#### 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 learn how to describe the orientation of an object by a 2×2 rotation matrix which has some special properties. 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 revisit the fundamentals of geometry that you would have learned at school: Euclidean geometry, Cartesian or analytic geometry, coordinate frames, points and vectors.

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We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.

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We learn to compute a trajectory that involves simultaneous smooth motion of many robot joints.

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The orientation of a body in 3D can also be described by a unit-Quaternion, an unusual but very useful mathematical object. In the MATLAB example starting at 3:48 I use the Quaternion class. For Toolbox version 10 (2017) please use UnitQuaternion instead.