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Vectorial backstepping method–based trajectory tracking control for an under-actuated stratospheric airship

  • S. Q. Liu (a1), S. J. Gong (a1), Y. X. Li (a1) and Z. R. Lu (a2)


A new trajectory tracking control approach for an under-actuated stratospheric airship is proposed. There is a two-level structure of the proposed controller. A low-level controller based on non-linear vectorial backstepping method, with the rigid-body dynamics expressed on vector form, stabilises the attitude and velocity of the airship, while a high-level controller performs guidance and trajectory tracking task in the three-dimensional (3D) space. Furthermore, a control allocation module based on the active set algorithm is incorporated into the low-level controller to optimise the practical control inputs under constraints of actuator saturation. The closed-loop trajectory tracking control plant is proved to be globally exponentially stable through the Lyapunov theory. Finally, simulations show that the vectorial backstepping trajectory tracking controller can achieve desired tracking performances even if the airship is affected by parametric uncertainties and exogenous disturbances.


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1. Kulczycki, E.A., Joshi, S.S., Hess, R.A. et al. Towards controller design for autonomous airships using SLC and LQR methods, AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA 2006-6778, 2006, Keystone, Colorado, US.
2. Trevino, R., Frye, M., Franz, J.A. et al. Robust receding horizon control of a tri-turbofan airship, IEEE International Conference on Control and Automation, ICCA 2007, Guang zhou, China, pp 671-676.
3. Benjovengo, F.P., Paiva, E.C. and Bueno, S.S. Sliding mode control approaches for an autonomous unmanned airship, The 18th Lighter-Than-Air Systems Technology Conference, AIAA 2009-2869, 2009, Seattle, Washington, US.
4. Wang, X. and Shan, X. Airship attitude tracking system, Applied Mathematics and Mechanics, 2006, 27, (7), pp 919-926.
5. Acosta, D.M. and Joshi, S.S. Adaptive nonlinear dynamic inversion control of an autonomous airship for the exploration of Titan, AIAA Guidance, Navigation and Control Conference and Exhibit, AIAA 2007-6502, 2007, Hilton Head, South Carolina, US.
6. Krstic, M., Kanellakopoulos, I. and Kokotovic, P.V. Nonlinear and Adaptive Control Design, 1995, Wiley Press, New York, New York, US.
7. Sonneveldt, L., Van Oort, E.R., Chu, Q.P. et al. Nonlinear adaptive trajectory control applied to an F-16 model, J Guidance, Control, and Dynamics, 2009, 32, (1), pp 25-39.
8. Zhang, C., Chen, Z.J. and Wei, C. Sliding mode disturbance observer-based backstepping control for a transport aircraft, Science China, Information Science, 2014, 57, (5), pp 1-16.
9. Fossen, T.I. Handbook of Marine Craft Hydrodynamics and Motion Control, 2011, Wiley Press, United Kingdom, pp 457-484.
10. Hygounenc, E. and Soueres, P. Automatic airship control involving backstepping techniques, IEEE International Conference on Systems, Man and Cybernetics, vol. 6, 2006, Yasmine Hammamet, Tunisia, pp 1-6.
11. Azinheira, J.R., Moutinho, A. and De Paiva, E.C. Airship hover stabilization using a backstepping control approach, J Guidance, Control, and Dynamics, 2006, 29, (4), pp 903-914.
12. Azinheira, J.R., Moutinho, A. and de Paiva, E.C. A backstepping controller for path-tracking of an underactuated autonomous airship, Int J Robust and Nonlinear, 2009, 19, (4), pp 418-441.
13. Lee, S., Lee, H., Won, D. et al. Backstepping approach of trajectory tracking control for the mid-altitude unmanned airship, AIAA Guidance, Navigation and Control Conference and Exhibit, AIAA 2007-6319, 2007, Hilton Head, South Carolina, US.
14. Yang, Y., Wu, J. and Zheng, W. Station-keeping control for a stratospheric airship platform via fuzzy adaptive backstepping approach, Advances in Space Research, 2013, 51, (7), pp 1157-1167.
15. Moutinho, A., Moutinho, A., de Paiva, E.C. and Bueno, S. Airship robust path tracking: A tutorial on airship modeling and gain scheduling control design, Control Engineering Practice, 2016, 50, pp 22-36.
16. Zheng, Z., Huo, W. and Wu, Z. Trajectory tracking control for underactuated stratospheric airship, Advances in Space Research, 2012, 50, (7), pp 906-917.
17. Liu, S.Q., Lu, J.G. and Jing, Z.L. Trajectory linearization based output tracking control of an unmanned tandem helicopter with variance constraints, Int J Control, Automation, and Systems, 2010, 8, (6), pp 1257-1270.
18. Repoulias, F. and Papadopoulos, E. Robotic airship trajectory tracking control using a backstepping methodology, IEEE International Conference on Robotics and Automation, 2008, Pasadena, California, US, pp 188-193.
19. Zheng, Z. and Wu, Z. Global path following control for underactuated stratospheric airship, Advances in Space Research, 2013, 52, (7), pp 1384-1395.
20. Daskiran, O. and Dogan, A. Airship control using expert demonstrations, AIAA Atmospheric Flight Mechanics Conference, AIAA 2016-3239, 2016, Washington, DC, US, pp 1-28.
21. Liesk, T., Nahon, M. and Boulet, B. Design and experimental validation of a nonlinear low-level controller for an unmanned fin-less airship, IEEE Transactions on Control Systems Technology, 2013, 21, (1), pp 149-161.
22. Harkegard, O. Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation, IEEE Proceedings of the 41st IEEE Conference on Decision and Control, vol. 2, 2002, Las Vegas, Nevada, US, pp 1295-1300.
23. Liesk, T., Nahon, M. and Boulet, B. Design and experimental validation of a controller suite for an autonomous finless airship, American Control Conference, Fairmont Queen Elizabeth, 2012, Montreal, Canada, pp 2491-2496.
24. Mueller, J.B., Paluszek, M.A. and Zhao, Y. Development of an aerodynamic model and control law design for a high altitudeairship, AIAA 3rd Workshop and Exhibit of “Unmanned Unlimited” Technical Conference, 2004, AIAA 2004-6479, Chicago, Illinois, US.
25. Sebbane, Y.B. Lighter than Air Robots: Guidance and Control of Autonomous Airships, 2011, Springer Press, Netherlands, pp 7-35.
26. Gomes, S.B.V. An investigation into the flight dynamics of airships with application to the YEZ-2A. Dissertation for the Doctoral Degree, 1990, Cranfield University, Cranfield, UK.
27. Gates, D.J. Nonlinear path following method. J Guidance, Control, and Dynamics, 2010, 33, (2), pp 321-332.
28. Khalil, H.K. Nonlinear Systems, 3rded. 2002, Prentice Hall Press, New Jersey, US, pp 154.
29. Liu, S.Q., Li, Y.X. and Jin, H.B. Robust model predictive control for a stratospheric airship using LPV techniques. Int J Robust and Nonlinear Control, 2017, pp 1-25 (to be published).



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