面向撲翼飛行機器人的飛行控制研究進展綜述

汪婷婷; 何修宇; 鄒堯; 付強; 賀威

doi:10.13374/j.issn2095-9389.2022.12.24.001

面向撲翼飛行機器人的飛行控制研究進展綜述

doi: 10.13374/j.issn2095-9389.2022.12.24.001

汪婷婷^{1, 2, 3},
何修宇^{1, 2, 3},
鄒堯^{1, 2, 3},
付強^{1, 2, 3},
賀威^{1, 2, 3, ,}

1.
北京科技大學智能科學與技術學院，北京 100083
2.
北京科技大學人工智能研究院，北京 100083
3.
北京科技大學智能仿生無人系統教育部重點實驗室，北京 100083

基金項目: 國家自然科學基金資助項目（62225304, 61933001）；北京市自然科學基金資助項目（JQ20026）；北京科技大學中央高校基本科研業務費專項資金資助項目（FRF-IDRY-21-030, FRF-TP-22-003C2）

詳細信息

通訊作者:
E-mail: weihe@ieee.org

中圖分類號: TP242.6
計量
- 文章訪問數: 288
- HTML全文瀏覽量: 63
- PDF下載量: 43
- 被引次數: 0
出版歷程
- 收稿日期: 2022-12-24
- 網絡出版日期: 2023-02-11
- 刊出日期: 2023-10-25

Research progress on the flight control of flapping-wing aerial vehicles

WANG Tingting^{1, 2, 3},
HE Xiuyu^{1, 2, 3},
ZOU Yao^{1, 2, 3},
FU Qiang^{1, 2, 3},
HE Wei^{1, 2, 3
, ,}

1.
School of Intelligence Science and Technology, University of Science and Technology Beijing, Beijing 100083, China
2.
Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing 100083, China
3.
Key Laboratory of Intelligent Bionic Unmanned Systems (Ministry of Education), University of Science and Technology Beijing, Beijing 100083, China

More Information

Corresponding author: E-mail: weihe@ieee.org

摘要

摘要: 近十年來，研究人員從飛行生物的飛行機理著手分析，對撲翼飛行機器人的姿態控制、位置控制設計以及系統穩定性分析展開了深入研究，基于魯棒控制、神經網絡等技術，提出了諸多控制方法實現撲翼飛行機器人的自主飛行，其中，姿態控制通過自適應等控制器并結合線性化方法來實現，位置控制則通過搭建層級架構的控制器等方法來完成，并通過設計擾動觀測器等來處理系統的不確定性，以提高系統穩定性能。通過對相關研究工作進行總結，可以看出目前撲翼飛行機器人的飛行控制研究仍大多處于理論階段，還需要進一步結合工程應用中的實際需求，推進撲翼飛行機器人的應用與推廣。最后，探討了撲翼飛行機器人飛行控制未來的研究方向。
- 撲翼飛行機器人 /
- 生物飛行原理 /
- 自主飛行控制 /
- 姿態控制 /
- 人工智能
Abstract: In nature, flying creatures flap their wings to generate lift, which is necessary for flight. Most birds change flight patterns by moving their wings using their wing muscles and adjusting their tail states. Insects, which are without tails, can achieve maneuverable flight using their chest and abdomen muscles and other structures such as hind wings. Owing to high mobility and high energy efficiency, researchers have developed various flapping-wing aerial vehicles according to the bionic principle to improve flight performance. However, a flapping-wing aerial vehicle is a nonlinear and time-variable system. The low Reynolds number and unsteady eddy are important characteristics of the flapping-wing aerial vehicle, and the values are different from those of traditional aircraft. The Reynolds number of the traditional aircraft is larger; thus, the air viscosity is small enough to be ignored. However, the air viscosity of the bionic flapping-wing aerial vehicle is high at low Reynolds number conditions. Adopting a conventional aerodynamic configuration will result in insufficient lift. In addition, the traditional aerodynamics theory cannot explain the high lift of the flapping-wing aerial vehicles, and the mature technologies in traditional aircraft design cannot be directly applied owing to the low Reynolds number. Owing to the periodic movement of the flapping wing, it is difficult for researchers to accurately analyze the aerodynamic model. The autonomous flight of a flapping-wing aerial vehicle is limited by several challenges. To solve this problem, researchers have studied the flight principle of birds and insects. Moreover, the attitude control, position control, and stability analysis of flapping-wing aerial vehicles have been studied. Several control strategies based on robust control, neural networks, and other methods have been proposed to realize the autonomous flight of flapping-wing aerial vehicles. Researchers have also adopted control methods such as adaptive controllers combined with linearization techniques to control attitude. Position control has been achieved using a hierarchical controller and other approaches. In addition, perturbation observation is used to deal with the uncertainty of the system to improve stability. In this paper, the flight control strategies of flapping-wing aerial vehicles of different scales are reviewed. The current research on the flight control of the flapping-wing aerial vehicle is mostly in the prototype phase. Most of these theories have not been verified in actual flight. Therefore, the flight control theory needs to be combined with actual missions to promote the application of the flapping-wing aerial vehicle. Finally, the future trend of the flight control of the flapping-wing aerial vehicle is highlighted.
- flapping-wing aerial vehicles /
- flight principle /
- autonomous flight /
- attitude control /
- artificial intelligence

