klampt.math.autodiff.se3_ad module

se3 module AD functions:

Note that each function takes a 12 element vector which is the concatenation of the R and t terms in an se3 element. In other words, to convert from an se3 element T to an entry that can be properly eval’ed, use the code np.array(T[0] + T[1]). Alternatively, you can use the join function se3_ad.join(T[0],T[1]) which is differentiable.

To extract out the rotation / translation from an autodiff-ed function, use the se3_ad.rotation and se3_ad.translation functions.

Function	Derivative	Notes
join	Y	Creates a 12-element vector from R,t
identity	N/A	A constant function with no args
apply	1
apply_rotation	1
mul	N
inv	N
rotation	Y
from_rotation	Y
translation	Y
from_translation	Y
distance	N
interpolate	N
error	N

Note

To do gradient descent on se3 elements, you will need to either project to the se3 submanifold or use a non-redundant representation. The rotation vector representation (see so3_ad.rotation_vector and so3_ad.from_rotation_vector) is recommended.

The code se3_ad.join(so3_ad.from_rotation_vector(x[0:3]),x[3:6])) will convert from a 6-element vector x (first 3 elements encoding the rotation vector, final 3 elements encoding the translation) to a se3 element.

Module contents

join	Autodiff function to join SO(3) rotation matrix and 3D translation vector into an SE(3) 12-element vector.
identity()	A 0 argument function that returns the SO(3) identity (just an alias to so3.identity)
apply	Autodiff wrapper of se3.apply.
apply_rotation	Autodiff wrapper of se3.apply_rotation.
mul	Autodiff wrapper of se3.mul.
inv	Autodiff wrapper of se3.inv.
rotation	Autodiff function to extract the SO(3) rotation component of an SE(3) 12-element vector.
from_rotation	Autodiff wrapper of se3.from_rotation.
translation	Autodiff function to extract the 3-D translation component of an SE(3) 12-element vector.
from_translation	Autodiff wrapper of se3.from_translation.
distance	Autodiff wrapper of se3.distance.
interpolate	Autodiff wrapper of se3.interpolate.
error	Autodiff wrapper of se3.error.

klampt.math.autodiff.se3_ad.SIZE = 12

Constant giving the dimension of an se3_ad element

klampt.math.autodiff.se3_ad.to_klampt(T)

Converts an autodiff se3 representation as a length-12 numpy array to the native Klampt representation (R,t).

klampt.math.autodiff.se3_ad.from_klampt(T)

Converts a native Klampt se3 representation (R,t) to the length-12 numpy array representation used in autodiff.

klampt.math.autodiff.se3_ad.join(*args) = <klampt.math.autodiff.ad._ad_se3.join object>

Autodiff function to join SO(3) rotation matrix and 3D translation vector into an SE(3) 12-element vector. All derivatives are implemented.

klampt.math.autodiff.se3_ad.rotation(*args) = <klampt.math.autodiff.ad._ad_se3.rotation object>

Autodiff function to extract the SO(3) rotation component of an SE(3) 12-element vector. All derivatives are implemented.

klampt.math.autodiff.se3_ad.translation(*args) = <klampt.math.autodiff.ad._ad_se3.translation object>

Autodiff function to extract the 3-D translation component of an SE(3) 12-element vector. All derivatives are implemented.

klampt.math.autodiff.se3_ad.identity()

A 0 argument function that returns the SO(3) identity (just an alias to so3.identity)

klampt.math.autodiff.se3_ad.apply(*args) = <klampt.math.autodiff.ad._ad_se3.apply object>

Autodiff wrapper of se3.apply. First derivatives are implemented.

klampt.math.autodiff.se3_ad.apply_rotation(*args) = <klampt.math.autodiff.ad._ad_se3.apply_rotation object>

Autodiff wrapper of se3.apply_rotation. First derivatives are implemented.

klampt.math.autodiff.se3_ad.mul(*args) = <klampt.math.autodiff.ad._ad_se3.mul object>

Autodiff wrapper of se3.mul.

klampt.math.autodiff.se3_ad.inv(*args) = <klampt.math.autodiff.ad._ad_se3.inv object>

Autodiff wrapper of se3.inv.

klampt.math.autodiff.se3_ad.from_rotation(*args) = <klampt.math.autodiff.ad._ad_se3.from_rotation object>

Autodiff wrapper of se3.from_rotation. All derivatives are implemented.

klampt.math.autodiff.se3_ad.from_translation(*args) = <klampt.math.autodiff.ad._ad_se3.from_translation object>

Autodiff wrapper of se3.from_translation. All derivatives are implemented.

klampt.math.autodiff.se3_ad.error(*args) = <klampt.math.autodiff.ad._ad_se3.error object>

Autodiff wrapper of se3.error.

klampt.math.autodiff.se3_ad.distance(*args) = <klampt.math.autodiff.ad._ad_se3.distance object>

Autodiff wrapper of se3.distance.

klampt.math.autodiff.se3_ad.interpolate(*args) = <klampt.math.autodiff.ad._ad_se3.interpolate object>

Autodiff wrapper of se3.interpolate.