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Robust Flight Control of an Underactuated Quadrotor via Sliding Modes

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Applications of Sliding Mode Control

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 79))

Abstract

An underactuated quadrotor has four actuators and six degrees of freedom to be controlled. Nevertheless, by deliberately controlling the velocities of the four propellers, the underactuated quadrotor can track the desired position trajectory and maintain the correct attitude during flight. To improve the robustness and performance of the underactuated quadrotor system, we propose two sliding mode control to deal with the parametric variations and the external disturbances. We first establish the quadrotor model in terms of the translational and rotational dynamics along with the disturbances and the model uncertainties. By specifying the desired pitch and roll angle as the virtual control, we then design dual sliding modes: one for the translational and the other for the rotational dynamics. Our Lyapunov-based stability analysis shows that the proposed control schemes can guarantee the asymptotical stability of the error dynamics for the position and attitude control of the underactuated quadrotor. Numerical simulations also indicate that the sliding mode control can effectively follow the desired trajectory and maintain the proper attitude in the presence of parametric variations and external disturbances.

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Abbreviations

B :

\(\equiv \) quadrotor body

\(P_i\) :

\(\equiv \) propeller i

\(F_w\) :

\(\equiv \) inertia world frame

\(F_B\) :

\(\equiv \) body frame

\(F_{P_i}\) :

\(\equiv \) ith propeller frame

\(R_T\) :

\(\equiv \) transform matrix from body angular rates to Euler ones

p :

\(\equiv \) position of B in \(F_\omega \)

q :

\(\equiv \) Euler angle of B in \(F_\omega \)

\(\omega _{R_B}\) :

\(\equiv \) rotation matrix from \(F_B\) to \(F_\omega \)

\(~^B R_{P_i}\) :

\(\equiv \) rotation matrix from \(F_{P_i}\) to \(F_B\)

\(\omega _i\) :

\(\equiv \) ith propeller spinning velocity about \(Z_{P_i}\)

\(\omega _{P_i}\) :

\(\equiv \) angular velocity in the ith propeller frame

\(T_{P_i}\) :

\(\equiv \) force in the ith propeller frame

\(\omega _B\) :

\(\equiv \) angular velocity of B in \(F_B\)

\(\tau _B\) :

\(\equiv \) torque in \(F_B\)

\(\tau _{P_i}\) :

\(\equiv \) torque in \(F_{P_i}\)

\(\tau _{di}\) :

\(\equiv \) ith propeller air drag torque about \(Z_{P_i}\)

\(T_i\) :

\(\equiv \) ith propeller thrust along \(Z_{P_i}\)

\(\tau _{\omega _i}\) :

\(\equiv \) motor torque along \(Z_{P_i}\)

m :

\(\equiv \) total quadrotor mass

\(I_{P_i}\) :

\(\equiv \) inertia of the ith propeller \(P_i\)

\(I_B\) :

\(\equiv \) inertia of the quadrotor body B

\(k_f\) :

\(\equiv \) propeller thrust coefficient

\(k_m\) :

\(\equiv \) propeller drag coefficient

L :

\(\equiv \) distance of \(F_{P_i}\) to \(F_B\)

g :

\(\equiv \) gravity constant

References

  • Alexis, K., Nikolakopoulos, G., & Tzes, A. (2011a). Autonomous quadrotor position and attitude PID/PIDD control in GPS-denied environments. The International Review of Automatic Control, 3, 421–430.

    Google Scholar 

  • Alexis, K., Nikolakopoulos, G., & Tzes, A. (2011b). Switching model predictive attitude control for a quadrotor helicopter subject to atmospheric disturbances. Control Engineering Practice, 19, 1195–1207.

    Article  Google Scholar 

  • Alexis, K., Nikolakopoulos, G., & Tzes, A. (2012). Model predictive quadrotor control: Attitude, altitude and position experimental studies. IET Control Theory & Applications, 6, 1812–1827.

    Article  MathSciNet  Google Scholar 

  • Bartolini, G., Ferrara, A., & Usai, E. (1998). Chattering avoidance by second order sliding modes control. IEEE Transactions on Automatic Control, 43, 241–247.

    Article  MathSciNet  MATH  Google Scholar 

  • Bartolini, G., Pisano, A., Punta, E., & Usai, E. (2003). A survey of applications of second–order sliding mode control to mechanical systems. International Journal of Control, 76, 875–892.

    Article  MathSciNet  MATH  Google Scholar 

  • Beballegue, A., Mokhtari, A., & Fridman, L. (2008). High-order sliding-mode observer for a quadrotor UAV. International Journal of Robust and Nonlinear Control, 18, 427–440.

    Article  MathSciNet  MATH  Google Scholar 

  • Besnard, L., Shtessel, Y. B., & Landrum, B. (2012). Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbance observer. Journal of the Franklin Institute, 349, 658–684.

