Robotics: 3D 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

Direction Cosine Form ,[object Object]

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]

Rotation Matrix  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

Robotics: 3D Movements

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Robotics: 3D Movements