# Research on the Flight Performance of Biomimetic Moth Based on Flapping Function Control
###### Abstract  
Flapping flight is an important mode of insect flight, and its unique flapping motion pattern enables it to fly efficiently in complex environments. This paper takes a biomimetic moth flapping-wing aircraft as the research object and proposes a periodic function composed of two sine functions with different frequencies as the flapping function. This paper explores the effect of this flapping function on the flight performance of flapping-wing aircraft and verifies whether it can be applied to the flight control of flapping-wing aircraft. Firstly, through the study of biomimetic mechanisms, the basic structure of the flapping-wing aircraft is roughly designed; then, the flapping motion is simplified, a rigid wing flapping motion model is established, and the key parameters affecting the average lift are determined. Next, a virtual wind tunnel simulation platform is built, and the key parameters of the flapping function that affect lift generation are simulated and calculated. Finally, an experimental prototype of a biomimetic moth flapping-wing aircraft is designed and manufactured. Through flight experiments, the effects of flapping amplitude, flapping frequency, and mid-position angle in the flapping function on the flight performance of the biomimetic flapping-wing aircraft are verified. The key control parameters are clarified, the control strategy of the flapping-wing aircraft is optimized, and the maneuverability and controllability of the aircraft are improved, providing a theoretical basis and practical support for the development of control methods for biomimetic flapping-wing aircraft. biomimetic flapping-wing aircraft; flapping function; simulation calculation; flight experiment +
Footnote †: journal: applied sciences  
0000-0002-4000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-000000-00000-000000-000000-0000000-000000000000000000000000000000000000000000000001. Biomimetic design of insect wing structure and flapping motion, such as Festo's eMotionButterflies [6] and BionicOpter [7];
2. Miniaturization design based on special driving methods, such as the micro flapping-wing aircraft \"Mentor\" from the Stanford Research Institute (SRI) and the micro robotic fly from the Harvard Micro Robotics Laboratory [8];
3. Research on the collective flight behavior of insects and the control of flapping-wing aircraft clusters, such as Festo's BionicBee [9], autonomous formation flight control based on a leader-follower strategy [10] and three flapping wings with unequal spacing [11]. Biomimetic flight vehicles with Lepidoptera insects as biomimetic objects are a classic type of biomimetic insect flapping-wing aircraft, commonly known as biomimetic butterflies. They differ from other types of biomimetic insect flapping-wing aircraft due to their larger wingspan and lower flapping frequency. A representative example is Festo's eMotionButterflies. Its mechanical structure is quite simple, with the fore-wings and hindwings on the same side slightly overlapping, simulating the amplexi form wing coupling device found in natural butterflies. This design creates an air gap during the flapping motion, thereby achieving favorable aerodynamic characteristics. Using a similar driving structure, [PERSON] [12] designed two flapping-wing aircraft. It has insufficient lift due to its lower flapping frequency. [PERSON] [13] made a flapping-wing aircraft named UST Butterfly-S, which achieves turning by pulling ropes to change the area of the left and right fore-wings. [PERSON] and others [14] developed a low-cost biomimetic butterfly, which uses sensors to collect flight data and explores better flapping frequency and amplitude ranges. [PERSON] and others [15; 16] paid more attention to the posture control mechanism during flapping. They designed a biomimetic flapping-wing aircraft with a new slider-crank mechanism, which uses elastic links to store and release energy to flapping the wings, thus realizing the lead-lag motion.