    Article  MathSciNet  MATH  Google Scholar 

  • Bouabdallah, S., & Siegwart, R. (2005). Backstepping and sliding–mode techniques applied to an indoor micro quadrotor. International Conference on Robotics and Automation, Proceedings, ICRA 2005 (pp. 2247–2252).

    Google Scholar 

  • Bouabdallah, S., Noth, A., & Siegwart, R. (2004). PID vs LQ control techniques applied to an indoor micro quadrotor. International Conference on Intelligent Robots and Systems, Proceedings, IROS, 2004(3), 2451–2456.

    Google Scholar 

  • Byung-Yoon, L., Hae-In, L., & Min-Jea, T. (2013). Analysis of adaptive control using on-line neural networks for a quadrotor UAV. 13th International Conference on in Control, Automation and Systems, Proceedings, ICCAS 2013 (pp. 1840–1844).

    Google Scholar 

  • Cabecinhas, D., Cunha, R., & Silvestre, C. (2015). A globally stabilizing path following controller for rotorcraft with wind disturbance rejection. IEEE Transactions on Control Systems Technology, 23, 708–714.

    Article  Google Scholar 

  • Das, A., Lewis, F., & Subbarao, K. (2009a). Backstepping approach for controlling a quadrotor using lagrange form dynamics. Journal of Intelligent and Robotic Systems, 56, 127–151.

    Article  MATH  Google Scholar 

  • Das, A., Subbarao, K., & Lewis, F. (2009b). Dynamic inversion with zero-dynamics stabilisation for quadrotor control. IET Control Theory & Applications, 3, 303–314.

    Article  MathSciNet  Google Scholar 

  • Derafa, L., Benallegue, A., & Fridman, L. (2012). Super twisting control algorithm for the attitude tracking of a four rotors UAV. Journal of the Franklin Institute, 349, 685–699.

    Article  MathSciNet  MATH  Google Scholar 

  • Dierks, T., & Jagannathan, S. (2010). Output feedback control of a quadrotor UAV using neural networks. IEEE Transactions on Neural Networks, 21, 50–66.

    Article  Google Scholar 

  • Emelyanov, S., Korovin, S., & Levant, A. (1996). High–order sliding modes in control systems. Computational Mathematics and Modeling, 7, 294–318.

    Google Scholar 

  • Hoffmann, G., Huang, H., Waslander, S., & Tomlin, C. (2007). Quadrotor helicopter flight dynamics and control: Theory and experiment. Proceedings of the AIAA Guidance, Navigation, Control Conference (pp. 1 –20).

    Google Scholar 

  • Hyon, L., Jaemann, P., Daewon, L., & Kim, H. J. (2012). Build your own quadrotor: Open-source projects on unmanned aerial vehicles. IEEE Robotics & Automation Magazine, 19, 33–45.

    Article  Google Scholar 

  • Islam, S., Liu, P. X., & El Saddik, A. (2015). Robust control of four-rotor unmanned aerial vehicle with disturbance uncertainty. IEEE Transactions on Industrial Electronics, 62(1563–1571), 2015.

    Google Scholar 

  • Lee, H., & Utkin, V. I. (2007). Chattering suppression methods in sliding mode control systems. Annual Reviews in Control, 31, 179–188.

    Article  Google Scholar 

  • Lee, D., Kim, H. J., & Sastry, S. (2009). Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter. International Journal of Control, Automation and Systems, 7, 419–428.

    Google Scholar 

  • Levant, A. (1993). Sliding order and sliding accuracy in sliding mode control. International Journal of Control, 58, 1247–1263.

    Google Scholar 

  • Levant, A. (2001). Universal SISO sliding-mode controllers with finite-time convergence. IEEE Transactions on Automatic Control, 49, 1447–1451.

    Article  MathSciNet  MATH  Google Scholar 

  • Levant, A. (2007). Principles of 2-sliding mode design. Automatica, 43, 576–586.

    Article  MathSciNet  MATH  Google Scholar 

  • Madani, T., & Benallegue, A. (2006). Backstepping Control for a Quadrotor Helicopter, International Conference on Intelligent Robots and Systems, Proceedings, IEEE/RSJ 2006 (pp. 3255–3260).

    Google Scholar 

  • Mahony, R., Kumar, V., & Corke, P. (2012). Multirotor aerial vehicles: Modeling, estimation, and control of quadrotor. IEEE Robotics & Automation Magazine, 19, 20–32.

    Article  Google Scholar 

  • Mellinger, D., Michael, N., & Kumar, V. (2012). Trajectory generation and control for precise aggressive maneuvers with quadrotors. The International Journal of Robotics Research, 31, 664–674.

