Flight dynamics and nonlinear control design for variable-pitch quadrotors

This paper introduces the mathematical model for quadrotor with variable-pitch propellers that facilitates generation of negative thrust, thereby augmenting the rate of change of thrust generation suitable for aggressive maneuvering. Blade element theory along with momentum theory is used to estimate aerodynamic loads essential for formulating rigid body dynamics model of the vehicle. Further, the paper develops a nonlinear controller using dynamic inversion technique to stabilize and/or to track a reference trajectory. The controller uses three loops. The outer loop solves the translation dynamics to generate the thrust, pitch angle, and roll angle commands required to achieve a given state or trajectory. Using the commands generated in the outer loop, the inner loop simplifies the rotational dynamics to provide the desired angular velocities. The control allocation loop is added to address the nonlinear relation between control input and rotor thrust and torque. This is done by introducing the derivative of thrust coefficient as a virtual control to the system. These virtual inputs control the derivatives of thrust and body moments, which in turn generates the required thrust and body moments. The performance of the proposed design is shown through simulated results for attitude stabilization and trajectory following.