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:

• Modern Robotics
• Planning Algorithms by Steven M. Lavalle
• Visual SLAM book

Concepts

• tf2 implementation of transforms in ROS

Some lectures:

• 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:

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.

Concepts

• Spatial Algebra for the stuff learned through Robot Manipulation
• Linear Transformation
• Coordinate Frame
• Rotation Matrix
• Quaternion
• tf2
• URDF