Abstract
Modern non-inertial robots are usually underactuated, such as fix or rotary wing Unmanned Aerial Vehicles (UAVs), underwater or nautical robots, to name a few. Those systems are subject to complex aerodynamic or hydrodynamic forces which make the dynamic model more difficult, and typically are subject to bounded smooth time-varying disturbances. In these systems, it is preferred a formal control approach whose closed-loop system can predict an acceptable performance since deviations may produce instability and may lead to catastrophic results. Backstepping provides an intuitive solution since it solves underactuation iteratively through slaving the actuated subsystem so as to provide a virtual controller in order to stabilize the underactuated subsystem. However it requires a full knowledge of the plant and derivatives of the state, which it is prone to instability for any uncertainty; and although robust sliding mode has been proposed, discontinuities may be harmful for air- or water-borne nonlinear plants. In this paper, a novel robust backstepping-based controller that induces integral sliding modes is proposed for the Newton–Euler underactuated dynamic model of a quadrotor subject to smooth bounded disturbances, including wind gust and sideslip aerodynamics, as well as dissipative drag in position and orientation dynamics. The chattering-free sliding mode compensates for persistent or intermittent, and possible unmatched state dependant disturbances with reduced information of the dynamic model. Representative simulations are presented and discussed.
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Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)
Jafari Koshkouei, A., Zinober, A.-S.-I.: Adaptive sliding backstepping control of nonlinear semi-strict feedback form systems. In: Proc. of the 7th Mediterranean Conf. on Control and Automation, pp. 2376–2386 (1999)
Skjetne, R., Fossen, T.: On integral control in backstepping: Analysis of different techniques. In: Proc. American Control Conf., vol. 2, pp. 1899–1904 (2004)
Cunha, R., Cabecinhas, D., Silvestre, C.: Nonlinear trajectory tracking control of a quadrotor vehicle. In: European Control Conf. (2009)
Das, A., Lewis, F., Subbarao, K.: Backstepping approach for controlling a quadrotor using Lagrange form dynamics. J. Intell. Robot. Syst. 56(1–2), 127–151 (2009)
Zhang, T., Ge, S.S., Hang, C.C.: Adaptive neural network control for strict-feedback nonlinear systems using backstepping design. In: American Control Conf., vol. 2, pp. 1062–1066 (1999)
Bartolini, G., Ferrara, A., Giacomini, L., Usai, A.: Properties of a combined adaptive/second-order sliding mode control algorithm for some classes of uncertain nonlinear systems. IEEE Trans. Autom. Control 45(7), 1334–1341
Isidori, A., Marconi, L., Serrani, A.: Robust nonlinear motion control of a helicopter. IEEE Trans. Autom. Control 48(3), 413–426
Bouabdallah, S., Siegwart, R.: Backstepping and sliding-mode techniques applied to an indoor micro quadrotor. In: 2005 IEEE International Conf. on Robotics and Automation, pp. 2247–2252
Gu, W.-J., Zhao, H., Pan, Ch.: Sliding mode control for an aerodynamic missile based on backstepping design. J. Control Theory Appl. 1, 71–75 (2005)
Swaroop, D., Hedrick, J.K., Yip, P.P., Gerdes, J.C.: Dynamic surface control for a class of nonlinear systems. IEEE Trans. Autom. Control 45(10), 1893–1899 (2000)
Nersesov, S.-G., Ashrafiuon, H., Ghorbanian, P.: On the stability of sliding mode control for a class of underactuated nonlinear systems. In: 2010 American Control Conf., pp. 3446–3451
Bouadi, H., Bouchoucha, M., Tadjine, M.: Sliding Mode Control based on Backstepping Approach for an UAV Type-Quadrotor. World Acad. Sci. Eng. Technol. 2, 22–27 (2007)
Luque-Vega, L., Castillo-Toledo, B., Loukianov, A.G.: Robust block second order sliding mode control for a quadrotor. J. Frankl. Inst. 349, 719–739 (2012)
Levant, A.: Robust exact differentiation via sliding mode technique. Automatica 34(3), 379–384 (1998)
Madani, T., Benallegue, A.: backstepping control with exact 2-sliding mode estimation for a quadrotor unmanned aerial vehicle. In: 2007 IEEE/RSJ Int. Conf. on Int. Robots and Systems, pp. 141–146
Parra-Vega, V., Arimoto, S., Liu, Y.-H., Hirzinger, G., Akella, P.: Dynamic sliding pid control for tracking of robots manipulators: theory and experiments. IEEE Trans. Robot. Autom. 19(6), 967–976 (2003)
Stengel, R.F.: Flight Dynamics. Princeton University Press (2004)
Leishman, J.G.: Principles of Helicopter Aerodynamics. Cambridge University Press, Cambridge, MA (2006)
Bazov, D.I.: Helicopter Aerodynamics. NASA, Washington (1972)
Koo, T.J., Sastry, S.: Output tracking control design of a helicopter model based on approximate linearization. In: Proc. IEEE Conf. on Decision and Control, pp. 3635–3640 (1998)
Frazzoli, E., Dahleh, M., Feron, E.: Trajectory tracking control design for autonomous helicopters using a backstepping algorithm. In: Proc. American Control Conference, vol. 6, pp. 4102–4107 (2000)
Madani, T., Benallegue, A.: Backstepping control for a quadrotor helicopter. In: Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3255–3260 (2006)
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This work was supported in Mexico by the Conacyt grants 133346, 133544 and the Conacyt MSc Scholarship 262513.
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Ramirez-Rodriguez, H., Parra-Vega, V., Sanchez-Orta, A. et al. Robust Backstepping Control Based on Integral Sliding Modes for Tracking of Quadrotors. J Intell Robot Syst 73, 51–66 (2014). https://doi.org/10.1007/s10846-013-9909-4
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DOI: https://doi.org/10.1007/s10846-013-9909-4