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Omar Rizwan . @omar,

https://www.cs.rpi.edu/~trink/Courses/RobotManipulation/lectures/lecture6.pdf

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Why representing rotations is hard.

e Rotations do not commute.

e The topology of spatial rotations does not permit a smooth
embedding in Euclidean three space.

Lecture 6. Mechanics of Manipulation -

Choices

More than three numbers
e Rotation matrices
e Unit quaternions. (aka Euler parameters)
Many-to-one
e Axis times angle (matrix exponential)
Unsmooth and many-to-one
e Euler angles
Unsmooth and many-to-one and more than three numbers
e Axis-angle

Why representing rotations is hard.

e Rotations do not commute.

e The topology of spatial rotations does not permit a smooth
embedding in Euclidean three space.

Lecture 6. Mechanics of Manipulation -

Choices

More than three numbers
e Rotation matrices
e Unit quaternions. (aka Euler parameters)
Many-to-one
e Axis times angle (matrix exponential)
Unsmooth and many-to-one
e Euler angles
Unsmooth and many-to-one and more than three numbers
e Axis-angle

Dec 08, 2023, 17:57

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Email: omar@omar.website