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Quadrotor Energy-Based Control Laws: a Unit-Quaternion Approach

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Abstract

This article presents the designs, simulations and real-time experimental results of two energy-based control strategies to stabilize an Unmanned Aerial Vehicles (UAV) using a quaternion representation of the attitude. The mathematical model is based on Euler-Lagrange formulation using a logarithmic mapping in the quaternion space. The proposed solutions introduce a new approach: a quaternion-energy-based control, which use an energy-based expression defined as a Lyapunov function. The control laws are described with unit quaternions and their axis-angle representation. The proposed algorithms allow the stabilization of the quadrotor in all its states. The strategies ensure the stability of the closed loop system. Simulation results and experimental validations are developed to verify the effectiveness of the proposed controllers.

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References

  1. Fritsch, O., De Monte, P., Buhl, M., Lohmann, B.: Quasi-static feedback linearization for the translational dynamics of a quadrotor helicopter. In: American Control Conference (ACC), pp 125–130 (2012)

  2. Djamel, K., Abdellah, M., Benallegue, A.: Attitude Optimal Backstepping Controller Based Quaternion for a UAV. Hindawi Publishing Corporation Mathematical Problems in Engineering (2016). Article ID 8573235

  3. Chovancová, A., Fico, T., Hubinský, P., Duchon, F.: Comparison of various quaternion-based control methods applied to quadrotor with disturbance observer and position estimator. IEEE Robotics and Autonomous Systems 79, 87–98 (2016)

    Article  Google Scholar 

  4. Tayebi, A., McGilvray, S.: Attitude stabilization of a VTOL quadrotor aircraft. IEEE Trans. Control Syst. Technol. 14(3), 562–571 (2006)

    Article  Google Scholar 

  5. Sanchez, A., Parra-Vega, V., Garcia, O., Ruiz-Sanchez, F., Ramos-Velasco, L.E.: Time-parametrization control of quadrotors with a robust quaternion-based sliding mode controller for aggressive maneuvering. In: European Control Conference (ECC), Zurich, Switzerland, pp 3876–3881 (2013)

  6. Fresk, E., Nikolakopoulos, G.: Full quaternion based attitude control for a quadrotor. In: IEEE European Control Conference (ECC), Zurich, Switzerland (2013)

  7. Cariño, J., Abaunza, H., Castillo, P.: Quadrotor Quaternion Control. In: International Conference on Unmanned Aircraft Systems (ICUAS), Denver, USA (2015)

  8. Dargham, R., Medromi, H.: Euler and quaternion parameterization in VTOL UAV dynamics with test model efficiency. International Journal of Applied Information Systems (IJAIS) 9(8) (2015)

  9. Honglei, A., Jie, L., Jian, W., Jianwen, W., Hongxu, M.: Backstepping-based inverse optimal attitude control of quadrotor. Int. J. Adv. Robot. Syst. 10 (2013). doi:10.5772/56337

  10. El-Badawy, A.A., Bakr, M.A.: Quadrotor aggressive maneuvers along singular configurations: an energy-quaternion based approach. Journal of Control Science and Engineering, 7324540 (2016)

  11. Fritsch, O., Tromba, D., Lohmann, B.: Cascaded energy based trajectory tracking control of a quadrotor. Automatisierungstechnik 62(6), 408–422 (2014)

    Article  Google Scholar 

  12. Guerrero, M.E., Lozano, R., García, C.D.: Control Basado En Pasividad Para Un Quadrotor UAV. In: IEEE Congreso Nacional De Control Automático (AMCA), Morelos, Mexico (2015)

  13. Souza, C., Raffo, G.V., Castelan, E.B.: Passivity based control of a quadrotor. In: 19th World Congress the International Federation of Automatic Control (IFAC) Cape Town, South Africa, pp 24–29 (2014)

  14. Muñoz, L.E., Santos, O., Castillo, P., Fantoni, I.: Energy-based nonlinear control for a quadrotor rotorcraft. In: American Control Conference (ACC), Washington, DC, USA, pp 1177–1182 (2013)

  15. Kottenstette, N., Porter, J.: Digital passive attitude and altitude control schemes for quadrotor aircraft. In: IEEE International Conference on Control and Automation (ICCA), Christchurch, New Zealand, pp 1761–1768 (2009)

  16. Spring, K.W.: Euler parameters and the use of quaternion algebra in the manipulation of finite rotations: a review. Mech. Mach. Theory 21(5), 365–373 (1986)

    Article  Google Scholar 

  17. Altmann, S.L.: Hamilton, Rodrigues, and the quaternion scandal. Math. Mag., 291–308 (1989)

  18. Campa, R., Camarillo, K.: Unit quaternions: a mathematical tool for modeling, path planning and control of robot manipulators. In: Ceccarelli, M. (ed.) Robot Manipulators, In-Teh, pp 21–48 (2008)

  19. Kuipers, J.B.: Quaternions and Rotation Sequences, vol. 66. Princeton University Press, Princeton (1999)

    Google Scholar 

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Acknowledgment

The authors would like to thank the Mexican National Council for Science and Technology (CONACYT) for their support with the doctoral scholarships program, as well as the French National Network of Robotics Platforms (ROBOTEX).

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Authors and Affiliations

  1. Instituto Tecnológico Superior de Coatzacoalcos, Carretera Ant. Mina-Coatza Km. 16.5, Col. Las Gaviotas, CP 96536, Coatzacoalcos, Ver., México

    M. E. Guerrero-Sánchez

  2. Sorbonne Universités, UTC CNRS UMR 7253 Heudiasyc, Compiégne, France

    H. Abaunza, P. Castillo & R. Lozano

  3. Centro Nacional de Investigación y Desarrollo Tecnol´ogico, Interior Internadao Palmira S/N, Palmira, 62490, Cuernavaca, Mor., Mexico

    C. D. García-Beltrán

Authors
  1. M. E. Guerrero-Sánchez
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  2. H. Abaunza
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  3. P. Castillo
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  4. R. Lozano
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  5. C. D. García-Beltrán
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Correspondence to M. E. Guerrero-Sánchez.

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Guerrero-Sánchez, M.E., Abaunza, H., Castillo, P. et al. Quadrotor Energy-Based Control Laws: a Unit-Quaternion Approach. J Intell Robot Syst 88, 347–377 (2017). https://doi.org/10.1007/s10846-017-0528-3

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  • DOI: https://doi.org/10.1007/s10846-017-0528-3

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