Kinematics and Dynamics of Fixed-Wing UAVs

Abstract

This chapter provides a review of basic knowledge required for accurate mathematical modeling of flight of a fixed-wing UAV. These include the kinematics and dynamics of motion, and the transformation of forces and moments acting on the airplane. The detailed discussion of the “kinematics–dynamics–actions” triad in application to a generic fixed-wing UAV is the main objective of this chapter. Therefore, the presentation starts with an introduction to the coordinate frames, their transformations, and differential rotations. Kinematics of the coordinate frames is what connects states of a fixed-wing UAV and transforms forces and moments acting in different coordinate frames. Understanding of reference frames and their dynamics is essential for the guidance, navigation, and control systems design. Next, the chapter provides a detailed derivation of the equations of motion using the Newtonian approach. Assuming that a fixed-wing UAV can be represented as a rigid body moving in an inertial space allows for the derivation of the linear and angular momentum equations. Starting in an inertial frame, it is shown how the final form of translational and rotational equations of motion becomes written in a body-fixed coordinate frame. The development of both the kinematic and dynamic equations is carried out first in a general vector form; then, using simplifying assumptions applicable to a generic fixed- wing symmetric UAV, the vector equations are expanded into a scalar form to better represent the resulting simplification and the physical meaning of the remaining components. Finally, the chapter presents the principles of defining the external forces and moments acting on a generic fixed-wing airplane. Since the forces and moments found on an airplane act in a number of coordinate frames including inertial, body-fixed, and wind frames, the chapter utilizes the concepts and tools built in the kinematics section to transform the forces and moments into the body-fixed frame. Such transformations complete the presentation of the “kinematics–dynamics–actions” triad.