Rigid-Body Transformations

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.

Best Tool: https://www.andre-gaschler.com/rotationconverter/

  • Allows you to easily convert between different formats

Books that cover this topic:


  • tf2 implementation of transforms in ROS

Some lectures:

There are two types of transformations:

  1. Static Transformations (ex: between laser and base_link)
    • fixed, never moves
  2. Dynamic Transformations (ex: between laser and map),
    • 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.