Attitude Kinematics: Modeling and Feedback

This chapter presents the state-space equations of the attitude kinematics for the three representations treated in Chapter 2 (rotation matrix matrix, Euler angles, quaternion). After an introduction to the kinematics of the rotation matrix and Euler angles, with examples and exercises, the chapter focuses on the quaternion kinematics and, specifically, on the error quaternion kinematics as the fundamental model for the feedback design of attitude prediction/estimation and control. The emphasis is just on attitude prediction and not on attitude control, as the latter requires the addition of the attitude dynamics to the design model of the attitude control. Attitude dynamics is treated in Chapter 7 . A specific state predictor, whose aim is to predict the attitude and the bias of the angular rate sensor (3D gyroscope), is designed and extensively studied. The simulated results are compared with the classical Kalman filter.