Skip to main content
Search
Search
Quick Search anywhere
Quick Search fdjslkfh
Advanced search
Cart
Join AIAA Institution Login
Skip main navigationClose Drawer MenuOpen Drawer Menu
Journal of Guidance, Control, and Dynamics logo
Skip to article control options
No AccessFull-Length Paper

Time-Varying Model Identification of Flapping-Wing Vehicle Dynamics Using Flight Data

Published Online:16 Dec 2015https://doi.org/10.2514/1.G001470

Abstract

A time-varying model for the forward flight dynamics of a flapping-wing micro aerial vehicle is identified from free-flight optical tracking data. The model is validated and used to assess the validity of the widely applied time-scale separation assumption. Based on this assumption, each aerodynamic force and moment is formulated as a linear addition of decoupled time-averaged and time-varying submodels. The resulting aerodynamic models are incorporated in a set of linearized equations of motion, yielding a simulation-capable full dynamic model. The time-averaged component includes both the longitudinal and the lateral aerodynamics and is assumed to be linear. The time-varying component is modeled as a third-order Fourier series, which approximates the flapping dynamics effectively. Combining both components yields a more complete and realistic simulation. Results suggest that while in steady flight the time-scale separation assumption applies well during maneuvers the time-varying dynamics are not fully captured. More accurate modeling of flapping-wing flight during maneuvers may require considering coupling between the time scales.

References

  • [1] De Croon G. C. H. E., De Clercq K. M. E., Ruijsink R., Remes B. D. and De Wagter C., “Design, Aerodynamics, and Vision-Based Control of the DelFly,” International Journal of Micro Air Vehicles, Vol. 1, No. 2, 2009, pp. 71–97. doi:https://doi.org/10.1260/175682909789498288 CrossrefGoogle Scholar

  • [2] Keennon M., Klingebiel K. and 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, AIAA Paper  2012-0588, Jan. 2012. doi:https://doi.org/10.2514/6.2012-588 Google Scholar

  • [3] Wood R. J., “The First Takeoff of a Biologically Inspired At-Scale Robotic Insect,” IEEE Transactions on Robotics, Vol. 24, No. 2, 2008, pp. 341–347. doi:https://doi.org/10.1109/TRO.2008.916997 ITREAE 1552-3098 CrossrefGoogle Scholar

  • [4] Shyy W., Lian Y. and Tang J., Aerodynamics of Low Reynolds Number Flyers, Cambridge Aerospace Series, Cambridge Univ. Press, New York, 2008, pp. 101–158. doi:https://doi.org/10.1017/CBO9780511551154 CrossrefGoogle Scholar

  • [5] Ellington C. P., Van den Berg C., Willmott A. P. and Thomas A. L. R., “Leading-Edge Vortices in Insect Flight,” Nature, Vol. 384, No. 6610, 1996, pp. 626–630. doi:https://doi.org/10.1038/384626a0 CrossrefGoogle Scholar

  • [6] Nagai H., Isogai K., Fujimoto T. and Hayase T., “Experimental and Numerical Study of Forward Flight Aerodynamics of Insect Flapping Wing,” AIAA Journal, Vol. 47, No. 3, March 2009, pp. 730–742. doi:https://doi.org/10.2514/1.39462 AIAJAH 0001-1452 LinkGoogle Scholar

  • [7] Ramamurti R. and Sandberg W. C., “A Three-Dimensional Computational Study of the Aerodynamic Mechanisms of Insect Flight,” The Journal of Experimental Biology, Vol. 1518, No. 10, 2002, pp. 1507–1518. Google Scholar

  • [8] Ansari S. A., Zbikowski R. and Knowles K., “Non-Linear Unsteady Aerodynamic Model for Insect-Like Flapping Wings in the Hover. Part 2: Implementation and Validation,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 220, No. 3, Jan. 2006, pp. 169–186. doi:https://doi.org/10.1243/09544100JAERO50 CrossrefGoogle Scholar

  • [9] Deng X., Schenato L., Wu W. C. and Sastry S., “Flapping Flight for Biomimetic Robotic Insects: Part I—System Modeling,” IEEE Transactions on Robotics, Vol. 22, No. 4, 2006, pp. 776–788. doi:https://doi.org/10.1109/TRO.2006.875480 ITREAE 1552-3098 CrossrefGoogle Scholar

