Contents
What is the purpose of quaternions?
Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis.
What is attitude error?
Attitude error is defined as the rotation between true and estimated orientations. Two distinct approaches to attitude error kinematics are developed. In the first, the estimated angular velocity is defined in the true attitude axes frame, while in the second, it is defined in the estimated attitude axes frame.
How do you calculate attitude error?
The attitude error is described by the corrective attitude matrix: δ C = C C ^ T . In fact, the product between δ C and the estimated attitude C ^ provides the true attitude: δ C C ^ = ( C C ^ T ) C ^ = C .
What are modified Rodrigues parameters?
The modified Rodrigues parameters (MRPs) constitute a minimal rotation parameterization with attractive properties. An important finding is that the Jacobian of a quaternion is a polynomial function of its scalar and vector parts, thereby yielding simple expressions in rotation derivatives.
How do you find the inverse quaternion?
The inverse of a quaternion refers to the multiplicative inverse (or 1/q) and can be computed by q-1=q’/(q*q’) for any non-zero quaternion.
How is attitude determined using quaternion based method?
To construct a feedback control system, we need to extract quaternion information from vector measurements; we therefore discuss the quaternion based attitude determination method. With all these preparations, we will discuss the control system design methods based on quaternion models and quaternion attitude information.
How are quaternions used to represent an orientation?
When used to represent an orientation (rotation relative to a reference coordinate system), they are called orientation quaternions or attitude quaternions. A spatial rotation around a fixed point of radians about a unit axis that denotes the Euler axis is given by the quaternion
Are there any problems with a quaternion based control system?
The main problem with the quaternion model based control system design is that the linearized quaternion model is not controllable, therefore most published design methods heavily rely on Lyapunov functions for the nonlinear system, and there is not a systematic way to get the Lyapunov functions.
Which is an example of an attitude error?
ATTITUDE ERROR: “Low Frequency” spacecraft misalignment; usually the intended topic of attitude control. ATTITUDE JITTER: “High Frequency” spacecraft misalignment; usually ignored by ADCS; reduced by good design or fine pointing/optical control.