Jacobian matrix J commonly used in slam

Catalog

1. Knowledge background

1.1 Li Qun SE(3) And Li Dai SO(3) The transformation of

 2.  Commonly used Jacobian matrix J

2.1 The left perturbation Jacobian of the rotation point

2.2  The right perturbation Jacobian of the rotation point

2.3  Jacobian of rotation and multiplication

2.4  Jacobian of rotation and multiplication

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Reference resources ： Vision SLAM Fourteen speak , Deep Blue College VIO Course

1. Knowledge background

1.1 Li Qun SE(3) And Li Dai SO(3) The transformation of

 

  Logarithmic mapping （ Congruent Lie group SO3 To Li Dai so3）:

  Exponential mapping （ from Li Dai so3 To Li Qun SO3）:

 2.  Commonly used Jacobian matrix J

2.1 The left perturbation Jacobian of the rotation point

2.2  The right perturbation Jacobian of the rotation point

2.3  Jacobian of rotation and multiplication

among ,θ、ω For the rotation matrix （R1R2） Corresponding rotation angle and rotation axis .

2.4  Jacobian of rotation and multiplication