A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 8 Issue 1
Jan.  2021

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 6.171, Top 11% (SCI Q1)
    CiteScore: 11.2, Top 5% (Q1)
    Google Scholar h5-index: 51, TOP 8
Turn off MathJax
Article Contents
Wei He, Xinxing Mu, Liang Zhang and Yao Zou, "Modeling and Trajectory Tracking Control for Flapping-Wing Micro Aerial Vehicles," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 148-156, Jan. 2021. doi: 10.1109/JAS.2020.1003417
Citation: Wei He, Xinxing Mu, Liang Zhang and Yao Zou, "Modeling and Trajectory Tracking Control for Flapping-Wing Micro Aerial Vehicles," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 148-156, Jan. 2021. doi: 10.1109/JAS.2020.1003417

Modeling and Trajectory Tracking Control for Flapping-Wing Micro Aerial Vehicles

doi: 10.1109/JAS.2020.1003417
Funds:  This work was supported in part by the National Natural Science Foundation of China (61933001, 62061160371), Joint Funds of Equipment Pre-Research and Ministry of Education of China (6141A02033339), and Beijing Top Discipline for Artificial Intelligent Science and Engineering, University of Science and Technology Beijing
More Information
  • This paper studies the trajectory tracking problem of flapping-wing micro aerial vehicles (FWMAVs) in the longitudinal plane. First of all, the kinematics and dynamics of the FWMAV are established, wherein the aerodynamic force and torque generated by flapping wings and the tail wing are explicitly formulated with respect to the flapping frequency of the wings and the degree of tail wing inclination. To achieve autonomous tracking, an adaptive control scheme is proposed under the hierarchical framework. Specifically, a bounded position controller with hyperbolic tangent functions is designed to produce the desired aerodynamic force, and a pitch command is extracted from the designed position controller. Next, an adaptive attitude controller is designed to track the extracted pitch command, where a radial basis function neural network is introduced to approximate the unknown aerodynamic perturbation torque. Finally, the flapping frequency of the wings and the degree of tail wing inclination are calculated from the designed position and attitude controllers, respectively. In terms of Lyapunov’s direct method, it is shown that the tracking errors are bounded and ultimately converge to a small neighborhood around the origin. Simulations are carried out to verify the effectiveness of the proposed control scheme.


