`jaxlie._se3`

Module Contents

Classes

SE3

Special Euclidean group for proper rigid transforms in 3D. Broadcasting

class jaxlie._se3.SE3(parameters)[source]

Bases: jaxlie.SEBase[jaxlie.SO3]

Special Euclidean group for proper rigid transforms in 3D. Broadcasting rules are the same as for numpy.

Internal parameterization is (qw, qx, qy, qz, x, y, z). Tangent parameterization is (vx, vy, vz, omega_x, omega_y, omega_z). .. py:attribute:: wxyz_xyz

type:

jax.Array

Internal parameters. wxyz quaternion followed by xyz translation. Shape should be (*, 7).

__repr__()[source]

Return repr(self).

Return type:: str

classmethod from_rotation_and_translation(rotation, translation)[source]

Construct a rigid transform from a rotation and a translation.

Parameters:

rotation (jaxlie.SO3) – Rotation term.
translation (jaxlie.hints.Array) – translation term.

Returns:

Constructed transformation.

Return type:

SE3

rotation()[source]

Returns a transform’s rotation term.

Return type:: jaxlie.SO3

translation()[source]

Returns a transform’s translation term.

Return type:: jax.Array

classmethod identity(batch_axes=())[source]

Returns identity element.

Parameters:: batch_axes (jax_dataclasses.Static[Tuple[int, Ellipsis]]) – Any leading batch axes for the output transform.
Returns:: Identity element.
Return type:: SE3

classmethod from_matrix(matrix)[source]

Get group member from matrix representation.

Parameters:: matrix (jaxlie.hints.Array) – Matrix representaiton.
Returns:: Group member.
Return type:: SE3

as_matrix()[source]

Get transformation as a matrix. Homogeneous for SE groups.

Return type:: jax.Array

parameters()[source]

Get underlying representation.

Return type:: jax.Array

classmethod exp(tangent)[source]

Computes expm(wedge(tangent)).

Parameters:: tangent (jaxlie.hints.Array) – Tangent vector to take the exponential of.
Returns:: Output.
Return type:: SE3

log()[source]

Computes vee(logm(transformation matrix)).

Returns:: Output. Shape should be (tangent_dim,).
Return type:: jax.Array

adjoint()[source]

Computes the adjoint, which transforms tangent vectors between tangent spaces.

More precisely, for a transform GroupType:

GroupType @ exp(omega) = exp(Adj_T @ omega) @ GroupType

In robotics, typically used for transforming twists, wrenches, and Jacobians across different reference frames.

Returns:: Output. Shape should be (tangent_dim, tangent_dim).
Return type:: jax.Array

jlog()[source]

Computes the Jacobian of the logarithm of the group element when a local perturbation is applied.

This is equivalent to the inverse of the right Jacobian, or:

jax.jacrev(lambda x: (T @ exp(x)).log())(jnp.zeros(tangent_dim))

where T is the group element and exp(x) is the tangent vector.

Returns:: The Jacobian of the logarithm, having the dimensions (tangent_dim, tangent_dim,) or batch of these Jacobians.
Return type:: jax.Array

classmethod sample_uniform(key, batch_axes=())[source]

Draw a uniform sample from the group. Translations (if applicable) are in the range [-1, 1].