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Quaternion-based nonlinear trajectory tracking control of a quadrotor unmanned aerial vehicle

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Abstract

At present, most controllers of quadrotor unmanned aerial vehicles(UAVs) use Euler angles to express attitude. These controllers suffer a singularity problem when the pitch angle is near 90°C, which limits the maneuverability of the UAV. To overcome this problem, based on the quaternion attitude representation, a 6 degree of freedom(DOF) nonlinear controller of a quadrotor UAV is designed using the trajectory linearization control(TLC) method. The overall controller contains a position sub-controller and an attitude sub-controller. The two controllers regulate the translational and rotational motion of the UAV, respectively. The controller is improved by using the commanded value instead of the nominal value as the input of the inner control loop. The performance of controller is tested by simulation before and after the improvement, the results show that the improved controller is better. The proposed controller is also tested via numerical simulation and real flights and is compared with the traditional controller based on Euler angles. The test results confirm the feasibility and the robustness of the proposed nonlinear controller. The proposed controller can successfully solve the singularity problem that usually occurs in the current attitude control of UAV and it is easy to be realized.

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References

  1. GOODARZI F, LEE D, LEE T. Geometric nonlinear PID control of a quadrotor UAV on SE(3)[C]//Proceeding of European Control Conference, Zurich, Switzerland, July 7–19, 2013: 3845–3850.

    Google Scholar 

  2. BOLANDI H, REZAEI M, MOHSENIPOUR R, et al. Attitude control of a quadrotor with optimized PID controller[J]. Intelligent Control & Automation, 2013, 4(3): 342–349.

    Article  Google Scholar 

  3. LUQUE-VEGA L, CASTILLO-TOLEDO B, LOUKIANOV A G. Robust block second order sliding mode control for a quadrotor[J]. Journal of the Franklin Institute, 2012, 349(2): 719–739.

    Article  MathSciNet  MATH  Google Scholar 

  4. ZHENG E H, XIONG J J, LUO J L. Second order sliding mode control for a quadrotor UAV[J]. Isa Transactions, 2014, 53(4): 1350–1356.

    Article  Google Scholar 

  5. PANOMRATTANARUG B, HIGUCHI K, MORA-CAMINO F. Attitude control of a quadrotor aircraft using LQR state feedback controller with full order state observer[C]//SICE Annual Conference, 2013 Proceedings of, Nagoya, Japan, September 14–17, 2013: 2041–2046.

    Google Scholar 

  6. ZHAO S L, AN H L, ZHANG D B, et al. A new feedback linearization LQR control for attitude of quadrotor[C]//2014 13th International Conference on Control Automation Robotics & Vision(ICARCV), Singapore, December 10–12, 2014: 1593–1597.

    Google Scholar 

  7. ZHENG F, GAO W N. Adaptive integral backstepping control of a micro-quadrotor[C]//International Conference on Intelligent Control and Information Processing, Harbin, China, July 25–28, 2011: 910–915.

    Google Scholar 

  8. DAS A, LEWIS F, SUBBARAO K. Backstepping approach for controlling a quadrotor using Lagrange form dynamics[J]. Journal of Intelligent & Robotic Systems, 2009, 56(1): 127–151.

    Article  MATH  Google Scholar 

  9. HAN J D, ZHU Z Q, JIANG Z Y, et al. Simple PID parameter tuning method based on outputs of the closed loop system[J]. Chinese Journal of Mechanical Engineering, 2016, 29(3): 465–474.

    Article  Google Scholar 

  10. REN H P, FAN J T. Adaptive backstepping slide mode control of pneumatic position servo system[J]. Chinese Journal of Mechanical Engineering, 2016, 29(6): 1003–1009.

    Article  Google Scholar 

  11. MELLINGER D, MICHAEL N, KUMAR V. Trajectory generation and control for precise aggressive maneuvers with quadrotors[J]. International Journal of Robotics Research, 2012, 31(5): 664–674.

    Article  Google Scholar 

  12. MELLINGER D, KUMAR V. Minimum snap trajectory generation and control for quad rotors[C]//2011 IEEE International Conference on Robotics and Automation(ICRA), Shanghai, China, May 9–13, 2011: 2520–2525.

    Chapter  Google Scholar 

  13. YU Y S, DING X L. On hybrid modeling and control of a multi-propeller multifunction aerial robot with flying-walking locomotion[J]. Autonomous Robots, 2015, 38(3): 225–242.

    Article  Google Scholar 

  14. DING X L, YU Y S, ZHU J J. Trajectory linearization tracking control for dynamics of a multi-propeller and multifunction aerial robot-MMAR[C]//Proceedings of IEEE International Conference on Robotics and Automation, Shanghai, China, May 9–13, 2011: 757–762.

    Google Scholar 

  15. PARK J. Interpolation and tracking of rigid body orientations[C]//2010 International Conference on Control Automation and System(ICCAS), Gyeonggi-do, October 27–30, 2010: 668–673.

    Google Scholar 

  16. LI J H, P W. Smooth interpolation on homogeneous matrix groups for computer animation[J]. Journal of Zhejiang University Science A(Science in Engineering), 2006, 7(7): 1168–1177.

    Article  MATH  Google Scholar 

  17. YU Y S, DING X L, ZHU J J. Attitude tracking control of a quadrotor UAV in the exponential coordinates[J]. Journal of the Franklin Institute, 2013, 350(8): 2044–2068.

