A fundamental requirement in robotics and computer vision is to represent the position and orientation of objects in an environment. Such objects include robots, cameras, workpieces, obstacles and paths. Position and orientation together is referred to as pose.

This chapter covers position, orientation and pose in 2D:

- Points in 2D space
- 2D coordinate frames
- Representing orientation in 2D using angles, orthonormal rotation matrices and matrix exponentials
- Representing pose in 2D using homogeneous transformation matrices and twists

and position, orientation and pose in 3D:

- Points in 3D space
- 3D coordinate frames
- Representing orientation in 3D using orthonormal rotation matrices, Euler angles, roll-pitch-yaw angles, unit-quaternions, matrix exponentials
- Representing pose in 3D using homogeneous transformation matrices and twists

as well as an introduction to configuration space.

## Gimbal lock

- LMA790-3-LM Appolo operations handbook, Fig 2.13 from my book is on page 44, and the vehcile’s coordinate frame is on page 16.
- Consideration of Apollo IMU gimbal lock, David Hoag (1963)
- Gimbal Angles, Gimbal Lock, and a Fourth Gimbal for Christmas, Eric Jones & Paul Fjeld.

### Quaternions

- Animating rotation with quaternion curves, Shoemake (1985). The classic paper on quaternion interpolation.
- Hamilton, Rodrigues, and the quaternion scandal

### Videos

- Transformation matrix, FAST lab