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

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 statespace 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.