    Article  MathSciNet  MATH  Google Scholar 

  18. LIU H, WANG X, ZHONG Y. Quaternion-based robust attitude control for uncertain robotic quadrotors[J]. IEEE Transactions on Industrial Informatics, 2015, 11(2): 406–415.

    Article  Google Scholar 

  19. ZHA C L, DING X L, YU Y S, et al. Design and implementation of a compact integrated navigation system for micro multi-propeller multifunction aerial robots[J]. Applied Mechanics & Materials, 2014, 556–562: 1553–1559.

    Article  Google Scholar 

  20. HUANG R, LIU Y, ZHU J J. Guidance, navigation, and control system design for tripropeller vertical-takeoff-and-landing unmanned air vehicle[J]. Journal of Aircraft, 2009, 46(6): 1837–1856.

    Article  Google Scholar 

  21. TITTERTON D H, WESTON J L. Strapdown inertial navigation technology[M] 2nd ed. London, United Kingdom: The Institution of Electrical Engineer, 2004.

    Book  Google Scholar 

  22. LI B K, CAO Y, ZHANG Q J, et al. Orientation-singularity representation and qrientation-capability computation of a special class of the gough-stewart parallel mechanisms using unit quaternion[J]. Chinese Journal of Mechanical Engineering, 2012, 25(6): 1096–1104.

    Article  Google Scholar 

  23. WU X F, IGNATOV R, MUENST G, et al. A nonlinear flight controller design for a UFO by trajectory linearization method. I. modeling[C]//System Theory, 2002. Proceedings of the Thirty-Fourth Southeastern Symposium on, Huntsville, Alabama, March 18–19, 2002: 97–102.

    Google Scholar 

  24. TAYEBI A, MCGILVRAY S. Attitude stabilization of a VTOL quadrotor aircraft[J]. IEEE Transactions on Control Systems Technology, 2006, 14(3): 562–571.

    Article  Google Scholar 

  25. MAHONY R, HAMEL T. Adaptive compensation of aerodynamic effects during takeoff and landing manoeuvres for a scale model autonomous helicopter[J]. European Journal of Control, 2001, 7(1): 43–57.

    Article  MATH  Google Scholar 

  26. ZHU J J. PD-spectral theory for multivariable linear time-varying systems[C]//Proceedings of IEEE Conference on Decision and Control, San Diego, CA, December 10–12, 1997: 3908–3913.

    Chapter  Google Scholar 

  27. WU X F, ADAMI T, CAMPBELL J, et al. A nonlinear flight controller design for a UFO by trajectory linearization method. II. controller design[C]//System Theory, 2002. Proceedings of the Thirty-Fourth Southeastern Symposium on, Huntsville, Alabama, March 18–19, 2002: 103–107.

    Google Scholar 

  28. LIU Y, ZHU J J, WILLIAMS R L, et al. Omni-directional mobile robot controller based on trajectory linearization[J]. Robotics and Autonomous Systems, 2008, 56(5): 461–479.

    Article  Google Scholar 

  29. SHEPPARD, S W, Quaternion from rotation Matrix[J]. Journal of Guidance and Control, 1978, 1(3): 223–224.

    Google Scholar 

  30. LEE T. Geometric tracking control of the attitude dynamics of a rigid body on SO(3)[C]//Proceedings of American Control Conference. San Francisco, CA, June 29–July 1, 2011: 1200–1205.

    Google Scholar 

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Beihang University, Beijing, 100191, China

    Changliu Zha, Xilun Ding, Yushu Yu & Xueqiang Wang

Authors
  1. Changliu Zha
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  2. Xilun Ding
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  3. Yushu Yu
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  4. Xueqiang Wang
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Corresponding author

Correspondence to Xilun Ding.

Additional information

Supported by National Science Foundation for Distinguished Young Scholars of China(Grant No. 51125020), National Natural Science Foundation of China(Grant No.51505014), and China Postdoctoral Science Foundation(Grant No. 2016T90024)

ZHA Changliu, born in 1975, is currently a PhD candidate at School of Mechanical Engineering and Automation, Beihang University, China. His research interests include navigation and control of robotic systems, in particular, aerial robots.

DING Xilun, born in 1967, is currently a professor and a PhD candidate supervisor at School of Mechanical Engineering and Automation, Beihang University, China. He received his PhD degree from Harbin Institute of Technology, China, in 1997. His research interests include the dynamics of compliant mechanical systems and robots, nonholonomic control of space robots, dynamics and control of aerial robots, and biomimetic robots.

YU Yushu, born in 1985, is currently a postdoctoral fellow at School of Mechanical Engineering and Automation, Beihang University, China. His research interests include dynamics and control of robotic systems, in particular, aerial robots.

WANG Xueqiang, born in 1988, is currently a PhD candidate at School of Mechanical Engineering and Automation, Beihang University, China. His research interests include dynamics and control of robotic systems, in particular, aerial robots.

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Zha, C., Ding, X., Yu, Y. et al. Quaternion-based nonlinear trajectory tracking control of a quadrotor unmanned aerial vehicle. Chin. J. Mech. Eng. 30, 77–92 (2017). https://doi.org/10.3901/CJME.2016.1026.127

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  • DOI: https://doi.org/10.3901/CJME.2016.1026.127

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