Kris Hauser · University of Illinois · Course chapter

Coordinates and Transformations

A mathematical chapter connecting vectors, coordinates and transformations to physical quantities in robotics.

Source text reviewed October 27, 2026. Study notes and exercises are written by botstest.

Read the original ↗

Where to start

Review vectors and frame conventions before composing transformations.

Use it in your project

Label the source and destination frames of a small calculation, then check it against a visualization.

Scope and limitations

Requires linear-algebra foundations. The textbook is a draft, and numerical examples should be checked independently.

Follow a related roadmap

Learn robot mathematics and control through experiments · Beginner →

Read: Review vectors and frame conventions before composing transformations.

Use explicit frame conventions to catch reversed transforms, mixed units and misleading visual alignment.

Produce: Compute one camera-to-base point transform and label every frame and unit.

Integrate sensors and calibrate robot perception · Intermediate →

Read: Review vectors and frame conventions before composing transformations.

Use explicit frame conventions to catch reversed transforms, mixed units and misleading visual alignment.

Produce: Verify transformation direction and coordinate conventions before interpreting alignment residuals.