HTML全文

圖 1 鴿子的一對飛羽間的反作用力隨分離距離的變化^[35]

Figure 1. Change in the opposing force between the two flight feathers of a pigeon with separation distance^[35]

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圖 2 蝴蝶的二維模型圖^[38]

Figure 2. Two-dimensional butterfly model^[38]

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圖 3 撲翼飛行機器人三維氣動力模型^[42]

Figure 3. Three-dimensional aerodynamic model of the flapping-wing aerial vehicle^[42]

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圖 4 仿鳥撲翼飛行機器人的自主著陸^[50]

Figure 4. Autonomous landing of a bird-like flapping-wing aerial vehicle^[50]

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圖 5 撲翼飛行機器人在完成快速躲避動作時的狀態^[59]

Figure 5. Emergency avoidance of a flapping-wing aerial vehicle^[59]

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圖 6 撲翼飛行機器人自主巡航示意圖^[65]

Figure 6. Autonomous cruise of a flapping-wing aerial vehicle^[65]

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圖 7 微型撲翼飛行機器人系統. (a)實物樣機; (b) 微型撲翼飛行機器人關鍵部件以及撲翼旋轉軸示意圖; (c) 滾轉力矩產生示意圖; (d) 俯仰力矩產生示意圖; (e) 偏航力矩產生示意圖^[74]

Figure 7. Flapping-wing microaerial vehicle: (a) the prototype; (b) critical components of the flapping-wing aerial vehicle; (c) rolling moment; (d) pitching moment; (e) yaw moment^[74]

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圖 8 仿生快速規避運動分解，其中機翼顏色表示不同大小的推力命令^[76]

Figure 8. Decomposition of bionic quick avoidance; wing color represents thrust value^[76]

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圖 9 微型撲翼飛行機器人動力學分析. (a) 機體與左翼三維視圖; (b) 撲翼行程平面俯視圖^[79]

Figure 9. Kinetics of the flapping-wing microaerial vehicle: (a) three-dimensional view of the body and the left wing; (b) top view of the stroke plane^[79]

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圖 10 處于狹窄通道中的微型撲翼飛行機器人^[83]

Figure 10. Flapping-wing microaerial vehicle in a narrow passage^[83]

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圖 11 利用光流和運動模型估計姿態. (a) 基于光流的飛行姿態控制方法; (b) 不穩定飛行系統的推力矢量運動模型; (c)所提出的姿態估計方法導致系統輕微的姿態振蕩^[87]

Figure 11. Attitude estimation using an optical flow and motion model: (a) attitude control based on optical flow; (b) thrust-vectoring motion model of an unstable system; (c) slight oscillation caused by the proposed attitude estimation method^[87]

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參考文獻(95)