  • loading
  • [1]
    C. Li, Q. Shi, Z. H. Gao, M. C. Ma, Q. Huang, H. Ishii, A. Takanishi, and T. Fukuda, “Bioinspired phase-shift turning action for a biomimetic robot,” IEEE/ASME Trans. Mechatron., vol. 25, no. 1, pp. 84–94, Feb. 2020. doi: 10.1109/TMECH.2019.2959375
    Q. Shi, C. Li, K. Li, Q. Huang, H. Ishii, A. Takanishi, and T. Fukuda, “A modified robotic rat to study rat-like pitch and yaw movements,” IEEE/ASME Trans. Mechatron., vol. 23, no. 5, pp. 2448–2458, Oct. 2018. doi: 10.1109/TMECH.2018.2863269
    W. He, T. T. Wang, X. Y. He, L. J. Yang, and O. Kaynak, “Dynamical modeling and boundary vibration control of a rigid-flexible wing system,” IEEE/ASME Trans. Mechatron., 2020. DOI: 10.1109/TMECH.2020.2987963
    N. T. Jafferis, E. F. Helbling, M. Karpelson, and R. J. Wood, “Untethered flight of an insect-sized flapping-wing microscale aerial vehicle,” Nature, vol. 570, no. 7762, pp. 491–495, Jun. 2019. doi: 10.1038/s41586-019-1322-0
    X. B. Ji, X. C. Liu, V. Cacucciolo, M. Imboden, Y. Civet, A. El Haitami, S. Cantin, Y. Perriard, and H. Shea, “An autonomous untethered fast soft robotic insect driven by low-voltage dielectric elastomer actuators,” Science Robotics, vol. 4, no. 37, pp. eaaz6451, Dec. 2019. doi: 10.1126/scirobotics.aaz6451
    G. Dimitriadis, “Finite wings,” in Introduction to Nonlinear Aeroelasticity, G. Dimitriadis. Chichester, UK: John Wiley & Sons, Ltd, 2017, pp. 503–553.
    D. Mackenzie, “A flapping of wings,” Science, vol. 335, no. 6075, pp. 1430–1433, Mar. 2012. doi: 10.1126/science.335.6075.1430
    B. Zhu, J. Z. Zhu, and Q. W. Chen, “A bio-inspired flight control strategy for a tail-sitter unmanned aerial vehicle,” Sci. China Inform. Sci., vol. 63, no. 7, pp. 170203, May 2020. doi: 10.1007/s11432-019-2764-1
    H. Y. Li, L. J. Wang, H. P. Du, and A. Boulkroune, “Adaptive fuzzy backstepping tracking control for strict-feedback systems with input delay,” IEEE Trans. Fuzzy Syst., vol. 25, no. 3, pp. 642–652, Jun. 2017. doi: 10.1109/TFUZZ.2016.2567457
    M. Keennon, K. Klingebiel, H. Won, and A. Andriukov, “Tailless flapping wing propulsion and control development for the nano hummingbird micro air vehicle,” in The American Helicopter Society 68th Annual Forum, Fort Worth, USA, 2012.
    A. Ramezani, S. J. Chung, and S. Hutchinson, “A biomimetic robotic platform to study flight specializations of bats,” Sci. Robot., vol. 2, no. 3, pp. eaal2505, Feb. 2017. doi: 10.1126/scirobotics.aal2505
    B. Wong, “Lab bench-new robot designs are for the birds,” Electronic Design, vol. 59, no. 6, pp. 14, 2011.
    D. S. Farner, “Dimensional relationships for flying animals. Crawford H. Greenewalt,” Auk, vol. 78, no. 4, pp. 653–654, Oct. 1961.
    Q. V. Nguyen, W. L. Chan, and M. Debiasi, “Hybrid design and performance tests of a hovering insect-inspired flapping-wing micro aerial vehicle,” J. Bionic Eng., vol. 13, no. 2, pp. 235–248, Jun. 2016. doi: 10.1016/S1672-6529(16)60297-4
    A. Hedenström, “Aerodynamics, evolution and ecology of avian flight,” Trends Ecol. Evol., vol. 17, no. 9, pp. 415–422, Sep. 2002. doi: 10.1016/S0169-5347(02)02568-5
    B. W. Tobalske, T. L. Hedrick, K. P. Dial, and A. A. Biewener, “Comparative power curves in bird flight,” Nature, vol. 421, no. 6921, pp. 363–366, Jan. 2003. doi: 10.1038/nature01284
    C. G. Yang, C. Z. Chen, N. Wang, Z. J. Ju, J. Fu, and M. Wang, “Biologically inspired motion modeling and neural control for robot learning from demonstrations,” IEEE Trans. Cogn. Dev. Syst., vol. 11, no. 2, pp. 281–291, Jun. 2019. doi: 10.1109/TCDS.2018.2866477
