#### 2-vector representation of rotation in 3D

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

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

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The orientation of a body in 3D can be described by three angles, examples of which are Euler angles and roll-pitch-yaw angles. Note that in the MATLAB example at 8:24 note that recent versions of the Robotics Toolbox (9.11, 10.x) give a different result: >> rpy2r(0.1,0.2,0.3)ans = 0.9363 -0.2751 0.2184 0.2896 0.9564 -0.0370 -0.1987 0.0978 […]

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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.

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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.

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

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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 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. Try your hand at some online MATLAB problems. You’ll need […]

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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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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.

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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. Note that in Robotics, Vision & Control (second edition) and RTB10.x the default definition of roll-pitch-yaw […]