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Robotics: 3D Movements

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Damian T. Gordon
Damian T. Gordon
Education
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3-D Movements
3-D Spaces and Points ,[object Object],[object Object],X Z Y v v 1 v 2 v 3 X Y Z
[object Object],[object Object],X 0 Y 0 Z 0 X 1 Y 1 Z 1
Rotation about the axes X Y Z
Direction Cosine Form ,[object Object]
Inverse of a rotation matrix
Composition of Rotations ,[object Object],[object Object],[object Object],[object Object],[object Object]
From origin P Left to right a From origin P Right to left a a a X Y Z X Y Z
Spatial Transformations ,[object Object],Representation of Orientation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Euler Angles ,[object Object],[object Object],[object Object],[object Object]
Roll, Pitch Yaw angles ,[object Object],X Y Z Roll  Yaw  Pitch 
Quaternions ,[object Object],[object Object],[object Object],[object Object],[object Object]
Quaternion Operations ,[object Object],[object Object],[object Object],[object Object],[object Object]
Quaternions as Rotations ,[object Object],[object Object],[object Object]
Quaternions as Rotations ,[object Object],[object Object],[object Object],[object Object],[object Object]
Quaternions as Rotations ,[object Object],[object Object],[object Object],[object Object],[object Object]
Rotation Matrix ο‚« Quaternion Conversion
Deconstructing the Quaternion ,[object Object]
Normalisation ,[object Object],[object Object]
Quaternion Rotation Composition ,[object Object],note the order ( q 2 after q 1 ) property of conjugation
Advantages of Quaternions for Rotations ,[object Object],[object Object],[object Object],[object Object],Operation Matrices Quaternions Storage 9 4 Transformation 9M 6A 15M 15A Composition 27M 18A 16M 12A Normalisation complicated 8M 3A 1sqrt

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