    A. L. R. Thomas, “On the aerodynamics of birds’ tails,” Phil. Trans. R. Soc. Lond. B:Biol. Sci., vol. 340, no. 1294, pp. 361–380, Jun. 1993. doi: 10.1098/rstb.1993.0079
    G. P. He, T. T. Su, T. M. Jia, L. Zhao, and Q. L. Zhao, “Dynamics analysis and control of a bird scale underactuated flapping-wing vehicle,” IEEE Trans. Control Syst. Technol., vol. 28, no. 4, pp. 1233–1242, Jul. 2020. doi: 10.1109/TCST.2019.2908145
    A. R. Shanmugam and C. H. Sohn, “Systematic investigation of a flapping wing in inclined stroke-plane hovering,” J. Braz. Soc. Mech. Sci. Eng., vol. 41, no. 8, pp. 347, Jul. 2019. doi: 10.1007/s40430-019-1840-6
    G. Xie, A. Q. Shangguan, R. Fei, W. J. Ji, W. G. Ma, and X. H. Hei, “Motion trajectory prediction based on CNN-LSTM sequential model,” Sci. China Inform. Sciences, 2020. DOI: 10.1007/s11432-019-2761-y
    M. Bortolini, M. Faccio, F. G. Galizia, M. Gamberi, and F. Pilati, “Design, engineering and testing of an innovative adaptive automation assembly system,” Assembly Autom., vol. 40, no. 3, pp. 531–540, Feb. 2020. doi: 10.1108/AA-06-2019-0103
    H. Qiao, M. Wang, J. H. Su, S. X. Jia, and R. Li, “The concept of ‘attractive region in environment’ and its application in high-precision tasks with low-precision systems,” IEEE/ASME Trans. Mechatron., vol. 20, no. 5, pp. 2311–2327, Oct. 2015. doi: 10.1109/TMECH.2014.2375638
    W. He, S. X. Nie, T. T. Meng, and Y. J. Liu, “Modeling and vibration control for a moving beam with application in a drilling riser,” IEEE Trans. Control Syst. Technol., vol. 25, no. 3, pp. 1036–1043, May 2017. doi: 10.1109/TCST.2016.2577001
    S. Tijmons, C. De Wagter, B. Remes, and G. de Croon, “Autonomous door and corridor traversal with a 20-gram flapping wing MAV by onboard stereo vision,” Aerospace, vol. 5, no. 3, pp. 69, Jun. 2018. doi: 10.3390/aerospace5030069
    F. Fei, Z. Tu, J. Zhang, and X. Y. Deng, Learning extreme hummingbird maneuvers on flapping wing robots. 2019. [Online]. Available: arXiv: 1902.09626.
    W. He, Z. C. Yan, C. Y. Sun, and Y. Chen, “Adaptive neural network control of a flapping wing micro aerial vehicle with disturbance observer,” IEEE Trans. Cybernet., vol. 47, no. 10, pp. 3452–3465, Oct. 2017. doi: 10.1109/TCYB.2017.2720801
    H. V. Phan, T. Kang, and H. C. Park, “Design and stable flight of a 21g insect-like tailless flapping wing micro air vehicle with angular rates feedback control,” Bioinspir. Biomim., vol. 12, no. 3, pp. 036006, Apr. 2017. doi: 10.1088/1748-3190/aa65db
    A. Ailon, “Simple tracking controllers for autonomous VTOL aircraft with bounded inputs,” IEEE Trans. Autom. Control, vol. 55, no. 3, pp. 737–743, Mar. 2010. doi: 10.1109/TAC.2010.2040493
    V. A. Tucker, “Pitching equilibrium, wing span and tail span in a gliding Harris’ hawk, parabuteo unicinctus,” J. Exp. Biol., vol. 165, no. 4, pp. 21–41, Jan. 1992.
    I. Fenercioglu and O. Cetiner, “Effect of unequal flapping frequencies on flow structures,” Aerosp. Sci. Technol., vol. 35, pp. 39–53, May 2014. doi: 10.1016/j.ast.2014.02.007
    M. V. OL, J. D. Eldredge, and C. J. Wang, “High-amplitude pitch of a flat plate: an abstraction of perching and flapping,” Int. J. Micro Air Veh., vol. 1, no. 3, pp. 203–216, Nov. 2009. doi: 10.1260/175682909789996186
    J. H. Kim, C. Y. Park, S. M. Jun, D. K. Chung, H. C. Hwang, P. Beran and D. Mrozinski, “Flight test measurement and assessment of a flapping micro air vehicle,” Int. J. Aeronaut. Space Sci., vol. 13, no. 2, pp. 238–249, Jun. 2012. doi: 10.5139/IJASS.2012.13.2.238
