Advertisement

Fully Coupled Six-DoF Nonlinear Suboptimal Control of a Quadrotor: Application to Variable-Pitch Rotor Design

  • Saeed Rafee NekooEmail author
  • José Ángel Acosta
  • Aníbal Ollero
Conference paper
  • 79 Downloads
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1093)

Abstract

In this work, a fully coupled six degree-of-freedom (DoF) nonlinear suboptimal control of a variable-pitch quadrotor is studied using a state-dependent Riccati equation (SDRE) controller. The quadrotor control has been widely considered for attitude control; however, the position control is an uncontrollable problem with the common design of the SDRE. Due to the under-actuated nature of a quadrotor, the state-dependent coefficient (SDC) parameterization of state-space representation of a nonlinear system leads to an uncontrollable SDC pair. The control law is divided into two sections of position and attitude control. The position control provides the main thrust. A virtual constraint is regarded to provide stabilization for the quadrotor in attitude control. Two methods were designed for selection of a state vector or in other words, selection of feedback. The first one uses the position and orientation and their derivatives in global coordinate. The second one uses position and orientation in global and their velocities in local coordinate. The dynamics of a variable-pitch propeller quadrotor was imported to the problem and compared with a fixed-pitch propeller system. The simulation of the systems shows that the SDRE is capable of controlling the system with both fixed- and variable-pitch rotor dynamics.

Keywords

Quadrotor Nonlinear optimal control SDRE Virtual constraint 

Notes

Acknowledgements

This work is supported by the HYFLIER project (HYbrid FLying-rolling with-snakE-aRm robot for contact inspection) funded by the European Commission H2020 Programme under grant agreement ID: 779411 (https://cordis.europa.eu/project/rcn/213049); and ARM-EXTEND funded by the Spanish RD scheme (DPI2017-89790-R).

References

  1. 1.
    Voos, H.: Nonlinear state-dependent Riccati equation control of a quadrotor UAV. In: IEEE Computer Aided Control System Design, IEEE International Conference on Control Applications, IEEE International Symposium on Intelligent Control, pp. 2547–2552. IEEE (2006)Google Scholar
  2. 2.
    Voos, H.: Nonlinear and neural network-based control of a small four-rotor aerial robot. In: IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 1–6. IEEE (2007)Google Scholar
  3. 3.
    Navabi, M., Mirzaei, H.: θ-D based nonlinear tracking control of quadcopter. In: 4th International Conference on Robotics and Mechatronics, pp. 331–336. IEEE (2016)Google Scholar
  4. 4.
    Babaie, R., Ehyaie, A.F.: Robust optimal motion planning approach to cooperative grasping and transporting using multiple UAVs based on SDRE. Trans. Inst. Measur. Control 39, 1391–1408 (2017)CrossRefGoogle Scholar
  5. 5.
    Chipofya, M., Lee, D.J.: Position and altitude control of a quadcopter using state-dependent Riccati equation (SDRE) control. In: 17th International Conference on Control, Automation and Systems, pp. 1242–1244. IEEE (2017)Google Scholar
  6. 6.
    Cutler, M., Ure, N.-K., Michini, B., How, J.: Comparison of fixed and variable pitch actuators for agile quadrotors. In: AIAA Guidance, Navigation, and Control Conference, pp. 6406–6423 (2011)Google Scholar
  7. 7.
    Bristeau, P.-J., Martin, P., Salaün, E., Petit, N.: The role of propeller aerodynamics in the model of a quadrotor UAV. In: European Control Conference, pp. 683–688. IEEE (2009)Google Scholar
  8. 8.
    Fresk, E., Nikolakopoulos, G.: Experimental model derivation and control of a variable pitch propeller equipped quadrotor. In: IEEE Conference on Control Applications, pp. 723–729. IEEE (2014)Google Scholar
  9. 9.
    Sheng, S., Sun, C.: Control and optimization of a variable-pitch quadrotor with minimum power consumption. Energies 9, 232–250 (2016)CrossRefGoogle Scholar
  10. 10.
    Panizza, P., Invernizzi, D., Riccardi, F., Formentin, S., Lovera, M.: Data-driven attitude control law design for a variable-pitch quadrotor. In: American Control Conference, pp. 4434–4439. IEEE (2016)Google Scholar
  11. 11.
    Chipade, V.S., Kothari, M., Chaudhari, R.R.: Systematic design methodology for development and flight testing of a variable pitch quadrotor biplane VTOL UAV for payload delivery. Mechatronics 55, 94–114 (2018)CrossRefGoogle Scholar
  12. 12.
    Bhargavapuri, M., Sahoo, S.R., Kothari, M.: Robust nonlinear control of a variable-pitch quadrotor with the flip maneuver. Control Eng. Pract. 87, 26–42 (2019)CrossRefGoogle Scholar
  13. 13.
    Korayem, M.H., Nekoo, S.R.: Finite-time state-dependent Riccati equation for time-varying nonaffine systems: rigid and flexible joint manipulator control. ISA Trans. 54, 125–144 (2015)CrossRefGoogle Scholar
  14. 14.
    Cimen, T.: Survey of state-dependent Riccati equation in nonlinear optimal feedback control synthesis. J. Guid. Control Dyn. 35, 1025–1047 (2012)CrossRefGoogle Scholar
  15. 15.
    Zuo, Z.: Trajectory tracking control design with command-filtered compensation for a quadrotor. IET Control Theory Appl. 4, 2343–2355 (2010)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Das, A., Subbarao, K., Lewis, F.L.: Dynamic inversion with zero-dynamics stabilisation for quadrotor control. IET Control Theory Appl. 3, 303–314 (2009)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Luukkonen, T.: Modelling and control of quadcopter. Independent research project in applied mathematics, Espoo 22 (2011)Google Scholar
  18. 18.
    Shastry, A.K., Bhargavapuri, M.T., Kothari, M., Sahoo, S.R.: Quaternion based adaptive control for package delivery using variable-pitch quadrotors. In: Indian Control Conference, pp. 340–345. IEEE (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Saeed Rafee Nekoo
    • 1
    Email author
  • José Ángel Acosta
    • 1
  • Aníbal Ollero
    • 1
  1. 1.GRVC Robotics Lab., Departamento de Ingeniería de Sistemas y Automática, Escuela Técnica Superior de IngenieríaUniversidad de SevillaSevilleSpain

Personalised recommendations