## Describing rotation and translation in 3D

Category : Robotics | No commentWe learn how to describe the 3D pose of an object by a 4×4 homogeneous transformation matrix which has a special structure.

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

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

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

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

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.

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

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.

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

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.

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.

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

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.

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

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.

This video gives summary of 2D geometry and pose.

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

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

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

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.

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.