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An unmanned helicopter control with partial small body force compensation: Experimental results

  • Bryan Godbolt (a1) and Alan F. Lynch (a1)

A generally accepted helicopter model used for control includes the effect of Small Body Forces (SBF) which couple the vehicle's rotational subsystem inputs to its translational dynamics. SBF result from tail rotor thrust and lateral forces due to main rotor flapping. It is well-known that SBF lead to a theoretically challenging stabilization problem for the tracking error dynamics. Hence, much of the existing work has neglected SBF in order to simplify control design. We design a controller that directly compensates the influence of the tail rotor component of the SBF. The design is validated in simulation and flight tests.

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1. Ahmed, B., Pota, H. R. and Garratt, M., “Flight control of a rotary wing UAV using backstepping,” Int. J. Robust Nonlinear Control 20, 639658 (2010).
2. Barczyk, M., Nonlinear State Estimation and Modeling of a Helicopter UAV. Ph.D. Thesis (Dept. of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, 2012).
3. Bisgaard, M., Modeling, Estimation, and Control of Helicopter Slung Load System. Ph.D. Thesis (Dept. of Control Engineering, Aalborg University, Denmark, 2007).
4. Bouabdallah, S., Design and Control of Quadrotors with Application to Autonomous Flying. Ph.D. Thesis (École Polytechnique Federale de Luasanne, Lausanne, Switzerland, 2007).
5. Bullo, F. and Murray, R. M., “Tracking for fully actuated mechanical systems: A geometric framework,” Automatica 35, 1735 (1999).
6. Cabecinhas, D., Cunha, R. and Silverstre, C., “A nonlinear quadrotor trajectory tracking controller with disturbance rejection,” Control Eng. Practice 26, 110 (2014).
7. Cai, G., Chen, B. M. and Lee, T. H., “Unmanned Rotorcraft Systems,” In: Advances in Industrial Control (Springer-Verlag, London, UK, 2011).
8. Castillo, P., Lozano, R. and Dzul, A. E., Modelling and Control of Mini-Flying Machines (Springer-Verlag, London, UK, 2005).
9. Farrell, J. A., Aided Navigation: GPS with High Rate Sensors (McGraw-Hill, New York, NY, 2008).
10. Godbolt, B., Experimental Nonlinear Control of a Helicopter Unmanned Aerial Vehicle (UAV). Ph.D. Thesis (Dept. of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, 2013).
11. Godbolt, B. and Lynch, A. F., “A Novel Cascade Controller for a Helicopter UAV with Small Body Force Compensation,” Proceedings of the American Control Conference, Washington, DC (2013) pp. 800–805.
12. Godbolt, B. and Lynch, A. F., “Physical Input Modelling and Identification for a Helicopter UAV,” Proceedings of the International Conference on Unmanned Aircraft Systems, Atlanta, GA (2013) pp. 890–896.
13. Godbolt, B., Vitzilaios, N., Bergen, C. and Lynch, A. F., “Helicopter UAV Control Validation Using Simulation and Experiment,” Proceedings of the International Conference on Unmanned Aircraft Systems, Atlanta, GA (2013) pp. 392–397.
14. Godbolt, B., Vitzilaios, N. I. and Lynch, A. F., “Experimental validation of a helicopter autopilot design using model-based PID control,” J. Intell. Robot. Syst. 70, 385399 (2013).
15. He, Y., Pei, H. and Sun, T., “Robust tracking control of helicopters using backstepping with disturbance observers,” Asian J. Control 16 (5), 13871402 (2014).
16. Hoffman, K. and Kunze, R., Linear Algebra, 2nd ed. (Prentice Hall, Upper Saddle River, NJ, 1971).
17. Hua, M. D., Contributions to the Automatic Control of Aerial Vehicles. Ph.D. Thesis (École Doctorale Science et Technologies de l'Information et de la Communication, Université Nice Sophia Antipolis, Nice, France, 2009).
