#### Describing rotation and translation in 3D

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

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

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We learn how to describe the 2D pose of an object by a 3×3 homogeneous transformation matrix which has a special structure. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.

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We can describe the relationship between a 3D world point and a 2D image plane point, both expressed in homogeneous coordinates, using a linear transformation – a 3×4 matrix. Then we can extend this to account for an image plane which is a regular grid of discrete pixels.

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Let’s recap the important points from the topics we have covered about homogeneous coordinates, image formation, camera modeling and planar homographies.

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We introduce serial-link robot manipulators, the sort of robot arms you might have seen working in factories doing tasks like welding, spray painting or material transfer. We will learn how we can compute the pose of the robot’s end-effector given knowledge of the robot’s joint angles and the dimensions of its links.

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We consider the simplest possible robot, which has one rotary joint and an arm.

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We consider a robot with four joints that moves its end-effector in 3D space.

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We consider a robot, which has two rotary joints and an arm.

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Let’s recap the basics of homogeneous coordinates to represent points on a plane.

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If it’s been a while since you last dealt with eigenvalues and eigenvectors here’s a quick recap of the basics.