Advertisement

Journal of Intelligent & Robotic Systems

, Volume 83, Issue 1, pp 105–131 | Cite as

Two-Step System Identification and Trajectory Tracking Control of a Small Fixed-Wing UAV

  • David J. Grymin
  • Mazen FarhoodEmail author
Article

Abstract

An approach for obtaining dynamically feasible reference trajectories and feedback controllers for a small unmanned aerial vehicle (UAV) based on an aerodynamic model derived from flight tests is presented. The modeling method utilizes stepwise multiple regression to determine relevant explanatory terms for the aerodynamic coefficients. A dynamically feasible trajectory is then obtained through the solution of an optimal control problem using pseudospectral optimal control software. Discrete-time feedback controllers are further designed to regulate the vehicle along the desired reference trajectory. Simulations in a realistic operational environment as well as flight testing of the feedback controllers on the aircraft platform demonstrate the capabilities of the approach.

Keywords

Unmanned aerial vehicles Small fixed-wing aircraft Time-domain system identification Trajectory generation Optimal control 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arifianto, O., Farhood, M.: Development and modeling of a low-cost unmanned aerial vehicle research platform. J. Intell. Robot. Syst. 80(1), 139–164 (2015). doi: 10.1007/s10846-014-0145-3
  2. 2.
    Arifianto, O., Farhood, M.: Optimal control of a small fixed-wing UAV about concatenated trajectories. Control Eng. Pract. 40, 113–132 (2015)CrossRefGoogle Scholar
  3. 3.
    Beal, T.R.: Digital simulation of atmospheric turbulence for Dryden and von Karmáń models. J. Guid. Control Dyn. 16(1), 132–138 (1993)CrossRefGoogle Scholar
  4. 4.
    Bittner, M., Bruhs, P., Richter, M., Holzapfel, F.: An automatic mesh refinement method for aircraft trajectory optimization problems. In: AIAA Guidance, Navigation, and Control Conference. AIAA 2013-4555, Boston, Massachusetts (2013)Google Scholar
  5. 5.
    Bittner, M., Fisch, F., Holzapfel, F.: A multi-model gauss pseudospectral optimization method for aircraft trajectories. In: AIAA Atmospheric Flight Mechanics Coneference. AIAA 2012-4728, Minneapolis, Minnesota (2012)Google Scholar
  6. 6.
    Bryson, A.E., Ho, Y.C.: Applied optimal Control: Optimization Estimation, and Control. Taylor & Francis (1975)Google Scholar
  7. 7.
    Crassidis, J.L., Junkins, J.L.: Optimal Estimation of Dynamic Systems. Chapman & Hall/CRC Press, Boca Raton, FL (2004)CrossRefzbMATHGoogle Scholar
  8. 8.
    Dever, C., Mettler, B., Feron, E., Popović, J., McConley, M.: Nonlinear trajectory generation for autonomous vehicles via parameterized maneuver classes. J. Guid. Control Dyn. 29(2), 289–302 (2006)CrossRefGoogle Scholar
  9. 9.
    Dorobantu, A., Murch, A., Mettler, B., Balas, G.: System identification for small, low-cost, fixed-wing, unmanned aircraft. J. Aircr. 50(4), 1117–1130 (2013)CrossRefGoogle Scholar
  10. 10.
    Draper, N.R., Smith, H.: Applied Regression Analysis. Wiley, Hoboken, NJ (1998)CrossRefzbMATHGoogle Scholar
  11. 11.
    Drury, R.G., Whidborne, J.F.: Quaternion-based inverse dynamics model for expressing aerobatic aircraft trajectories. J. Guid. Control Dyn. 32(4), 1388–1392 (2009)CrossRefGoogle Scholar
  12. 12.
    Dullerud, G.E., Lall, S.G.: A new approach to analysis and synthesis of time-varying systems. IEEE Trans. Autom. Control 44(8), 1486–1497 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Farhood, M.: LPV control of nonstationary systems: A parameter-dependent Lyapunov approach. IEEE Trans. Autom. Control 57(1), 209–215 (2012)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Farhood, M.: Nonstationary LPV control for trajectory tracking: a double pendulum example. Int. J. Control 85(5), 545–562 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Farhood, M., Dullerud, G.E.: LMI tools for eventually periodic systems. Syst. Control Lett. 47, 417–432 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Farhood, M., Dullerud, G.E.: Duality and eventually periodic systems. Int. J. Robust Nonlinear Control 15, 575–599 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Fisch, F., Lenz, J., Holzapfel, F., Sachs, G.: Trajectory optimization applied to air races. In: AIAA Atmospheric Flight Mechanics Conference. AIAA 2009-5930, Chicago, Illinois (2009)Google Scholar