18. Hua, M.-D., Hamel, T., Morin, P. and Samson, C., “Introduction to feedback control of underactuated VTOL vehicles: A review of basic control design ideas and principles,” Control Syst. Mag. 33, 6175 (2013).
19. Johnson, W., Helicopter Theory (Dover, New York, NY, 1980).
20. Kannan, S., Adaptive Control of Systems in Cascade with Saturation. Ph.D. Thesis (School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, 2005).
21. Kendoul, F., Fantoni, I. and Lozano, R., “Asymptotic Stability of Hierarchical Inner-Outer Loop-Based Flight Controllers,” Proceedings of the IFAC World Congress, Seoul, Korea (2008) pp. 1741–1746.
22. Khalil, H. K., Nonlinear Systems, 3rd ed. (Prentice Hall, Upper Saddle River, NJ, 2002).
23. Koditschek, D. E., Application of a New Lyapunov Function to Global Adaptive Attitude Tracking,” Proceedings of the Conference on Decision and Control, Austin, TX (1988) pp. 6368.
24. Koo, T. J. and Sastry, S., “Output Tracking Control Design of a Helicopter Model Based on Approximate Linearization,” Proceedings of the Conference on Decision and Control, Tampa, FL (1998) pp. 3635–3640.
25. Leishman, J. G., Principles of Helicopter Aerodynamics (Cambridge University Press, Cambridge, UK, 2016).
26. Mahony, R. and Hamel, T., “Robust trajectory tracking for a scale model autonomous helicopter,” Int. J. Robust Nonlinear Control 14, 10351059 (2004).
27. Marantos, P., Bechlioulis, C. P. and Kyriakopoulos, K. J., “Robust trajectory tracking control for small-scale unmanned helicopters with model uncertainties,” IEEE Trans. Control Syst. Technol. 25, 20102021 (2017).
28. Marconi, L. and Naldi, R., “Robust full degree-of-freedom tracking control of a helicopter,” Automatica 43, 19091920 (2007).
29. Mettler, B., Identification Modeling and Characteristics of Miniature Rotorcraft (Kluwer Academic Publishers, Norwell, MA, 2003).
30. Omari, S., Hua, M.-D., Ducard, G. and Hamel, T., “Nonlinear Control of VTOL UAVs Incorporating Flapping Dynamics,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan (2013) pp. 2419–2425.
31. Padfield, G. D., Helicopter Flight Dynamics: The Theory and Application of Flying Qualities and Simulation Modeling (John Wiley & Sons, New York, NY, 2008).
32. Patel, R. V. and Toda, M., “Quantitative Measures of Robustness for Multivariable Systems,” Proceedings of the Joint Automatic Control Conference, San Fransisco, CA (1980). paper TP8-A.
33. Prouty, R. W., Helicopter Performance, Stability, and Control (Krieger Publishing Company, Malabar, FL, 1986).
34. px4. PX4 autopilot. Online, 2018. URL Accessed Feb. 27, 2018.
35. QGroundControl. QGroundControl. online, 2013. URL Accessed Feb. 27, 2018.
36. Raptis, I. A., Valavanis, K. P. and Moreno, W. A., “A novel nonlinear backstepping controller design for helicopters using the rotation matrix,” IEEE Trans. Control Syst. Technol. 19, 465473 (2011).
37. Shao, X., Liu, J., Cao, H., Shen, C. and Wang, H., “Robust dynamic surface trajectory tracking control for a quadrotor UAV via extended state observer,” Int. J. Robust Nonlinear Control 28, 27002719 (2018).
38. Shuster, M. D., “A survey of attitude representations,” J. Astronaut. Sci. 41, 439517 (1993).
39. Valavanis, K. and Vachtsevanos, G. J., eds., Handbook of Unmanned Aerial Vehicles (Springer-Verlag, Dordrecht, The Netherlands, 2015).
40. van Nieuwstadt, M. J. and Murray, R. M., “Outer Flatness: Trajectory Generation for a Model Helicopter,” Proceedings of the European Control Conference, Brussels, Belgium (1997) pp. 325–330.
41. Xian, B., Zhao, B., Zhang, Y. and Zhang, X., “A low-cost hardware-in-the-loop-simulation testbed of quadrotor UAV and implementation of nonlinear control schemes,” Robotica 35, 588612 (2015).
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