[1]	Muijres F T, Elzinga M J, Melis J M, et al. Flies evade looming targets by executing rapid visually directed banked turns. Science, 2014, 344(6180): 172 doi: 10.1126/science.1248955
[2]	MacKenzie D. A flapping of wings. Science, 2012, 335(6075): 1430 doi: 10.1126/science.335.6075.1430
[3]	Sun M. Insect flight dynamics: Stability and control. Rev Mod Phys, 2014, 86(2): 615 doi: 10.1103/RevModPhys.86.615
[4]	Liang S R, Song B F, Yang W Q, et al. Experimental study on dynamic modeling of flapping wing micro aerial vehicle. Lect Notes Comput Sci, 2017: 602
[5]	Liu J T. Design and Flight Control of a Flapping-Wing Flying Robot with Airfoil [Dissertation]. Harbin: Harbin Institute of Technology, 2018 劉軍濤. 一種帶翼型撲翼飛行機器人設計及飛行控制研究[學位論文]. 哈爾濱: 哈爾濱工業大學, 2018
[6]	Zou Y. Design, Manufacture and Test of Insect-like Flapping-Wing Micro Air Vehicle [Dissertation]. Shanghai: Shanghai Jiao Tong University, 2018 鄒陽. 仿昆蟲撲翼微飛行器的設計、制造與測試研究[學位論文]. 上海: 上海交通大學, 2018
[7]	Graule M A, Chirarattananon P, Fuller S B, et al. Perching and takeoff of a robotic insect on overhangs using switchable electrostatic adhesion. Science, 2016, 352(6288): 978 doi: 10.1126/science.aaf1092
[8]	Prum R O. Development and evolutionary origin of feathers. J Exp Zool, 1999, 285(4): 291 doi: 10.1002/(SICI)1097-010X(19991215)285:4<291::AID-JEZ1>3.0.CO;2-9
[9]	Chin D D, Matloff L Y, Stowers A K, et al. Inspiration for wing design: How forelimb specialization enables active flight in modern vertebrates. J R Soc Interface, 2017, 14(131): 20170240 doi: 10.1098/rsif.2017.0240
[10]	Yu M K, Wu P, Widelitz R B, et al. The morphogenesis of feathers. Nature, 2002, 420(6913): 308 doi: 10.1038/nature01196
[11]	Zhang F L, Jiang L, Wang S T. Repairable cascaded slide-lock system endows bird feathers with tear-resistance and superdurability. Proc Natl Acad Sci USA, 2018, 115(40): 10046 doi: 10.1073/pnas.1808293115
[12]	Sullivan T N, Chon M, Ramachandramoorthy R, et al. Reversible attachment with tailored permeability: The feather vane and bioinspired designs. Adv Funct Mater, 2017, 27(39): 1702954 doi: 10.1002/adfm.201702954
[13]	Ravi S, Crall J, Fisher A, et al. Rolling with the flow: Bumblebees flying in unsteady wakes. J Exp Biol, 2013, 216(22): 4299
[14]	Sun M, Liu Y P, Wang J K. Dynamic flight stability of hovering insect: Theoretical analysis and numerical simulation. Acta Aerodynamica Sinica, 2008, 26(z1): 6 孫茂, 劉彥鵬, 王濟康. 昆蟲懸停飛行的動穩定性: 理論分析與數值模擬. 空氣動力學學報, 2008, 26(z1):6
[15]	Ellington C P, van den Berg C, Willmott A P, et al. Leading-edge vortices in insect flight. Nature, 1996, 384(6610): 626 doi: 10.1038/384626a0
[16]	Sun M, Tang J. Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion. J Exp Biol, 2002, 205(Pt 1): 55
[17]	Beatus T, Guckenheimer J M, Cohen I. Controlling roll perturbations in fruit flies. J R Soc Interface, 2015, 12(105): 20150075 doi: 10.1098/rsif.2015.0075
[18]	Maxworthy T. The formation and maintenance of a leading-edge vortex during the forward motion of an animal wing. J Fluid Mech, 2007, 587: 471 doi: 10.1017/S0022112007007616
[19]	Ramezani A, Chung S J, Hutchinson S. A biomimetic robotic platform to study flight specializations of bats. Sci Robot, 2017, 2(3): eaal2505 doi: 10.1126/scirobotics.aal2505
[20]	Keennon M, Klingebiel K, Won H. Development of the nano hummingbird: A tailless flapping wing micro air vehicle // 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Nashville, 2012: 588
[21]	Gerdes J, Holness A, Perez-Rosado A, et al. Robo raven: A flapping-wing air vehicle with highly compliant and independently controlled wings. Soft Robotics, 2014, 1(4): 275 doi: 10.1089/soro.2014.0019