  18. 18.
    Frazzoli, E., Dahlah, M., Feron, E.: Maneuver-based motion planning for nonlinear systems with symmetries. IEEE Trans. Robot. 21(6), 1077–1091 (2005)CrossRefGoogle Scholar
  19. 19.
    Gahinet, P.: Explicit controller formulas for LMI-based H synthesis. Automatica 32(7), 1007–1014 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Gahinet, P., Apkarian, P.: A linear matrix inequality approach to H control. Int. J. Robust Nonlinear Control 4, 421–448 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Garg, D., Hager, W.W., Rao, A.V.: Pseudospectral methods for solving infinite-horizon optimal control problems. Automatica 47(4), 829–837 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Garg, D., Patterson, M.A., Darby, C.L., Francolin, C., Huntington, G.T., Hager, W.W., Rao, A.V.: Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems via a Radau pseudospectral method. Comput. Opt. Appl. 49(2), 335–339 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Garg, D., Patterson, M.A., Hager, W.W., Rao, A.V., Benson, D.A., Huntington, G.T.: A unified framework for the numerical solution of optimal control problems using pseudospectral methods. Automatica 46(11), 1843–1851 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Gibbs, B.P.: Advanced Kalman Filtering, Least-Squares and Modeling: A Practical Handbook. Wiley, Hoboken, NJ (2011)CrossRefGoogle Scholar
  25. 25.
    Grymin, D.J.: Two-step system identification and primitive-based motion planning for control of small unmanned aerial vehicles. Ph.D. thesis, Virginia Tech, VA, USA (2013)Google Scholar
  26. 26.
    Grymin, D.J., Farhood, M.: Two-step system identification for control of small UAVs along pre-specified trajectories. In: Proceedings of the American Control Conference, pp 4404–4409, Portland, OR (2014)Google Scholar
  27. 27.
    Hall, J.K., Beard, R.W., McLain, T.W.: Quaternion control for autonomous path following maneuvers. In: AIAA Infotech Aerospace. AIAA 2012-2483, Garden Grove, California (2012)Google Scholar
  28. 28.
    Hall, J.K., McLain, T.W.: Aerobatic maneuvering of miniature air vehicles using attitude trajectories. In: AIAA Guidance, Navigation, and Control Conference. AIAA 2008-7257, Honolulu, Hawaii (2008)Google Scholar
  29. 29.
    Hepperle, M.: JavaProp - design and analysis of propellers. Technical Report, MH Aerotools (2010). Available from http://www.mh-aerotools.de
  30. 30.
    Hoffer, N.V., Coopmans, C., Jensen, A.M., Chen, Y.Q.: A survey and categorization of small low-cost unmanned aerial vehicle system identification. J. Intell. Robot Syst., 2013 (2013)Google Scholar
  31. 31.
    Jategaonkar, R.V.: Flight Vehicle System Identification - a Time-Domain Methodology. AIAA, Reston, VA (2006)CrossRefGoogle Scholar
  32. 32.
    Jung, D., Levy, E.J., Zhou, D., Fink, R., Moshe, J., Earl, A., Tsiotras, P.: Design and development of a low-cost test-bed for undergraduate education in UAVs. In: 44th IEEE Conference on Decision and Control and 2005 European Control Conference, pp 2739–2744, Seville, Spain (2005)Google Scholar
  33. 33.
    Klein, V., Morelli, E.: Aircraft System Identification - Theory and Practice. AIAA, Reston, VA (2006)CrossRefGoogle Scholar
  34. 34.
    Löfberg, J.: YALMIP : A toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD Conference. http://users.isy.liu.se/johanl/yalmip, Taipei, Taiwan (2004)
  35. 35.
    Moorhouse, D.J., Woodcock, R.J.: Background information and user guide for MIL-F-8785C, military specification - flying qualities of piloted airplanes. Technical Report, Air Force Wright Aeronautical Labs, Wright-Patterson AFB. OH (1982)Google Scholar