  • [10] DeLaurier J. D., “An Aerodynamic Model for Flapping-Wing Flight,” The Aeronautical Journal of the Royal Aeronautical Society, Vol. 97, No. 964, 1993, pp. 125–130. Google Scholar

  • [11] Sane S. P., “The Aerodynamics of Insect Flight,” Journal of Experimental Biology, Vol. 206, No. 23, 2003, pp. 4191–4208. doi:https://doi.org/10.1242/jeb.00663 JEBIAM 0022-0949 CrossrefGoogle Scholar

  • [12] Berman G. J. and Wang Z. J., “Energy-Minimizing Kinematics in Hovering Insect Flight,” Journal of Fluid Mechanics, Vol. 582, July 2007, pp. 153–168. doi:https://doi.org/10.1017/S0022112007006209 JFLSA7 0022-1120 CrossrefGoogle Scholar

  • [13] Sigthorsson D., Oppenheimer M. W. and Doman D. B., “Flapping Wing Micro Air Vehicle Aerodynamic Modeling Including Flapping and Rigid Body Velocity,” 50th AIAA Aerospace Sciences Meeting, AIAA Paper  2012-0026, Jan. 2012. doi:https://doi.org/10.2514/6.2012-26 LinkGoogle Scholar

  • [14] Grauer J., Ulrich E., Hubbard J. E., Pines D. and Humbert J. S., “Testing and System Identification of an Ornithopter in Longitudinal Flight,” Journal of Aircraft, Vol. 48, No. 2, March 2011, pp. 660–667. doi:https://doi.org/10.2514/1.C031208 LinkGoogle Scholar

  • [15] Caetano J. V., De Visser C. C., Remes B. D., De Wagter C., Van Kampen E.-J. and Mulder M., “Controlled Flight Maneuvers of a Flapping Wing Micro Air Vehicle: A Step Towards the Delfly II Identification,” AIAA Atmospheric Flight Mechanics Conference, AIAA Paper  2013-4843, Aug. 2013. doi:https://doi.org/10.2514/6.2013-4843 LinkGoogle Scholar

  • [16] Gogulapati A. and Friedmann P. P., “Approximate Aerodynamic and Aeroelastic Modeling of Flapping Wings in Hover and Forward Flight,” 52nd AIAA/ASME/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA Paper  2011-2008, April 2011. LinkGoogle Scholar

  • [17] Buler W., Loroch L. and Sibilski K., “Modeling and Simulation of the Nonlinear Dynamic Behavior of a Flapping Wings Micro-Aerial-Vehicle,” 42nd AIAA Aerospace Sciences Meeting, AIAA Paper  2004-0541, Jan. 2004. doi:https://doi.org/10.2514/6.2004-541 Google Scholar

  • [18] Lasek M. and Sibilski K., “Modelling and Simulation of Flapping Wing Control for a Micromechanical Flying Insect (Entomopter),” AIAA Modeling and Simulation Technologies Conference, AIAA Paper  2002-4973, 2002. doi:https://doi.org/10.2514/6.2002-4973 LinkGoogle Scholar

  • [19] Bolender M. A., “Rigid Multi-Body Equations-of-Motion for Flapping Wing MAVs Using Kane’s Equations,” AIAA Guidance, Navigation, and Control Conference, AIAA Paper  2009-6158, Aug. 2009. doi:https://doi.org/10.2514/6.2009-6158 LinkGoogle Scholar

  • [20] Grauer J. A. and Hubbard J. E., “Multibody Model of an Ornithopter,” Journal of Guidance, Control, and Dynamics, Vol. 32, No. 5, Sept. 2009, pp. 1675–1679. doi:https://doi.org/10.2514/1.43177 JGCODS 0731-5090 LinkGoogle Scholar

  • [21] Gebert G. and Evers J., “Equations of Motion for Flapping Flight,” AIAA Atmospheric Flight Mechanics Conference, AIAA Paper  2002-4872, 2002. doi:https://doi.org/10.2514/6.2002-4872 LinkGoogle Scholar

  • [22] Orlowski C. T. and Girard A. R., “Modeling and Simulation of Nonlinear Dynamics of Flapping Wing Micro Air Vehicles,” AIAA Journal, Vol. 49, No. 5, May 2011, pp. 969–981. doi:https://doi.org/10.2514/1.J050649 AIAJAH 0001-1452 LinkGoogle Scholar

