An application of the extended Kalman filter to the attitude control of a quadrotor

The focus of this thesis is the application of the extended Kalman filter to the attitude control system of a four-propellers unmanned aerial vehicle usually known as quadrotor. The Kalman filter is a mathematical tool well suited for an algorithmic implementation that estimates the state of a dynamic system influenced by random noise given a set of measurements which are also corrupted by random noise. If the system and measurement eqautions are linear functions of the state variables and the noises are both normally distributed, the filter is proven to be an optimal estimator. In practice, the linearity conditions are often not satisfyed, but some rielaborations of the filter algorithm have still been used for more than fourty years in many applications with good results. The extended Kalman filter (EKF), used in this thesis, is one of the first and best known nonlinear filter versions. A quadrotor is a helicopter lifted and propelled by four rotors. Small sized quadrotors are often used as UAVs (unamanned aerial vehicles) in research and amateur projects, because of the simple symmetric structure and relatively easy control law with respect to traditional helicopters. In this thesis, the extended Kalman filter is applied to estimate the state of the quadrotor from the noisy measurements of on board low-cost MEMS sensors. The estimated state is intended to be used by a control algorithm (not discussed in this work) to maintain the desired attitude during various maneouvers. The EKF is implemented in Simulink in both continuous and discrete time, as an extension of a pre-existing model, which simulates the dynamics and control of a quadrotor. The performance and stability of the system is then analyzed with many test cases, from simple hovering to complex trajectories, both with open and closed loop control. The model is also tested for robustness in case of errors in the measurements of physical parameters and incorrect sensor calibration.