[22]	Chen Y F, Wang H Q, Helbling E F, et al. A biologically inspired, flapping-wing, hybrid aerial-aquatic microrobot. Sci Robot, 2017, 2(11): eaao5619 doi: 10.1126/scirobotics.aao5619
[23]	Yang W Q, Wang L G, Song B F. Dove: A biomimetic flapping-wing micro air vehicle. Int J Micro Air Veh, 2018, 10(1): 70 doi: 10.1177/1756829317734837
[24]	Chi P C, Zhang W P, Chen W Y, et al. Design and fabrication of an SU-8 biomimetic flapping-wing micro air vehicle by MEMS technology. Robot, 2011, 33(3): 366 doi: 10.3724/SP.J.1218.2011.00366 遲鵬程, 張衛平, 陳文元, 等. 基于MEMS技術的SU-8仿昆蟲微撲翼飛行器設計及制作. 機器人, 2011, 33(3):366 doi: 10.3724/SP.J.1218.2011.00366
[25]	Ortega-Jimenez V M, Greeter J S M, Mittal R, et al. Hawkmoth flight stability in turbulent vortex streets. J Exp Biol, 2013, 216(Pt 24): 4567
[26]	Seelig J D, Jayaraman V. Feature detection and orientation tuning in the Drosophila central complex. Nature, 2013, 503(7475): 262 doi: 10.1038/nature12601
[27]	Dyhr J P, Morgansen K A, Daniel T L, et al. Flexible strategies for flight control: An active role for the abdomen. J Exp Biol, 2013, 216(Pt 9): 1523
[28]	Vance J T, Faruque I, Humbert J S. Kinematic strategies for mitigating gust perturbations in insects. Bioinspir Biomim, 2013, 8(1): 016004 doi: 10.1088/1748-3182/8/1/016004
[29]	Xu N, Sun M. Lateral dynamic flight stability of a model bumblebee in hovering and forward flight. J Theor Biol, 2013, 319: 102 doi: 10.1016/j.jtbi.2012.11.033
[30]	Pennycuick C. The flight of birds and other animals. Aerospace, 2015, 2(3): 505 doi: 10.3390/aerospace2030505
[31]	Lentink D, Müller U K, Stamhuis E J, et al. How swifts control their glide performance with morphing wings. Nature, 2007, 446(7139): 1082 doi: 10.1038/nature05733
[32]	Crandell K E, Tobalske B W. Aerodynamics of tip-reversal upstroke in a revolving pigeon wing. J Exp Biol, 2011, 214: 1867 doi: 10.1242/jeb.051342
[33]	Hieronymus T L. Flight feather attachment in rock pigeons (Columba livia): Covert feathers and smooth muscle coordinate a morphing wing. J Anat, 2016, 229(5): 631 doi: 10.1111/joa.12511
[34]	Stowers A K, Matloff L Y, Lentink D. How pigeons couple three-dimensional elbow and wrist motion to morph their wings. J R Soc Interface, 2017, 14(133): 20170224 doi: 10.1098/rsif.2017.0224
[35]	Matloff L Y, Chang E, Feo T J, et al. How flight feathers stick together to form a continuous morphing wing. Science, 2020, 367(6475): 293 doi: 10.1126/science.aaz3358
[36]	Dickinson M H, Lehmann F O, Sane S P. Wing rotation and the aerodynamic basis of insect flight. Science, 1999, 284(5422): 1954 doi: 10.1126/science.284.5422.1954
[37]	Whitehead S C, Beatus T, Canale L, et al. Pitch perfect: How fruit flies control their body pitch angle. J Exp Biol, 2015, 218(21): 3508
[38]	Jayakumar J, Senda K, Yokoyama N. Control of pitch attitude by abdomen during forward flight of two-dimensional butterfly. J Aircr, 2018, 55(6): 2327 doi: 10.2514/1.C034767
[39]	Senda K, Obara T, Kitamura M, et al. Modeling and emergence of flapping flight of butterfly based on experimental measurements. Robotics Auton Syst, 2012, 60(5): 670 doi: 10.1016/j.robot.2011.12.007
[40]	Fu Q, Wang J, Gong L, et al. Obstacle avoidance of flapping-wing air vehicles based on optical flow and fuzzy control. Trans Nanjing Univ Aeronaut Astronaut, 2021, 38(2): 206
[41]	Pan E Z, Liu J T, Chen L R, et al. The embedded on-board controller and ground monitoring system of a flapping-wing aerial vehicle // 2018 IEEE International Conference on Real-time Computing and Robotics (RCAR). Kandima, 2019: 72