  • [23] Taylor G. K. and Thomas A. L. R., “Dynamic Flight Stability in the Desert Locust Schistocerca Gregaria,” Journal of Experimental Biology, Vol. 206, No. 16, Aug. 2003, pp. 2803–2829. doi: https://doi.org/10.1242/jeb.00501 JEBIAM 0022-0949 CrossrefGoogle Scholar

  • [24] Caetano J. V., Weehuizen M. B., De Visser C. C., De Croon G. C. H. E. and De Wagter C., “Rigid vs. Flapping: The Effects of Kinematic Formulations in Force Determination of a Free Flying Flapping Wing Micro Air Vehicle,” International Conference on Unmanned Aircraft Systems, IEEE Publ., Piscataway, NJ, May 2014, pp. 949–959. doi:https://doi.org/10.1109/ICUAS.2014.6842345 Google Scholar

  • [25] Julian R. C., Rose C. J., Hu H. and Fearing R. S., “Cooperative Control and Modeling for Narrow Passage Traversal with an Ornithopter MAV and Lightweight Ground Station,” Proceedings of the 2013 International Conference on Autonomous Agents and Multi-Agent Systems, International Foundation for Autonomous Agents and Multiagent Systems, St. Paul, MN, May 2013, pp. 103–110. doi:https://doi.org/10.1.1.309.9545 Google Scholar

  • [26] Sun M. and Xiong Y., “Dynamic Flight Stability of a Hovering Bumblebee,” The Journal of Experimental Biology, Vol. 208, No. 3, Feb. 2005, pp. 447–459. doi:https://doi.org/10.1242/jeb.01407 CrossrefGoogle Scholar

  • [27] Faruque I. and Sean Humbert J., “Dipteran Insect Flight Dynamics. Part 1: Longitudinal Motion About Hover,” Journal of Theoretical Biology, Vol. 264, No. 2, May 2010, pp. 538–552. doi:https://doi.org/10.1016/j.jtbi.2010.02.018 JTBIAP 0022-5193 CrossrefGoogle Scholar

  • [28] Rifai H., Marchand N. and Poulin G., “Bounded Control of a Flapping Wing Micro Drone in Three Dimensions,” IEEE International Conference on Robotics and Automation, IEEE Publ., Piscataway, NJ, 2008, pp. 164–169. doi:https://doi.org/10.1109/ROBOT.2008.4543203 Google Scholar

  • [29] Khan Z. A. and Agrawal S. K., “Control of Longitudinal Flight Dynamics of a Flapping-Wing Micro Air Vehicle Using Time-Averaged Model and Differential Flatness Based Controller,” Proceedings of the 2007 American Control Conference, IEEE Publ., Piscataway, NJ, 2007, pp. 5284–5289. doi:https://doi.org/10.1109/ACC.2007.4283052 Google Scholar

  • [30] Schenato L., Campolo D. and Sastry S., “Controllability Issues in Flapping Flight for Biomimetic Micro Aerial Vehicles (MAVs),” Proceedings IEEE Conference Decision Control, Vol. 6, IEEE Publ., Piscataway, NJ, Dec. 2003, pp. 6441–6447. doi:https://doi.org/10.1.1.216.7484 Google Scholar

  • [31] Taha H. E., Woolsey C. A. and Hajj M. R., “A Geometric Control Approach for the Longitudinal Flight Stability of Hovering Insects/FWMAVs,” AIAA Atmospheric Flight Mechanics Conference, AIAA Paper  2015-1552, Jan. 2015. doi:https://doi.org/10.2514/6.2015-1552 LinkGoogle Scholar

  • [32] Taha H. E., Nayfeh A. H. and Hajj M. R., “Effect of the Aerodynamic-Induced Parametric Excitation on the Longitudinal Stability of Hovering MAVs/Insects,” Nonlinear Dynamics, Vol. 78, No. 4, Aug. 2014, pp. 2399–2408. doi:https://doi.org/10.1007/s11071-014-1596-6 NODYES 0924-090X CrossrefGoogle Scholar

