Using a Homogeneous Transformation Matrix to Combine Rotation and Translation

In this video we discuss how to properly deal with coordinate frames that are both rotated and translated from one another. We develop a homogeneous transformation matrix which combines a standard rotation matrix with a translation. This matrix can be used to relate the pose of a system in one frame to the pose in the other frame.

Topics and Timestamps:
0:03 – Introduction
1:24 – Development of homogeneous transformation in 2D
27:08 – Example
41:15 – Composite/successive transformations
59:35 – Extension to 3D

References:
-Expressing Vectors in Different Frames Using Rotation Matrices (
- Euler Angles and the Euler Rotation Sequence (

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Rotation matrix,translation and rotation,pose,robotic pose,