Analysis of the Dynamics and Control of a Morphing Quadrotor

This paper will model a morphing quadrotor that is based on the works of Falanga etal [1]. It starts with the dynamics of a fixed geometry quadrotors. Getting a good understanding of the equations of motion for the system can help determine how each of the parameters can affect the system response. The use of multiple frames allows for simplification of the equation. This mixed frame approach and the use of rotation matrices significantly make the problem easier to solve. After learning about how each of the parameters affect the system, the inclusion of variable geometry means that the moment of inertia, the attitude controller gains, and the actuator controller methods require modifications. Using point masses to represent the major components of the quadrotor, estimation for the changing Moment of Inertia as a function of the morphing angle βk is calculated. Using Linear Quadratic Regulator, an adaptive attitude control allows for the changing gains to be possible mid-flight for better stability. Using the position vectors of the rotors with respect to the center of mass, the mapping for controller input, [T, Mφ, Mθ, Mψ]T, and rotor speed are determined. When comparing the simulation results with Falanga etal [1], the response follow a similar trend. Overall, the simulation response is adequate in showing the system behaviour when changing geometry mid-flight. Analysis in the variable thrust coefficient can get the simulation closer to the experimental results.