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Small-scale flapping-wing micro air vehicles (FWMAVs) are an emerging robotic technology with many applications in areas including infrastructure monitoring and remote sensing. However, challenges such as inefficient energetics and decreased payload capacity preclude the useful implementation of FWMAVs. Insects serve as inspiration to FWMAV design owing to their energy efficiency, maneuverability, and capacity to hover. Still, the biomechanics of insects remain challenging to model, thereby limiting the translational design insights we can gather from their flight. In particular, it is not well-understood how wing flexibility impacts the energy requirements of flapping flight. In this work, we developed a simple model of an insect drive train consisting of a compliant thorax coupled to a flexible wing flapping with single-degree-of-freedom rotation in a fluid environment. We applied this model to quantify the energy required to actuate a flapping wing system with parameters based off a hawkmoth Manduca sexta. Despite its simplifications, the model predicts thorax displacement, wingtip deflection and peak aerodynamic force in proximity to what has been measured experimentally in flying moths. We found a flapping system with flexible wings requires 20% less energy than a flapping system with rigid wings while maintaining similar aerodynamic performance. Passive wing deformation increases the effective angle of rotation of the flexible wing, thereby reducing the maximum rotation angle at the base of the wing. We investigated the sensitivity of these results to parameter deviations and found that the energetic savings conferred by the flexible wing are robust over a wide range of parameters.
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This content will become publicly available on April 1, 2026
Reduced-Order Modeling and Optimization of a Flapping-Wing Flight System
Abstract Flapping-wing micro-air vehicles (FWMAVs) are an emerging technology inspired by flying insects that show promise in applications favoring maneuverability and vehicle compactness. However, current designs are limited by inefficient energetics, and current dynamical models of the flight system employ limiting assumptions when considering power demands. Here, we derive a system-level model of the insect flight system including the thorax, wing, and wing hinge that can inform insect-inspired FWMAV design. We applied the model to study the flight system of a hawkmoth, and used a genetic algorithm optimization to tune uncertain model parameters to minimize the power required to hover. Results show that performance is improved by utilizing multimodal excitation to produce favorable flapping kinematics. This is achieved by locating the flapping frequency of the moth between the nonlinear resonant frequencies, resulting in magnified flapping response and aerodynamically advantageous phase. The optimal flapping frequency can be predicted from the system’s underlying linear natural frequencies and is roughly 54% of the system’s mean natural frequency. Furthermore, effective solutions are configured so that the timing of the applied load and thorax responses are matched such that little effort is spent reversing the wing stroke. The optimized model parameters and corresponding kinematics show moderate agreement with those reported for the hawkmoth. To maintain hovering flight, the successful moths in the population expend approximately 58.5 W/kg. The system-level model and the governing principles identified here can inform the design of energy efficient FWMAVs moving forward.
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- PAR ID:
- 10601262
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- Journal of Computational and Nonlinear Dynamics
- Volume:
- 20
- Issue:
- 4
- ISSN:
- 1555-1415
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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