A Model Predictive Control (MPC) Approach on Unit Quaternion Orientation Based Quadrotor for Trajectory Tracking

  • Maidul IslamEmail author
  • Mohamed Okasha
  • Erwin SulaemanEmail author


The objective of this paper is to introduce with a quaternion orientation based quadrotor that can be controlled by Model Predictive Control (MPC). As MPC offers promising performance in different industrial applications, quadrotor can be another suitable platform for the application of MPC. The present study consistently adopts unit quaternion approach for quadrotor orientation in order to avoid any axes overlapping problem, widely known as singularity problem whereas Euler angle orientation approach is unable to resolve so. MPC works based on the minimal cost function that includes the attitude error and consequently, the cost function requires quaternion error in order to proceed with process of MPC. Therefore, the main contribution of this study is to introduce a newly developed cost function for MPC because by definition, quaternion error is remarkably different from the attitude error of Euler angle. As a result, a unit quaternion based quadrotor with MPC can ascertain a smooth singularity-free flight that is influenced by model uncertainty. MATLAB and Simulink environment has been used to validate the cost function for quaternion by simulating several trajectories.


Constraint handling cost function disturbance and noise path/trajectory tracking quadrotor quaternion 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



  1. [1]
    P. Foehn and D. Scaramuzza, “Onboard state dependent LQR for Agile Quadrotors,” Proc. of IEEE International Conference on Robotics and Automation (ICRA), IEEE, pp. 6566–6572, 2018.Google Scholar
  2. [2]
    E. Hernandez-Martinez, G. Fernandez-Anaya, E. Ferreira, J. Flores-Godoy, and A. Lopez-Gonzalez, “Trajectory tracking of a quadcopter UAV with optimal translational control,” IFAC-PapersOnLine, vol. 48, no. 19, pp. 226–231, 2015.CrossRefGoogle Scholar
  3. [3]
    A. K. Shastry, M. T. Bhargavapuri, M. Kothari, and S. R. Sahoo, “Quaternion based adaptive control for package delivery using variable-pitch quadrotors,” Proc. of Indian Control Conference (ICC), IEEE, pp. 340–345, 2018.Google Scholar
  4. [4]
    X. Zhang, X. Li, K. Wang, and Y. Lu, “A survey of modelling and identification of quadrotor robot,” Abstract and Applied Analysis, vol. 2014, Article ID 320526, 16 pages, 2014.Google Scholar
  5. [5]
    H. Parwana, J. S. Patrikar, and M. Kothari, “A novel fully quaternion based nonlinear attitude and position controller,” Proc. of AIAA Guidance, Navigation, and Control Conference, p. 1587, 2018.Google Scholar
  6. [6]
    S. Swarnkar, H. Parwana, M. Kothari, and A. Abhishek, “Biplane-quadrotor tail-sitter UAV: flight dynamics and control,” Journal of Guidance, Control, and Dynamics, vol. 41, no. 5, pp. 1049–1067, 2018.CrossRefGoogle Scholar
  7. [7]
    E. Fresk and G. Nikolakopoulos, “Full quaternion based attitude control for a quadrotor,” Proc. of European Control Conference (ECC), IEEE, pp. 3864–3869, 2013.Google Scholar
  8. [8]
    F. Kendoul, “Survey of advances in guidance, navigation, and control of unmanned rotorcraft systems,” Journal of Field Robotics, vol. 29, no. 2, pp. 315–378, 2012.CrossRefGoogle Scholar
  9. [9]
    M. Islam, M. Okasha, and M. M. Idres, “Trajectory tracking in quadrotor platform by using PD controller and LQR control approach,” IOP Conference Series: Materials Science and Engineering, vol. 260, no. 1, p. 012026, 2017.CrossRefGoogle Scholar