[42]	Wang T H, Jin S T, Hou Z S. Model free adaptive pitch control of a flapping wing micro aerial vehicle with input saturation // 2020 IEEE 9th Data Driven Control and Learning Systems Conference (DDCLS). Liuzhou, 2020: 627
[43]	Liu M, Ma D X, Li S. Neural dynamics for adaptive attitude tracking control of a flapping wing micro aerial vehicle. Neurocomputing, 2021, 456: 364 doi: 10.1016/j.neucom.2021.05.088
[44]	Li Q W, Duan H J. Modeling and adaptive control for flapping-wing micro aerial vehicle // International Conference on Intelligent Computing. Berlin, 2012: 269
[45]	Hu S B, Lu W H, Zhang X Y, et al. Adaptive fuzzy control of attitude of the flapping-wing micro air vehicles based on backstepping. Comput Simul, 2011, 28(5): 80 胡盛斌, 陸文華, 張興媛, 等. 微撲翼飛行機器人姿態反演自適應模糊控制. 計算機仿真, 2011, 28(5):80
[46]	Tijmons S, de Croon G C H E, Remes B D W, et al. Obstacle avoidance strategy using onboard stereo vision on a flapping wing MAV. IEEE Trans Robotics, 2017, 33(4): 858 doi: 10.1109/TRO.2017.2683530
[47]	Fu Q, Wang X Q, Zou Y, et al. A miniature video stabilization system for flapping-wing aerial vehicles. Guid Navigat Control, 2022, 2(1): 2250001 doi: 10.1142/S2737480722500017
[48]	Huang H F, He W, Fu Q, et al. A bio-inspired flapping-wing robot with cambered wings and its application in autonomous airdrop. IEEE/CAA J Autom Sin, 2022, 9(12): 2138 doi: 10.1109/JAS.2022.106040
[49]	Fu Q, Zhang S Y, Wang J B, et al. Indoor fixed-height control for bio-inspired flapping-wing aerial vehicles based on offboard monocular vision. Chin J Eng, 2020, 42(2): 249 付強, 張樹禹, 王久斌, 等. 基于外部單目視覺的仿生撲翼飛行器室內定高控制. 工程科學學報, 2020, 42(2):249
[50]	Liang S R, Song B F, Xuan J L. Active disturbance rejection attitude control for a bird-like flapping wing micro air vehicle during automatic landing. IEEE Access, 2020, 8: 171359 doi: 10.1109/ACCESS.2020.3024793
[51]	He W, Mu X X, Zhang L, et al. Modeling and trajectory tracking control for flapping-wing micro aerial vehicles. IEEE/CAA J Autom Sin, 2020, 8(1): 148
[52]	Rakotomamonjy T, Ouladsine M, Le Moing T. Longitudinal modelling and control of a flapping-wing micro aerial vehicle. Control Eng Pract, 2010, 18(7): 679 doi: 10.1016/j.conengprac.2010.02.002
[53]	Hsiao F Y, Yang L J, Lin S H, et al. Autopilots for ultra lightweight robotic birds: Automatic altitude control and system integration of a sub-10 g weight flapping-wing micro air vehicle. IEEE Control Syst Mag, 2012, 32(5): 35 doi: 10.1109/MCS.2012.2205475
[54]	Torres J Z, Davila J, Lozano R. Attitude and altitude control on board of an ornithopter // 2016 International Conference on Unmanned Aircraft Systems (ICUAS). Arlington, 2016: 1124
[55]	Qian C, Fang Y C. Adaptive tracking control of flapping wing micro-air vehicles with averaging theory. CAAI Trans Intell Technol, 2018, 3(1): 18 doi: 10.1049/trit.2018.0007
[56]	Chandrasekaran B K, Steck J. An adaptive flight control system for A flapping wing aircraft // 2018 AIAA Guidance, Navigation, and Control Conference. Kissimmee, 2018: 1
[57]	Chandrasekaran B K, Steck J E. An adaptive flight control system for a morphing flapping wing aircraft // Advances in Adaptive Control for Aerospace Systems I. Orlando, 2020: 1
[58]	Dietl J, Garcia E. Ornithopter control with periodic infinite horizon controllers. J Guid Control Dyn, 2011, 34(5): 1412 doi: 10.2514/1.52694
[59]	Fei F, Tu Z, Zhang J, et al. Learning extreme hummingbird maneuvers on flapping wing robots // 2019 International Conference on Robotics and Automation (ICRA). New York, 2019: 109