    Article  Google Scholar 

  • Moreno, A., & Osorio, M. (2012). Strict Lyapunov functions for the super-twisting algorithm. IEEE Transactions on Automatic Control, 57, 1035–1040.

    Article  MathSciNet  Google Scholar 

  • Mokhtari, A., Benallegue, A., & Orlov, Y. (2006a). Exact linearization and sliding mode observer for a quadrotor unmanned aerial vehicle. International Journal of Robotics and Automation, 21, 39–49.

    Article  Google Scholar 

  • Mokhtari, A., M’sirdi, N. K., Meghriche, K., & Belaidi, A., (2006b). Feedback linearization and linear observer for a quadrotor unmanned aerial vehicle. Advanced Robotics, 20, 71–91.

    Google Scholar 

  • Nonami, K., Kendoul, F., Suzuki, S., Wang, W., & Nakazawa, D. (2010). Autonomous flying robots. Japan: Springer.

    Google Scholar 

  • Pico, J., Pico-Marco, E., Vignoni, A., & De Battista, H. (2013). Stability preserving maps for finite-time convergence: Super-twisting sliding-mode algorithm. Automatica, 49, 534–539.

    Article  MathSciNet  MATH  Google Scholar 

  • Plestan, F., Shtessel, Y., Bregeault, V., & Poznyak, A. (2010). New methodologies for adaptive sliding mode control. International Journal of Control, 83, 1907–1919.

    Article  MathSciNet  MATH  Google Scholar 

  • Rabhi, A., Chadli, M., & Pegard, C. (2011). Robust fuzzy control for stabilization of a quadrotor. 15th International Conference on Advanced Robotics, Proceedings, ICAR 2011 (pp. 471–475).

    Google Scholar 

  • Raffo, G. V., Ortega, M. G., & Rubio, F. R. (2010). An integral predictive/nonlinear control structure for a quadrotor helicopter. Automatica, 46, 29–39.

    Article  MathSciNet  MATH  Google Scholar 

  • Satici, A. C., Poonawala, H., & Spong, M. W. (2013). Robust Optimal Control of Quadrotor UAVs. IEEE Access, 1, 79–93.

    Google Scholar 

  • Shtessel, Y., Edwards, C., Fridman, L., & Levant, A. (2014). Sliding mode control and observation. New York: Springer.

    Book  Google Scholar 

  • Slotine, J. J. E., & Li, W. (1991). Applied nonlinear control. New Jersey: Prentice Hall.

    MATH  Google Scholar 

  • Utkin, V. (1992). Sliding modes in control and optimization. Berlin: Springer.

    Book  MATH  Google Scholar 

  • Utkin, V. (2003). On convergence time and disturbance rejection of super-twisting control. IEEE Transactions on Automatic Control, 58, 2013–2017.

    Google Scholar 

  • Utkin, V. I., & Poznyak, A. S. (2013). Adaptive sliding mode control with application to super-twist algorithm: Equivalent control method. Automatica, 49, 39–47.

    Google Scholar 

  • Xilun, D., & Yushu, Y. (2013). Motion planning and stabilization control of a multipropeller multifunction aerial robot. IEEE/ASME Transactions on Mechatronics, 18, 645–656.

    Article  Google Scholar 

  • Xu, R., & Özgüner, Ãœ. (2006). Sliding mode control of a quadrotor helicopter. 45th IEEE Conference on Decision and Control, Proceedings, CDC 2006 (pp. 4957–4962).

    Google Scholar 

  • Young-Cheol, C., & Hyo-Sung, A. (2015). Nonlinear control of quadrotor for point tracking: Actual implementation and experimental tests. IEEE/ASME Transactions on Mechatronics, 20, 1179–1192.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Automation Engineering, I-Shou University, 84001, Kaohsiung, Taiwan

    Chih-Chen Yih

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  1. Chih-Chen Yih
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Correspondence to Chih-Chen Yih .

Editor information

Editors and Affiliations

  1. University of Sfax, Sfax, Tunisia

    Nabil Derbel

  2. University of Tunis Carthage, Urbain Nord, Tunisia

    Jawhar Ghommam

  3. University of the West of England, Bristol, United Kingdom

    Quanmin Zhu

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© 2017 Springer Science+Business Media Singapore

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Yih, CC. (2017). Robust Flight Control of an Underactuated Quadrotor via Sliding Modes. In: Derbel, N., Ghommam, J., Zhu, Q. (eds) Applications of Sliding Mode Control. Studies in Systems, Decision and Control, vol 79. Springer, Singapore. https://doi.org/10.1007/978-981-10-2374-3_5

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  • DOI: https://doi.org/10.1007/978-981-10-2374-3_5

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2373-6

  • Online ISBN: 978-981-10-2374-3

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