  10. [10]
    C. J. Ostafew, Learning-based Control for Autonomous Mobile Robots, Doctor of Philosophy, University of Toronto, Canada, 2016.Google Scholar
  11. [11]
    A. Kehlenbeck, Quaternion-based Control for Aggressive Trajectory Tracking with a Micro-quadrotor UAV, University of Maryland, College Park, 2014.Google Scholar
  12. [12]
    E. Reyes-Valeria, R. Enriquez-Caldera, S. Camacho-Lara, and J. Guichard, “LQR control for a quadrotor using unit quaternions: Modeling and simulation,” Proc. of International Conference on Electronics, Communications and Computing (CONIELECOMP), IEEE, pp. 172–178, 2013.Google Scholar
  13. [13]
    K. Djamel, M. Abdellah, and A. Benallegue, “Attitude optimal backstepping controller based quaternion for a uav,” Mathematical Problems in Engineering, vol. 2016, 2016.Google Scholar
  14. [14]
    C. Zha, X. Ding, Y. Yu, and X. Wang, “Quaternion-based nonlinear trajectory tracking control of a quadrotor unmanned aerial vehicle,” Chinese Journal of Mechanical Engineering, vol. 30, no. 1, pp. 77–92, 2017.CrossRefGoogle Scholar
  15. [15]
    T.-T. Tran and C. Ha, “Self-tuning proportional double derivative-like neural network controller for a quadrotor,” International Journal of Aeronautical and Space Sciences, vol. 19, no. 4, pp. 976–985, 2018.MathSciNetCrossRefGoogle Scholar
  16. [16]
    C. Liu, H. Lu, and W.-H. Chen, “An explicit MPC for quadrotor trajectory tracking,” Proc. of the 34th Chinese Control Conference (CCC), IEEE, pp. 4055–4060, 2015.Google Scholar
  17. [17]
    W. Zhao and T. H. Go, “Quadcopter formation flight control combining MPC and robust feedback linearization,” Journal of the Franklin Institute, vol. 351, no. 3, pp. 1335–1355, 2014.MathSciNetCrossRefGoogle Scholar
  18. [18]
    M. Bangura and R. Mahony, “Real-time model predictive control for quadrotors,” IFAC Proceedings Volumes, vol. 47, no. 3, pp. 11773–11780, 2014.CrossRefGoogle Scholar
  19. [19]
    M. Chipofya, D. J. Lee, and K. T. Chong, “Trajectory tracking and stabilization of a quadrotor using model predictive control of Laguerre functions,” Abstract and Applied Analysis, vol. 2015, Article ID 916864, 11 pages, 2015.Google Scholar
  20. [20]
    K. Alexis, G. Nikolakopoulos, and A. Tzes, “On trajectory tracking model predictive control of an unmanned quadrotor helicopter subject to aerodynamic disturbances,” Asian Journal of Control, vol. 16, no. 1, pp. 209–224, 2014.MathSciNetCrossRefGoogle Scholar
  21. [21]
    M. Islam, M. Okasha, and M. Idres, “Dynamics and control of quadcopter using linear model predictive control approach,” IOP Conference Series: Materials Science and Engineering, vol. 270, no. 1, p. 012007, 2017.CrossRefGoogle Scholar
  22. [22]
    T. Zhang, G. Kahn, S. Levine, and P. Abbeel, “Learning deep control policies for autonomous aerial vehicles with mpc-guided policy search,” Proc. of IEEE International Conference on Robotics and Automation (ICRA), IEEE, pp. 528–535, 2016.Google Scholar
  23. [23]
    C. Kanellakis, S. S. Mansouri, and G. Nikolakopoulos, “Dynamic visual sensing based on MPC controlled UAVs,” Proc. of the 25th Mediterranean Conference on Control and Automation (MED), IEEE, pp. 1201–1206, 2017.Google Scholar
  24. [24]
    T. Engelhardt, T. Konrad, B. Schäfer, and D. Abel, “Flatness-based control for a quadrotor camera helicopter using model predictive control trajectory generation,” Proc. of the 24th Mediterranean Conference on Control and Automation (MED), IEEE, pp. 852–859, 2016.Google Scholar