  36. 36.
    Mulder, J.A., Chu, Q.P., Sridhar, J.K.: Decomposition of aircraft state and parameter estimation problem. In: Proceedings of the 10th IFAC Symposium on System Identification, pp 61–66, Copenhagen, Denmark (1994)Google Scholar
  37. 37.
    Mulder, J.A., Chu, Q.P., Sridhar, J.K., Breeman, J.H., Laban, M.: Non-linear aircraft flight path reconstruction review and new advances. Progess Aerosp. Sci. 35, 673–726 (1999)CrossRefGoogle Scholar
  38. 38.
    Nelson, R.C.: Flight Stability and Automatic Control, 2nd edn. McGraw Hill, Boston, MA (1998)Google Scholar
  39. 39.
    Oliveira, J., Chu, Q.P., Mulder, J.A., Balini, H.M.N.K., Vos, W.G.M.: Output error method and two step method for aerodynamic model identification. In: AIAA Guidance, Navigation, and Control Conference, San Francisco, California (2005)Google Scholar
  40. 40.
    Packard, A.: Gain scheduling via linear fractional transformations. Syst. Control Lett. 22, 79–92 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Paris, A.C., Bonner, M.: Nonlinear model development from flight-test data for F/A-18E super hornet. J. Aircr. 41(4), 692–702 (2004)CrossRefGoogle Scholar
  42. 42.
    Park, S.: Autonomous aerobatic flight by three-dimensional path-following with relaxed roll constraint. In: AIAA Guidance, Navigation, and Control Conference. AIAA 2011-6593, Portland, Oregon (2011)Google Scholar
  43. 43.
    Phillips, W.F.: Mechanics of Flight. Wiley, Hoboken, NJ (2010)Google Scholar
  44. 44.
    Rao, A.V., Benson, D.A., Darby, C., Patterson, M.A., Francolin, C., Sanders, I., Huntington, G.T.: Algorithm 902: GPOPS, a MATLAB software for solving multiple-phase optimal control problems using the Gauss pseudospectral method. ACM Trans. Math. Softw. 37(2), 22:1–39 (2010)CrossRefGoogle Scholar
  45. 45.
    Raol, J.R., Girija, G., Singh, J.: Modeling and Parameter Estimation of Dynamical Systems. The Institution of Electrical Engineers, London, UK (2004)CrossRefzbMATHGoogle Scholar
  46. 46.
    Rauch, T.E., Tung, F., Striebel, C.T.: Maximum likelihood estimates of linear dynamic systems. AIAA J. 3, 1445–1450 (1965)MathSciNetCrossRefGoogle Scholar
  47. 47.
    Salman, S.A., Sreenatha, A.G., Choi, J.Y.: Attitude dynamics identification of unmanned aerial vehicle. Int. J. Control Autom. Syst. 4(6), 782–787 (2006)Google Scholar
  48. 48.
    Schouwennaars, T., Mettler, B., Feron, E., How, J.: Hybrid model for trajectory planning of agile autonomous vehicles. J. Aerosp. Comput. Inf. Commun. 1, 629–651 (2004)CrossRefGoogle Scholar
  49. 49.
    Sri-Jayantha, M., Stengel, R.F.: Determination of nonlinear aerodynamic coefficients using the estimation-before-modeling method. J. Aircr. 25(9), 796–804 (1988)CrossRefGoogle Scholar
  50. 50.
    Stalford, H.L.: High-alpha aerodynamic model identification of T-2C aircraft using the EBM method. J. Aircr. 18(10), 801–809 (1981)CrossRefGoogle Scholar
  51. 51.
    Stengel, R.F.: Optimal Control and Estimation. Dover Publications, New York (1994)zbMATHGoogle Scholar
  52. 52.
    Stevens, B.L., Lewis, F.L.: Aircraft Control and Simulation - Second Edition. Wiley, Hoboken, NJ (2003)Google Scholar
  53. 53.
    Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11–12, 625–653 (1999). Version 1.05 available from http://fewcal.kub.nl/sturm MathSciNetCrossRefzbMATHGoogle Scholar
  54. 54.
    Theil, H.: Economic Forecasts and Policy. North-Holland Publishing Company, Amsterdam, Netherlands (1961)Google Scholar
  55. 55.
    Tischler, M.: Aircraft and Rotorcraft System Identification: Engineering Methods with Flight Test Examples. AIAA, Reston, VA (2006)Google Scholar
  56. 56.
    Wächter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Programm. 106(1), 25–57 (2006)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Aerospace and Ocean Engineering, Virginia TechBlacksburgUSA

Personalised recommendations