Quaternions and Attitude Representation

• Rotation matrices: This is the most general form for representing attitude of a body, also called special orthogonal group SO(3) group, is the space of 3×3 matrices satisfying some constraints. Since it uses nine numbers to represent three angular degrees of freedom, there are six independent constraints on the matrix elements. Each column(and row) is unit vector, which gives us 3 constraints and the columns (and rows) are orthogonal to each other, yielding another 3 constraints. The translation (∈ R) and rotation together are represented as Special Euclidean group SE(3). The 6 constraints are larger compared to all other parameterizations mentioned below. They are therefore computationally more expensive than them. However, these have the advantage that they have no singularities or ambiguities such as double cover in attitude space in their representation as the rotation matrix is uniquely determined for a given configuration.