[60]	Xu W F, Pan E Z, Liu J T, et al. Flight control of a large-scale flapping-wing flying robotic bird: System development and flight experiment. Chin J Aeronaut, 2022, 35(2): 235 doi: 10.1016/j.cja.2021.03.009
[61]	Li Y H, Liu J T, Xu H, et al. An autonomous flight control strategy based on human-skill imitation for flapping-wing aerial vehicle // Intelligent Robotics and Applications: 14th International Conference. Yantai, 2021: 34
[62]	Ji B, Zhu Q L, Guo S J, et al. Design and experiment of a bionic flapping wing mechanism with flapping–twist–swing motion based on a single rotation. AIP Adv, 2020, 10(6): 065018 doi: 10.1063/5.0008792
[63]	He W, Liu S P, Huang H F, et al. System design and experiment of an independently driven bird-like flapping-wing robot. Control Theory Appl, 2022, 39(1): 12 賀威, 劉上平, 黃海豐, 等. 獨立驅動的仿鳥撲翼飛行機器人的系統設計與實驗. 控制理論與應用, 2022, 39(1):12
[64]	Paranjape A A, Chung S J, Kim J. Novel dihedral-based control of flapping-wing aircraft with application to perching. IEEE Trans Robotics, 2013, 29(5): 1071 doi: 10.1109/TRO.2013.2268947
[65]	Roberts L, Bruck H A, Gupta S K. Autonomous loitering control for a flapping wing miniature aerial vehicle with independent wing control // Proceedings of ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Buffalo, 2015: 1
[66]	Roberts L J, Bruck H A, Gupta S K. Modeling of dive maneuvers in flapping wing unmanned aerial vehicles // 2015 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR). West Lafayette, 2016: 1
[67]	Banazadeh A, Taymourtash N. Adaptive attitude and position control of an insect-like flapping wing air vehicle. Nonlinear Dyn, 2016, 85(1): 47 doi: 10.1007/s11071-016-2666-8
[68]	Qian C, Fang Y C, Li Y P. Neural network-based hybrid three-dimensional position control for a flapping wing aerial vehicle. IEEE Trans Cybern, 2022, PP(99): 1
[69]	Rifa? H L, Marchand N, Poulin-Vittrant G. Bounded control of an underactuated biomimetic aerial vehicle—Validation with robustness tests. Robotics Auton Syst, 2012, 60(9): 1165 doi: 10.1016/j.robot.2012.05.011
[70]	Mousavi S M S, Pourtakdoust S H. Improved neural adaptive control for nonlinear oscillatory dynamic of flapping wings. J Guid Control Dyn, 2023, 46(1): 97 doi: 10.2514/1.G006478
[71]	Li H, He G P, Bi F G. Sliding-mode adaptive attitude controller design for flapping-wing micro air vehicle. Aerosp Control Appl, 2018, 44(5): 81 李航, 何廣平, 畢富國. 一類微型撲翼飛行器的滑模自適應姿態控制. 空間控制技術與應用, 2018, 44(5):81
[72]	Wood R J. The first takeoff of a biologically inspired At-scale robotic insect. IEEE Trans Robotics, 2008, 24(2): 341 doi: 10.1109/TRO.2008.916997
[73]	Chen Y F, Zhao H C, Mao J, et al. Controlled flight of a microrobot powered by soft artificial muscles. Nature, 2019, 575(7782): 324 doi: 10.1038/s41586-019-1737-7
[74]	Chirarattananon P, Ma K Y, Wood R J. Adaptive control of a millimeter-scale flapping-wing robot. Bioinspir Biomim, 2014, 9(2): 025004 doi: 10.1088/1748-3182/9/2/025004
[75]	Phan H V, Aurecianus S, Kang T, et al. KUBeetle-S: an insect-like, tailless, hover-capable robot that can fly with a low-torque control mechanism. Int J Micro Air Veh, 2019, 11: 1
[76]	Karásek M, Muijres F T, Wagter C D, et al. A tailless aerial robotic flapper reveals that flies use torque coupling in rapid banked turns. Science, 2018, 361(6407): 1089 doi: 10.1126/science.aat0350
[77]	Jiao Z X, Wang L, Zhao L F, et al. Hover flight control of X-shaped flapping wing aircraft considering wing–tail interactions. Aerosp Sci Technol, 2021, 116: 106870 doi: 10.1016/j.ast.2021.106870
