 # Robotics

## Summary of 3D geometry and pose

This video gives summary of 3D geometry and pose.

## Describing rotation and translation in 3D

We learn how to describe the 3D pose of an object by a 4×4 homogeneous transformation matrix which has a special structure.

## Quaternions representation of rotation in 3D

The orientation of a body in 3D can also be described by a unit-Quaternion, an unusual but very useful mathematical object.

## Angle-axis representation of rotation in 3D

The orientation of a body in 3D can also be described by a single rotation about a particular axis in space.

## 2-vector representation of rotation in 3D

The orientation of a body in 3D can also be described by two vectors, often called the approach and orientation vectors.

## Singularity in 3D rotation angle sequences

A problem arises when using three-angle sequences and particular values of the middle angle leads to a condition called a singularity. This mathematical phenomena is related to a problem that occurs in the physical world with mechanical gimbal systems.

## Rotation angle sequences in 3D

The orientation of a body in 3D can be described by three angles, examples of which are Euler angles and roll-pitch-yaw angles.

## Rotations are non commutative in 3D

If we apply a sequence of 3D rotations to an objects we see that the order in which they are applied affects the final result.

## Describing rotation in 3D

We learn how to describe the orientation of an object by a 3×3 rotation matrix which has some special properties.

## Relative pose in 3D

We consider multiple objects each with their own 3D coordinate frame. Now we can describe the relationships between the frames and find a vector describing a point with respect to any of these frames. We extend our previous 2D algebraic notation to 3D and look again at pose graphs.

## Pose in 3D

We extend the idea of relative pose, introduced in the last lecture, to 3D. We learn another right-hand rule that indicates the direction of rotation about an axis, and we see how we can attach 3D coordinate frames to objects to determine their pose in 3D space.

## Build your own 3D coordinate frame

This is an exercise in which you can build a 3D coordinate frame by printing, cutting, folding and stapling.

## Right-Handed 3D Coordinate Frame

We discuss the structure of a right-handed 3D coordinate frame and the spatial relationship between its axes which is encoded in the right-hand rule.

## Describing Position in 3D

We revisit the fundamentals of 3D geometry that you would have learned at school: coordinate frames, points and vectors.

## Introduction to 3D Geometry

We learn how to describe the position and orientation of objects in the 3-dimensional space that we live in. This builds on our understanding of describing position and orientation in two dimensions.

## Summary of 2D geometry and pose

This video gives summary of 2D geometry and pose.

## Describing rotation and translation in 2D

We learn how to describe the 2D pose of an object by a 3×3 homogeneous transformation matrix which has a special structure.

## Describing rotation in 2D

We learn how to describe the orientation of an object by a 2×2 rotation matrix which has some special properties.

## Developing a real representation of pose in 2D

The pose of an object can be considered in two parts, the position of the object and the orientation of the object.

## Relative pose in 2D

We consider multiple objects each with its own coordinate frame. Now we can describe the relationships between the frames and find a vector describing a point with respect to any of these frames. We extend our algebraic notation to ease the manipulation of relative poses.