Abdominal Undulation with Compliant Mechanism Improves Flight Performance of Biomimetic Robotic Butterfly

TL;DR

This work addresses improving flight performance of biomimetic FWAVs by enabling coupled wing-abdomen motion through a compliant mechanism in a robotic butterfly. A coupled dynamics model is developed, combining a pseudo-rigid half-thorax for flapping, a quasi-steady blade-element aerodynamic analysis, and an abdomen-undulation mechanism to predict lift, stroke, and stability, with key quantities such as $F_{lift}$, $F_{drag}$, and the wing stroke governed by design parameters. Experimental validation with three BRB configurations demonstrates that abdominal undulation increases average lift by $3.4\%$, extends forward travel to about $10\,\mathrm{m}$, and sustains flight for around $4\,\mathrm{s}$, while affecting pitch dynamics in a manner consistent with the model. These findings highlight wing-abdomen interaction as a critical mechanism for energy-efficient, stable biomimetic flight and provide practical guidance for future FWAV designs.

Abstract

Abdominal Undulation with Compliant Mechanism Improves Flight Performance of Biomimetic Robotic ButterflThis paper presents the design, modeling, and experimental validation of a biomimetic robotic butterfly (BRB) that integrates a compliant mechanism to achieve coupled wing-abdomen motion. Drawing inspiration from the natural f light dynamics of butterflies, a theoretical model is developed to investigate the impact of abdominal undulation on flight performance. To validate the model, motion capture experi ments are conducted on three configurations: a BRB without an abdomen, with a fixed abdomen, and with an undulating abdomen. The results demonstrate that abdominal undulation enhances lift generation, extends flight duration, and stabilizes pitch oscillations, thereby improving overall flight performance. These findings underscore the significance of wing-abdomen interaction in flapping-wing aerial vehicles (FWAVs) and lay the groundwork for future advancements in energy-efficient biomimetic flight designs.

Figures (10)

• Figure 1: Illustration of the proposed biomimetic robotic butterfly (BRB) with compliant mechanism.
• Figure 2: (a) The prototype robot showing degree of freedom of flapping wing. (b) Flapping mechanism, (c) abdominal undulation mechanism and (d) wing design based on morphological similarity.
• Figure 3: (a) Pseudo-rigid model of the half-thorax in static equilibrium (black) and activated state (green). (b) Schematic drawing depicting the geometric parameters of the wing model and simplified outline (green). (c) Simplified model of abdomen mechanism in static state (black) and upstroke state (green).
• Figure 4: (a) The time-dependent relationship curves of the wing base rotation angle $\theta_\mathrm{A}$ under different torque values. (b) The time-dependent relationship curves of the wing base rotation angle $\theta_\mathrm{A}$ with and without the use of flexible hinges.
• Figure 5: (a) The relationship between the abdominal rotation angle $\theta_\mathrm{D}$ and the wing base rotation angle $\theta_\mathrm{A}$. (b) The relationship between the vertical force $F_1$ exerted on the slider by a 0.03 $\mathrm{N\cdot m}$ torque and the vertical force $F_2$ generated by abdominal undulation, as well as their resultant force $F_3$. (c) The time-dependent relationship of the wing base rotation angle $\theta_\mathrm{A}^\prime$ under the resultant force $F_3$. The discrepancy in alignment of the shaded regions for the two curves is attributed to the differing durations of the downstrokes. (d) The time-dependent relationship between the wing lift force with and without abdominal undulation, denoted as $F_\mathrm{lift}^\prime$ and $F_\mathrm{lift}$, respectively.