Attitude and Orientation Page

[tordnat]

Use lie groups to derive the SO(3) and SE(3) to make it obvious why we use skew-symmetric matrices and orthogonal matrices etc.

[tordnat]

Need to derive rodrigues formula from trigonometric series and skew symmetric exponentials -> VERY clearly an exponential map from so(3) to SO(3)

[tordnat]

• Terminology: https://en.wikipedia.org/wiki/Orientation_(geometry) attitude vs orientation
• Why SO(3)? Why not O(3) -> Intuitive lens on reflections and preserving vector space
• Intuitive relation to so(3) and skew-symmetry -> Why rank deficiency -> Compact constraints etc
• Some brief history anecdote about Sophus Lie

[tordnat]

Sources:

• Edmund Brekke's Sensor fusion book
• https://dominicplein.medium.com/extrinsic-intrinsic-rotation-do-i-multiply-from-right-or-left-357c38c1abfd
• Introduction to 3D Vision - Ma, Soatto