A 26-Gram Butterfly-Inspired Robot Achieving Autonomous Tailless Flight

TL;DR

AirPulse demonstrates the first untethered, onboard-controlled, two-wing tailless flapping-wing micro air vehicle at 26 g with butterfly-inspired biomechanics. The work establishes a quantitative mapping from flapping modulation (amplitude, frequency, stroke offset, and STAR-based stroke timing) to force-torque generation and introduces the Stroke Timing Asymmetry Rhythm (STAR) to provide smooth, linearly tunable wingstroke asymmetry. An onboard PID-based attitude controller, state estimator, and a rotorless CPG translate commands into differential wing actuation, enabling stable pitch and yaw control while the body undergoes active undulation due to rapid inertial variations. Free-flight experiments demonstrate climbing and turning maneuvers with modest power (≈5.9 W), validating a lightweight, collision-tolerant platform for confined-environment inspection and ecological monitoring and offering a physical model to decode the flight principles of real butterflies.

Abstract

Flapping-wing micro air vehicles (FWMAVs) have demonstrated remarkable bio-inspired agility, yet tailless two-winged configurations remain largely unexplored due to their complex fluid-structure and wing-body coupling. Here we present \textit{AirPulse}, a 26-gram butterfly-inspired FWMAV that achieves fully onboard, closed-loop, untethered flight without auxiliary control surfaces. The AirPulse robot replicates key biomechanical traits of butterfly flight, including low wing aspect ratio, compliant carbon-fiber-reinforced wings, and low-frequency, high-amplitude flapping that induces cyclic variations in the center of gravity and moment of inertia, producing characteristic body undulation. We establish a quantitative mapping between flapping modulation parameters and force-torque generation, and introduce the Stroke Timing Asymmetry Rhythm (STAR) generator, enabling smooth, stable, and linearly parameterized wingstroke asymmetry for flapping control. Integrating these with an attitude controller, the AirPulse robot maintains pitch and yaw stability despite strong oscillatory dynamics. Free-flight experiments demonstrate stable climbing and turning maneuvers via either angle offset or stroke timing modulation, marking the first onboard controlled flight of the lightest two-winged, tailless butterfly-inspired FWMAV reported in peer-reviewed literature. This work corroborates a foundational platform for lightweight, collision-proof FWMAVs, bridging biological inspiration with practical aerial robotics. Their non-invasive maneuverability is ideally suited for real-world applications, such as confined-space inspection and ecological monitoring, inaccessible to traditional drones, while their biomechanical fidelity provides a physical model to decode the principles underlying the erratic yet efficient flight of real butterflies.

Figures (11)

• Figure 1: Biomimetic design of the butterfly-inspired flapping-wing robot. (A) Comparison of biological specimen (Papilio demoleus, left) and the AirPulse prototype (right). (B) Mass distribution of the flight-ready robot. (C) Robotic body core showing thoracic actuation (two micro servos), avionics (9-axis IMU, barometer), and power module; ELRS receiver included for safety ovveride only. Scale bar: 10 mm. (D) Actuation schematic and body frame {$\mathcal{B}$} (+x forward, +y left, +z up); each forewing-hindwing pair driven by a micro servo with a fixed V-shaped dihedral. (E) Forewing venation of P. demoleus. (F) Morphological statistics of Dc-Cu1 angles and aspect ratios across three butterfly families (Nymphalidae, Pieridae, Papillionidae). Aspect ratio (AR) redefined geometrically as the length along the hind margin divided by the perpendicular width, offering a more shape-relevant metric than the conventional formula. (G) Biomimetic wing design of AirPulse, showing venation-inspired carbon-fiber rod layout for graded stiffness distribution.
• Figure 2: Inertial and aerodynamic characteristics. (A, B) Fore-aft and vertical CG displacement and principal inertia variation over a full wingstroke. (C) Static aerodynamic forces and moments under a 3 m/s horizontal wind; positive pitching moment is nose-up. (D) Test rig with six-axis force-torque (F/T) sensor and motion capture system for wing performance analyses. (E) Three wing variants: intact four-vein forewings (blue), two-vein forewings (orange), and four-vein forewings with de-winged hindwings (green). (F, G) Cycle-resolved axial and vertical aerodynamic forces for each wing variant. (H) Cycle-averaged axial and vertical forces. (I, J) Forewing bending angles during flapping for intact four-vein and two-vein wings. (K) Chordwise deformation illustrating higher distal compliance in two-vein wings.
• Figure 3: Stroke timing modulation using the STAR generator. (A) Stroke angle offset modulation shifts the neutral stroke plane. (B) Stroke timing modulation produces asymmetric upstroke/downstroke velocities. (C, D) Limitations of existing polynomial phase-shaping and split-cycle methods. (E–G) STAR generates continuous, monotonic up-down asymmetry with smooth first derivatives across the wingbeat cycle for varying modulation parameter $A$. (H, I) IIR filtering applied to $1/p$. (J–L) STAR with IIR filtering preserves cycle-averaged flapping frequency while enabling stable and linear tuning of stroke asymmetry without introducing phase distortion.
• Figure 4: Force-torque mapping of flapping-wing modulation. (A, B) Effect of flapping amplitude on cycle-averaged forces and torques: increased amplitude primarily enhances forward force. (C, D) Effect of flapping frequency: higher frequency increases forward force with minimal impact on mean torque. (E-G) Symmetric angle offset modulation increases pitch torque while slightly reducing total force. Antisymmetric angle offset modulation generates roll moments with minimal yaw and total force changes. (H-J) Symmetric stroke timing modulation via STAR parameter $A$ produces nose-up pitch moments. Antisymmetric STAR modulation generates roll moments with minor yaw effects.
• Figure 5: Free-flight dynamics and closed-loop control. (A) Tri-axial accelerometer measurements showing forward and vertical oscillatory accelerations during free flight. (B, C) Intra-cycle acceleration profiles under angle offset and stroke timing modulation, respectively. (D, E) Composite images of free-flight climbing and turning maneuvers. (F) Pitch angle tracking using angle offset modulation; RLS-extracted low-frequency mean enables stable feedback. (H) Pitch angle tracking using STAR stroke timing modulation with RLS filtering. (J, L) Yaw control for directional turning using angle offset and STAR modulation. (G, I, K, M) Corresponding average power consumption during maneuvers for each modulation strategy, demonstrating low energy demand relative to conventional micro aerial vehicles.