  25. [25]
    A. Chovancová, T. Fico, P. Hubinský, and F. Duchonˇ, “Comparison of various quaternion-based control methods applied to quadrotor with disturbance observer and position estimator,” Robotics and Autonomous Systems, vol. 79, pp. 87–98, 2016.CrossRefGoogle Scholar
  26. [26]
    J.-F. Guerrero-Castellanos, J. J. Téllez-Guzmán, S. Durand, N. Marchand, J. Alvarez-Muñoz, and V. R. Gonzalez-Diaz, “Attitude stabilization of a quadrotor by means of event-triggered nonlinear control,” Journal of Intelligent & Robotic Systems, vol. 73, no. 1–4, pp. 123–135, 2014.CrossRefGoogle Scholar
  27. [27]
    A. Sudbery, “Quaternionic analysis,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 85, no. 2, pp. 199–225, Cambridge University Press, 1979.MathSciNetCrossRefGoogle Scholar
  28. [28]
    J. Diebel, “Representing attitude: Euler angles, unit quaternions, and rotation vectors,” Matrix, vol. 58, no. 15–16, pp. 1–35, 2006.Google Scholar
  29. [29]
    A. Chovancová, T. Fico, L’. Chovanec, and P. Hubinsk, “Mathematical modelling and parameter identification of quadrotor (a survey),” Procedia Engineering, vol. 96, pp. 172–181, 2014.CrossRefGoogle Scholar
  30. [30]
    S. Lindblom and A. Lundmark, Modelling and Control of a Hexarotor UAV, Linköpings universitet, 2015.Google Scholar
  31. [31]
    J.-L. Blanco, “A tutorial on se (3) transformation parameterizations and on-manifold optimization,” University of Malaga, Tech. Rep, vol. 3, 2010.Google Scholar
  32. [32]
    S. Bouabdallah, “Design and control of quadrotors with application to autonomous flying,” 2007.Google Scholar
  33. [33]
    J. Zhang, X. Cheng, and J. Zhu, “Control of a laboratory 3-DOF helicopter: Explicit model predictive approach,” International Journal of Control, Automation and Systems, vol. 14, no. 2, pp. 389–399, 2016.CrossRefGoogle Scholar
  34. [34]
    M. H. Murillo, A. C. Limache, P. S. R. Fredini, and L. L. Giovanini, “Generalized nonlinear optimal predictive control using iterative state-space trajectories: Applications to autonomous flight of UAVs,” International Journal of Control, Automation and Systems, vol. 13, no. 2, pp. 361–370, 2015.CrossRefGoogle Scholar
  35. [35]
    A.-W. A. Saif, A. Aliyu, M. Al Dhaifallah, and M. Elshafei, “Decentralized Backstepping Control of a Quadrotor with Tilted-rotor under Wind Gusts,” International Journal of Control, Automation and Systems, vol. 16, no. 5, pp. 2458–2472, 2018.CrossRefGoogle Scholar
  36. [36]
  37. [37]
    I. Kugelberg, Black-box Modeling and Attitude Control of a Quadcopter, Master of Science Thesis, Linköping University, 2016.Google Scholar
  38. [38]
    Y. Wang, A. Ramirez-Jaime, F. Xu, and V. Puig, “Nonlinear model predictive control with constraint satisfactions for a quadcopter,” Journal of Physics: Conference Series, vol. 783, no. 1, p. 012025, 2017.Google Scholar
  39. [39]
    W. Zhu, H. Du, Y. Cheng, and Z. Chu, “Hovering control for quadrotor aircraft based on finite-time control algorithm,” Nonlinear Dynamics, vol. 88, no. 4, pp. 2359–2369, 2017.MathSciNetCrossRefGoogle Scholar
  40. [40]
    L. V. Santana, A. S. Brandão, and M. Sarcinelli-Filho, “Navigation and cooperative control using the ar. drone quadrotor,” Journal of Intelligent & Robotic Systems, vol. 84, no. 1–4, pp. 327–350, 2016.CrossRefGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringInternational Islamic University MalaysiaKuala LumpurMalaysia

Personalised recommendations