Module 3
Transformations
Transformations are the language of robot motion. This module covers how matrices represent rotations, translations, and scaling in 2D and 3D, building toward the homogeneous transformation matrices used in every robotics application.
What You'll Learn
- Represent rotations, translations, and scaling as matrices
- Compose transformations in the correct order (right-to-left)
- Work with Euler angles and understand gimbal lock
- Use homogeneous transformation matrices (SE(2), SE(3))
- Apply transformation chaining to compute robot forward kinematics
Lessons
3
Interactives
3
Duration
~100 min
Lesson 1 30 min
2D Transformations
Master rotation, translation, and scaling in 2D. Understand transformation composition order and see how a mobile robot's pose is described mathematically.
RotationTranslationScalingComposition Mobile Robot Pose
Lesson 2 35 min
3D Rotations
Explore rotations around X, Y, Z axes and Euler angle representations. Discover gimbal lock and understand robot end-effector orientation.
Euler AnglesRotation MatricesGimbal Lock End-Effector Orientation
Lesson 3 35 min
Homogeneous Coordinates
Combine rotation and translation into a single matrix using homogeneous coordinates. Build a 2-link robot arm and compute forward kinematics through transformation chaining.
SE(2)SE(3)Coordinate Frames Forward Kinematics
Module Objectives
By the end of this module, you'll understand transformations and be able to:
- Build rotation, translation, and scaling matrices in 2D and 3D
- Compose transformations correctly (understanding non-commutativity)
- Use Euler angles and recognize gimbal lock situations
- Construct homogeneous transformation matrices in SE(2) and SE(3)
- Chain transforms to compute forward kinematics for a robot arm