This is the first in a series of posts about the data driven control of an aircraft. This post will be about coordinate conventions.
There are many coordinate systems used in aerospace engineering. The most common ones are the inertial frame, the body frame, and the wind (or stability) frame. In the further work of this project I will assume the inertial frame to be defined relative to a stationary point on the surface of the earth. I will align the x-direction with north, the y-direction with east, and the z-direction with the gravity vector. I neglect the effects of the earth’s rotation and curvature due to the small size of the aircraft and the short time scales and distances of the flight.
The body frame is centered at the centre of mass of the aircraft, the x-axis of the body frame runs through the nose of the aircraft, the y-axis runs through the right wing, and the z-axis is perpendicular to these in a right-handed manner (pointing down).
The stability frame is rotated relative to the body frame around the y-axis by the angle of attack. This coordinate frame is often used to treat aerodynamic forces and moments. This frame is not currently used in this project as the forces are calculated directly in the body frame.
Coordinate transformations between these frames will be addressed following the definition of the state vector.
]]>This post will be about the state definition.
Taken from the book “Aircraft Control and Simulation” by Stevens and Lewis, the state is defined as: \(\begin{bmatrix} \vec{x}_i \\ \vec{v}_i \\ \bar{q}_i^b \\ \vec{\omega}_b \end{bmatrix}\)
Where $\vec{x}_i$ is the position of the aircraft in the inertial frame, $\vec{v}_i$ is the velocity of the aircraft in the inertial frame, $\bar{q}_i^b$ is the attitude of the aircraft in the inertial frame, and $\vec{\omega}_b$ is the angular velocity of the aircraft in the body frame.
]]>In this post I will be discussing the coordinate transformations between the inertial frame, the body frame, and the wind (or stability) frame.
The conversion from the body frame to the inertial frame is done using the following transformation: \(\vec{v}_i = q_i^b \otimes \vec{v}_b \otimes q_b^i\) whereby $\otimes$ is the quaternion multiplication and $q_b^i = (q_i^b)^{-1}$ is the attitude quaternion that represents the rotation from the inertial frame to the body frame.
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