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.
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References
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)
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)
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)
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)
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)
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)
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)
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)
Sheng, S., Sun, C.: Control and optimization of a variable-pitch quadrotor with minimum power consumption. Energies 9, 232–250 (2016)
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)
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)
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)
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)
Cimen, T.: Survey of state-dependent Riccati equation in nonlinear optimal feedback control synthesis. J. Guid. Control Dyn. 35, 1025–1047 (2012)
Zuo, Z.: Trajectory tracking control design with command-filtered compensation for a quadrotor. IET Control Theory Appl. 4, 2343–2355 (2010)
Das, A., Subbarao, K., Lewis, F.L.: Dynamic inversion with zero-dynamics stabilisation for quadrotor control. IET Control Theory Appl. 3, 303–314 (2009)
Luukkonen, T.: Modelling and control of quadcopter. Independent research project in applied mathematics, Espoo 22 (2011)
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)
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).
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Nekoo, S.R., Acosta, J.Á., Ollero, A. (2020). Fully Coupled Six-DoF Nonlinear Suboptimal Control of a Quadrotor: Application to Variable-Pitch Rotor Design. In: Silva, M., Luís Lima, J., Reis, L., Sanfeliu, A., Tardioli, D. (eds) Robot 2019: Fourth Iberian Robotics Conference. ROBOT 2019. Advances in Intelligent Systems and Computing, vol 1093. Springer, Cham. https://doi.org/10.1007/978-3-030-36150-1_7
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