CPSC 452 Spatial Descriptions and Coordinate Transform

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Presentation transcript:

CPSC 452 Spatial Descriptions and Coordinate Transform Prof. Oussama Khatib, Stanford University Prof. Dezhen Song, Texas A&M University

Generalized Coordinates

End-Effector Configuration Parameters

Operational Coordinates

Coordinate Frames

Position Description Coordinate System A

Orientation Description Coordinate System A Attach Frame Coordinate System B Rotation matrix

Orthogonal Matrix 9 Parameters to describe orientation!

Example 30 30

Description of a frame Position + orientation

Mapping Between Two Coordinate Frames

Mapping - Homogeneous Transformation

Operators

Rotational Operators

Translation Operator Translation operator

General Operators

Inverse Transform

Homogeneous Transform Interpretations

Transform Equation

Compound Transformations

Transform Equation