Position and posture recognition
Mathematical basis
Position vector, plane coordinate system
Start with plane
Synthesis method
- Point and vector
analysis method
-algebraic operation far away
Use array to represent coordinate axis
[three-dimensional represent coordinate axis]
P0 = [P1 P2 P3]
coordinate rotation
P0 °= [X1° | Y1°]
This matrix is a rotation matrix
The rotation in the plane is
changed to a two-dimensional matrix
R0= [Xo X1 Yo X1]
----- [Xo Y1 Y0 Y1]
向量矩阵的转换率 遵循 矩阵转置定理
向里 正
Matrix positive and negative → right hand →
negative outward
, rotate in three-dimensional space
-------【Cos -sin 0】
Ro =【 sin cos 0】 = R (z,)
-------【 0 0 1 】The
above is the rotation around the Z axis, which
can be
derived.
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around the Y-axis
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- 2.13 pose description
/position vector
/rotation matrix
translation coordinate change
AP=Bp+ApB
Rotation coordinate change
vector component expression
- Compound change
Homogeneous coordinate change
Homogeneous coordinate adds a row or column to the original matrix to indicate rotation or translation
Homogeneous change matrix
Homogeneous change
Rotate homogeneous coordinate change