[78]	Dong W Z, Wang Z D. Indirect control and design of insect-like flapping-wing micro aerial vehicle // 2017 IEEE 3rd Information Technology and Mechatronics Engineering Conference (ITOEC). Chongqing, 2017: 1257
[79]	Deng X Y, Schenato L, Sastry S S. Flapping flight for biomimetic robotic insects: Part II-flight control design. IEEE Trans Robotics, 2006, 22(4): 789 doi: 10.1109/TRO.2006.875483
[80]	Helps T, Romero C, Taghavi M, et al. Liquid-amplified zipping actuators for micro-air vehicles with transmission-free flapping. Sci Robot, 2022, 7(63): eabi8189 doi: 10.1126/scirobotics.abi8189
[81]	Huang H F, He W, Zou Y, et al. System design and control of flapping-wing flying robot imitating butterfly based on wire-driven steering. Control Theory Appl, 2022, 39(7): 1203 黃海豐, 賀威, 鄒堯, 等. 基于線驅轉向的仿蝴蝶撲翼飛行機器人系統設計與控制. 控制理論與應用, 2022, 39(7):1203
[82]	Phan H V, Park H C. Mechanisms of collision recovery in flying beetles and flapping-wing robots. Science, 2020, 370(6521): 1214 doi: 10.1126/science.abd3285
[83]	Tu Z, Fei F, Zhang J, et al. Acting is seeing: Navigating tight space using flapping wings // 2019 International Conference on Robotics and Automation (ICRA). Montreal, 2019: 95
[84]	Peng K M, Lin F, Chen B M. Modeling and control analysis of a flapping-wing micro aerial vehicle // 2017 13th IEEE International Conference on Control & Automation (ICCA). Ohrid, 2017: 295
[85]	Ma K Y, Chirarattananon P, Fuller S B, et al. Controlled flight of a biologically inspired, insect-scale robot. Science, 2013, 340(6132): 603 doi: 10.1126/science.1231806
[86]	Fuller S B, Karpelson M, Censi A, et al. Controlling free flight of a robotic fly using an onboard vision sensor inspired by insect ocelli. J R Soc Interface, 2014, 11(97): 20140281 doi: 10.1098/rsif.2014.0281
[87]	Croon G C H E, Dupeyroux J J G, Wagter C D, et al. Accommodating unobservability to control flight attitude with optic flow. Nature, 2022, 610(7932): 485 doi: 10.1038/s41586-022-05182-2
[88]	He W, Sun C Y. Design of Flapping-wing Flying Robot System. Beijing: Chemical Industry Press, 2019 賀威, 孫長銀. 撲翼飛行機器人系統設計. 北京: 化學工業出版社, 2019
[89]	He W, Tang X Y, Wang T T, et al. Trajectory tracking control for a three-dimensional flexible wing. IEEE Trans Control Syst Technol, 2022, 30(5): 2243 doi: 10.1109/TCST.2021.3139087
[90]	Paranjape A A, Guan J Y, Chung S J, et al. PDE boundary control for flexible articulated wings on a robotic aircraft. IEEE Trans Robotics, 2013, 29(3): 625 doi: 10.1109/TRO.2013.2240711
[91]	Paranjape A A, Chung S J, Hilton H H, et al. Dynamics and performance of tailless micro aerial vehicle with flexible articulated wings. AIAA J, 2012, 50(5): 1177 doi: 10.2514/1.J051447
[92]	Lhachemi H, Saussié D, Zhu G C. Boundary feedback stabilization of a flexible wing model under unsteady aerodynamic loads. Automatica, 2018, 97: 73 doi: 10.1016/j.automatica.2018.07.029
[93]	Chen W Y, Zhang W P. Micro Flapping-wing Bionic Aircraft. Shanghai: Shanghai Jiao Tong University Press, 2010 陳文元, 張衛平. 微型撲翼式仿生飛行器. 上海: 上海交通大學出版社, 2010
[94]	Jafferis N T, Helbling E F, Karpelson M, et al. Untethered flight of an insect-sized flapping-wing microscale aerial vehicle. Nature, 2019, 570(7762): 491 doi: 10.1038/s41586-019-1322-0
[95]	Caetano J V, Percin M, Visser C C, et al. Tethered vs. free flight force determination of the DelFly II Flapping Wing Micro Air Vehicle // 2014 International Conference on Unmanned Aircraft Systems (ICUAS). Orlando, 2014: 942