  • [33] Taha H. E., Tahmasian S., Woolsey C. A., Nayfeh A. H. and Hajj M. R., “The Need for Higher-Order Averaging in the Stability Analysis of Hovering, Flapping-Wing Flight,” Bioinspiration & Biomimetics, Vol. 10, No. 1, 2015, Paper 016002. doi:https://doi.org/10.1088/1748-3190/10/1/016002 CrossrefGoogle Scholar

  • [34] Dietl J., Herrmann T., Reich G. and Garcia E., “Dynamic Modeling, Testing, and Stability Analysis of an Ornithoptic Blimp,” Journal of Bionic Engineering, Vol. 8, No. 4, Dec. 2011, pp. 375–386. doi:https://doi.org/10.1016/S1672-6529(11)60043-7 1672-6529 CrossrefGoogle Scholar

  • [35] Caetano J. V., De Visser C. C., De Croon G. C. H. E., Remes B. D., De Wagter C. and Mulder M., “Linear Aerodynamic Model Identification of a Flapping Wing MAV Based on Flight Test Data,” International Journal of Micro Air Vehicles, Vol. 5, No. 4, 2013, pp. 273–286. doi:https://doi.org/10.1260/1756-8293.5.4.273 CrossrefGoogle Scholar

  • [36] Mulder J. A., Chu Q. P., Sridhar J. K., Breeman J. H. and Laban M., “Non-Linear Aircraft Flight Path Reconstruction Review and New Advances,” Progress in Aerospace Sciences, Vol. 35, No. 7, 1999, pp. 673–726. doi:https://doi.org/10.1016/S0376-0421(99)00005-6 PAESD6 0376-0421 CrossrefGoogle Scholar

  • [37] Armanini S. F., De Visser C. C. and De Croon G. C. H. E., “Black-Box LTI Modelling of Flapping-wing Micro Aerial Vehicle Dynamics,” AIAA Atmospheric Flight Mechanics Conference, AIAA Paper  2015-0234, Jan. 2015. doi:https://doi.org/10.2514/6.2015-0234 LinkGoogle Scholar

  • [38] Scheper K. Y. W., “Behaviour Trees for Evolutionary Robotics: Reducing the Reality Gap,” Master’s Thesis, TU Delft, Delft, The Netherlands, 2014 (unpublished). Google Scholar

  • [39] Koopmans A., “Delfly Freeflight, ” Master’s Thesis, TU Delft, Delft, The Netherlands, 2012 (unpublished). Google Scholar

  • [40] De Croon G. C. H. E., Groen M. A., De Wagter C., Remes B. D., Ruijsink R. and Van Oudheusden B. W., “Design, Aerodynamics and Autonomy of the DelFly,” Bioinspiration & Biomimetics, Vol. 7, No. 2, June 2012, Paper 025003. doi:https://doi.org/10.1088/1748-3182/7/2/025003 CrossrefGoogle Scholar

  • [41] Caetano J. V., De Visser C. C., Remes B. D., De Wagter C. and Mulder M., “Modeling a Flapping Wing MAV: Flight Path Reconstruction of the Delfly II,” AIAA Modeling and Simulation Technologies Conference, AIAA Paper  2013-4597, Aug. 2013. doi:https://doi.org/10.2514/6.2013-4597 LinkGoogle Scholar

  • [42] Jategaonkar R., Flight Vehicle System Identification: A Time Domain Methodology, Progress in Astronautics and Aeronautics, AIAA, Reston, VA, 2006, pp. 79–129. LinkGoogle Scholar

  • [43] Maine R. E. and Iliff K. W., “Application of Parameter Estimation to Aircraft Stability and Control: The Output-Error Approach,” NASA Reference Publ.  1168, 1986. Google Scholar

  • [44] Klein V. and Morelli E. A., Aircraft System Identification, AIAA Education Series, AIAA, Reston, VA, 2006, pp. 181–223. CrossrefGoogle Scholar

  • [45] Caetano J. V., Percin M., van Oudheusden B. W., Remes B., de Wagter C., de Croon G. C. H. E. and de Visser C. C., “Error Analysis and Assessment of Unsteady Forces Acting on a Flapping Wing Micro Air Vehicle: Free Flight Versus Wind-Tunnel Experimental Methods,” Bioinspiration and Biomimetics, Vol. 10, No. 5, 2015, Paper 056004. doi:https://doi.org/10.1088/1748-3190/10/5/056004 1748-3182 CrossrefGoogle Scholar

Previous article
Next article