Representing Rotation

There are multiple ways to represent rotation so here is an overview of the ways, which are defined in ROS REP 103. The following are described in descending order of preferred use.

Quaternions

The preferred way of representing rotation.

Consists of a 4 element vector. Even though there are only 3 axis around which to rotate, a certain situation called gimbal lock can occur when describing rotation around the 3 axis (not important to know what gimbal lock is for our purposes). Quaternions are used to eliminate the problem of gimbal lock in computations.

Rotation Matrix

Often used to represent the rotation of a vector since vector-matrix multiplication is easy and fast to do. Rotation of a vector in 2D is given by a 2 x 2 rotation matrix while rotation of a vector in 3D is given by a 3 x 3 rotation matrix. Read More

We most see rotation matrices when using OpenCV for image processing and computer vision tasks.

Roll, Pitch, & Yaw

• Roll describes rotation about the x axis

• Pitch describes rotation about the y axis

• Yaw describes rotation about the z axis Often used for angular velocities.

Euler Angles

Similar to roll, pitch, and yaw expect instead of being in the x, y, z representation, they are in the z, y, x representation of yaw, pitch, and roll.

Generally discouraged from using Euler Angles in ROS robotics applications.