    D. Mueller, H. A. Bruck, and S. K. Gupta, “Measurement of thrust and lift forces associated with drag of compliant flapping wing for micro air vehicles using a new test stand design,” Exp. Mech., vol. 50, no. 6, pp. 725–735, Jul. 2010. doi: 10.1007/s11340-009-9270-5
    A. Banazadeh and N. Taymourtash, “Adaptive attitude and position control of an insect-like flapping wing air vehicle,” Nonlinear Dyn., vol. 85, no. 1, pp. 47–66, Jul. 2016. doi: 10.1007/s11071-016-2666-8
    S. M. Nogar, A. Serrani, A. Gogulapati, J. J. McNamara, M. W. Oppenheimer, and D. B. Doman, “Design and evaluation of a model-based controller for flapping-wing micro air vehicles,” J. Guid. Control Dyn., vol. 41, no. 12, pp. 2513–2528, Dec. 2018. doi: 10.2514/1.G003293
    M. H. Dickinson, F. O. Lehmann, and S. P. Sane, “Wing rotation and the aerodynamic basis of insect flight,” Science, vol. 284, no. 5422, pp. 1954–1960, Jun. 1999. doi: 10.1126/science.284.5422.1954
    M. Pachter, J. J. D’Azzo, and A. W. Proud, “Tight formation flight control,” J. Guid. Control Dyn., vol. 24, no. 2, pp. 246–254, Mar.-Apr. 2001. doi: 10.2514/2.4735
    H. W. Lin, B. Zhao, D. R. Liu, and C. Alippi, “Data-based fault tolerant control for affine nonlinear systems through particle swarm optimized neural networks,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 954–964, Jul. 2020. doi: 10.1109/JAS.2020.1003225
    B. Xu, Y. X. Shou, J. Luo, H. Y. Pu, and Z. K. Shi, “Neural learning control of strict-feedback systems using disturbance observer,” IEEE Trans. Neural Netw. Learn. Syst., vol. 30, no. 5, pp. 1296–1307, May 2019. doi: 10.1109/TNNLS.2018.2862907
    S. L. Dai, S. D. He, M. Wang, and C. Z. Yuan, “Adaptive neural control of underactuated surface vessels with prescribed performance guarantees,” IEEE Trans. Neural Netw. Learn. Syst., vol. 30, no. 12, pp. 3686–3698, Dec. 2019. doi: 10.1109/TNNLS.2018.2876685
    J. Z. Zhang and C. X. Xu, “Trust region dogleg path algorithms for unconstrained minimization,” Ann. Oper. Res., vol. 87, pp. 407–418, Apr. 1999. doi: 10.1023/A:1018957708498
    H. J. Yang and J. K. Liu, “An adaptive RBF neural network control method for a class of nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 457–462, Mar. 2018. doi: 10.1109/JAS.2017.7510820
    B. Zhu and W. Huo, “Nonlinear control for a model-scaled helicopter with constraints on rotor thrust and fuselage attitude,” Acta Autom. Sinica, vol. 40, no. 11, pp. 2654–2664, Nov. 2014. doi: 10.1016/S1874-1029(14)60411-0


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(8)  / Tables(3)

    Article Metrics

    Article views (1100) PDF downloads(94) Cited by()


    • This paper formulates the aerodynamic force and torque generated by the actual flapping frequency of flapping wings and tail wing inclination when constructing the system model of the FWMAV. Moreover, a hierarchical framework is introduced to exploit the cascaded structure of the established model for control scheme development.
    • This paper considers the unknown aerodynamic perturbation of flapping wings on the torque generated by the tail wing. A radial basis function neural network is introduced to estimate and compensate for this perturbation and for improving tracking accuracy.
    • This paper designs a bounded position controller with hyperbolic tangent functions to guarantee a bounded aerodynamic force. Also, this design effectively alleviates the coupling between the closed-loop position and attitude error systems, and thus facilitates the stability analysis greatly.


    DownLoad:  Full-Size Img  PowerPoint