Rigid-body transformations enable us to systematically describe a rigid body’s position and orientation by attaching a reference frame to the body. Exciting!!!
See Spatial Algebra for the rigorous notation.
- Allows you to easily convert between different formats
Books that cover this topic:
- tf2 implementation of transforms in ROS
- Matrix algebra and 2D rotations by Steven M. Lavalle
- F1TENTH L03 - Rigid Body Transformations by F1TENTH (only really covers 2D well), Google Slides
There are two types of transformations:
- Static Transformations (ex: between
- fixed, never moves
- Dynamic Transformations (ex: between
- changes as the robot moves
Rotate first, and then translate
I think that intuition is sort of confusing. You don’t get any idea of why. See Spatial Algebra, just break down the transform.