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## 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.

## Relative Positions in 2D

We introduce the idea of attaching a coordinate frame to an object. We can describe points on the object by constant vectors with respect to the object’s coordinate frame, and then relate those to the points described with respect to a world coordinate frame. We introduce a simple algebraic notation to describe this.

## Position and Pose in 2D

To fully describe an object on the plane we need to not only describe its position, but also which direction it is pointing. This combination is referred to as pose.

## 2D Geometry Refresher

We revisit the fundamentals of geometry that you would have learned at school: Euclidean geometry, Cartesian or analytic geometry, coordinate frames, points and vectors.

## Introduction to 2D Geometry

We learn how to describe the position and orientation of objects on a 2-dimensional plane. We introduce the notion of reference frames as a basis for describing the position of objects in two dimensions.

## Summary of robots and why we need them

This video gives summary of robots and why we need them.

## Why do we need robots?

Without doubt robots are cool, but why do we need them? Let’s discuss some of the things that robots can help people do.