual layers. (d) Steps for manufacturing the actuator. (e) Proprioceptive wing. (f) Color-coded stackup for the proprioceptive wing showing individual layers. (g) Steps for manufacturing the wing.

PVDF Material Properties
Parameter	Symbol	Value	Units
Piezo Stress Constant	$g_{31}$	216	mVm/N
Relative Dielectric Constant	$\epsilon_{r}$	13	unitless
PVDF Young’s Modulus	$E_{p}$	2.8	GPa
PVDF Thickness	$t_{p}$	12	$\mu$ m
Proprioceptive Actuator Parameters

TABLE I: Proprioceptive sensor parameters

Fig. 3: (a) Photo of the setup used for controlling the robot and measuring the output from the proprioceptive sensors. (b) Block diagram of the experimental setup. The real-time Speedgoat computer sends signals to the actuator through a voltage amplifier and receives analog signals from the sensor through a charge amplifier circuit. A high speed camera records the motion of the actuator for post-processing. We use the same setup for tracking the wing motion. (c) Charge amplifier circuit diagram. Equation 6 describes VOUT as a function of sensor displacement and circuit components.

Fig. 4: (a) Frequency response for the stroke angle (blue) as calculated from the proprioceptive actuator–sensor data vs. ground-truth (orange). (b) Frequency response for the proprioceptive wing (blue) vs. ground-truth (orange). The magnitude plot shows the pitch amplitude as a function of frequency while the phase plot shows the phase difference between pitch angle and stroke angle.

Fig. 5: (a) In this experiment we set a solid bar above the wing so the wing collides on every flap and let the system reach steady state. The actuator input is a pure sine wave at a frequency of 100 Hz. Three points are labeled within a wingbeat: before, at, and following the collision. (b) FFT of the collision trial, a no-collision trial at the same input frequency, and a pure 100 Hz sine wave. We include insets of the collision and no-collision trial pitch angles as functions of time. The differences between the collision FFT vs. the no-collision and 100 Hz sine FFTs are circled in red.

Fig. 6: (a) Block diagram for the synchronous to asynchronous transition. Stroke angle is measured with the proprioceptive actuator. The stroke velocity is fed into the delayed stretch activation filter (dSA) which is described by the differential equations 7 . The synchronous force is a constant frequency and amplitude sine wave. The parameter $K_{r}$ determines what fraction of actuator input force ( $F_{m}$ ) comes from synchronous vs. asynchronous, where $K_{r}$ = 1 is fully synchronous and $K_{r}$ = 0 is fully asynchronous. (b) Transition from open-loop synchronous to asynchronous flapping. The first plot shows $K_{r}$ as a function of time followed by the stroke angle for the trial. The final two plots are the filtered Hilbert transform of the stroke angle plot, showing stroke frequency and amplitude. At the start of the trial, the synchronous frequency is set to a value much lower than the resonance frequency leading to low stroke amplitude. However, as $K_{r}$ decreases to 0 and the asynchronous dynamics take over, the emergent frequency is slightly higher than the system resonance frequency. The emergent frequency and stroke amplitude are controlled by the three main dSA coefficients: $r_{3}$ , $\kappa$ , and $\mu$ which can be seen in the dSA filter coefficients in Equation 8 .

Aerial Robotics

Aerial robotics studies the design, perception, control, and coordination of flying robots for navigation, inspection, transport, and physical interaction.

See all 340 papers

Characterizing pitch and roll torque coupling in insect-sized flapping-wing robots using a microfabricated gimbal
Apr 23, 2026Aaron Weber, Daksh Dhingra, Sawyer B. FullerAerial Robotics
Department of Mechanical Engineering, University of Washington, Seattle, USA · Humanoid, Boston, USA · Department of Mechanical Engineering and Paul G. Allen School of Computer Science, University of Washington, Seattle, USA
Self-excited actuation enables adaptive and resilient flapping-wing flight
Sep 16, 2026Rundong Yang, Ethan S. Wold, Ellen Liu +5Robotic Control Aerial Robotics
Mechanical and Aerospace Engineering, University of California San Diego, San Diego, CA, 92161, USA · School of Biological Sciences and School of Physics, Georgia Institute of Technology, Atlanta, GA, 30332, USA · Mechanical Industrial Engineering, Montana State University, MT, 59717, USA
Multilaminate piezoelectric polymer actuators for insect-scale softrobots
Nov 15, 2025Nicholas Gunter, Heiko Kabutz, Alexander Hedrick +1Robotics Soft Robotics
Animal Inspired Movement and Robotics Laboratory, Paul M. Rady Department of Mechanical Engineering, University of Colorado Boulder

Apr 23, 2026J/K move · Enter open · S save

Characterizing pitch and roll torque coupling in insect-sized flapping-wing robots using a microfabricated gimbal

Aaron Weber, Daksh Dhingra, Sawyer B. Fuller

Department of Mechanical Engineering, University of Washington, Seattle, USA · Humanoid, Boston, USA · Department of Mechanical Engineering and Paul G. Allen School of Computer Science, University of Washington, Seattle, USA

Aerial Robotics

Open paper AskPDF arXiv

Sub-gram flapping-wing flying insect robots (FIRs) are challenging to model because of mechanical complexity in their wings, unsteady aerodynamic flow, and the difficulty of making precise measurements at a small scale. Coupling effects between roll and pitch torque actuation have not previously been measured because a two-axis sensor that is sensitive enough has not been realized. To address this shortcoming, we introduce a microfabricated gimbal design capable of precisely and simultaneously measuring roll and pitch torques as well as thrust. We then used it to measure the extent to which a pitch torque command affects roll torque and vice versa on a 180 mg piezo-actuated flapping-wing flying platform. Our results show a high coefficient of determination in the linear regression for both pitch (0.95) and roll (0.98) and low cross-correlation coefficients (-0.001 and -0.085, respectively) across the full range of simultaneous torque commands, indicating negligible cross-axis coupling. Similarly, thrust force deviates by a maximum of only 5.8% from the mean thrust value. These results validate the assumption that pitch and toll can be considered independently in control and will inform future models of how inputs affect the aerodynamics of resonant flapping-wing systems.

Abstract

Aerial Robotics

Explore similar work

Characterizing pitch and roll torque coupling in insect-sized flapping-wing robots using a microfabricated gimbal

Self-excited actuation enables adaptive and resilient flapping-wing flight

Multilaminate piezoelectric polymer actuators for insect-scale softrobots