# I. Fundamentals

This part discusses what the word robot means to roboticists and the wider public, the history of the field, and the different forms that robots take today. A definition that will serve us well is:

## a goal oriented machine that can sense, plan and act

We then move on to cover how we can represent the position and orientation of objects in 2- or 3-dimensional environments in terms of graphical coordinate frames. The objects might be robots, cameras, objects or obstacles. In order to use these frames in a computer program we need an appropriate representation and we discuss vectors, orthonormal rotation matrices, triple angles, homogeneous transformation matrices and quaterions.

Finally we discuss motion, how to generate a sequence of coordinate frames that represent smooth motion from one pose to another. We also consider how to process information from sensors on a moving frame to determine the pose of that frame.

1. Representing position & orientation
• Pose in 2-dimensions
• Pose in 3-dimensions
• Orthonormal rotation matrices, homogeneous transformation matrices
• Euler angles, roll-pitch-yaw angles, gimbal lock, quaternions
2. Time & motion
• Trajectories: 1-dimensional, multi-dimensional, multi-segment
• Interpolation of rotation
• Smooth Cartesian motion
• Time-varying coordinate frames, angular velocity