Attitude Estimation and Control

Attitude kinematics, which describes the orientation of three-dimensional shapes, is one of the fundamental properties of objects in a three-dimensional space. As one of the attitude parameterization methods, we introduce the intuitive concept of quaternions used in various applications. We present a rigorous approach for simulating the stochastic noise of attitude sensors and the attitude estimation problem. We introduce the quaternion estimation algorithm and the core concept of the Kalman filter. The extended Kalman filter ( EKF ) for the gyroscope bias estimation is derived. Symbolic computations help simplify the derivations and minimize the possible algebraic mistakes. We introduce attitude dynamics given by Euler's rigid-body rotational equation. The dynamics of a quadcopter including propellers and motors is derived. The attitude control problem for stabilizing the quadcopters is established. A controller based on Lyapunov stability is implemented for the quadcopter attitude stabilization. Finally, the robustness of the non-linear closed-loop system is verified using the Monte Carlo simulations. Multi-core parallel processing accelerates the computing speed for the Monte Carlo simulations.