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
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1093)


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.


Quadrotor Nonlinear optimal control SDRE Virtual constraint 



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 (; and ARM-EXTEND funded by the Spanish RD scheme (DPI2017-89790-R).


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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

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