jaxlie._se2

Module Contents

Classes

SE2	Special Euclidean group for proper rigid transforms in 2D. Broadcasting

class jaxlie._se2.SE2(parameters)

Bases: jaxlie.SEBase[jaxlie.SO2]

Special Euclidean group for proper rigid transforms in 2D. Broadcasting rules are the same as for numpy.

Internal parameterization is (cos, sin, x, y). Tangent parameterization is (vx, vy, omega). .. py:attribute:: unit_complex_xy

type:

jax.Array

Internal parameters. (cos, sin, x, y). Shape should be (*, 4).

__repr__()

Return repr(self).

Return type:

str

static from_xy_theta(x, y, theta)

Construct a transformation from standard 2D pose parameters.

Note that this is not the same as integrating over a length-3 twist.

Parameters:

• x (jaxlie.hints.Scalar) –

• y (jaxlie.hints.Scalar) –

• theta (jaxlie.hints.Scalar) –

Return type:

SE2

classmethod from_rotation_and_translation(rotation, translation)

Construct a rigid transform from a rotation and a translation.

Parameters:

• rotation (jaxlie.SO2) – Rotation term.

• translation (jaxlie.hints.Array) – translation term.

Returns:

Constructed transformation.

Return type:

SE2

rotation()

Returns a transform’s rotation term.

Return type:

jaxlie.SO2

translation()

Returns a transform’s translation term.

Return type:

jax.Array

classmethod identity(batch_axes=())

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:

SE2

classmethod from_matrix(matrix)

Get group member from matrix representation.

Parameters:

matrix (jaxlie.hints.Array) – Matrix representaiton.

Returns:

Group member.

Return type:

SE2

parameters()

Get underlying representation.

Return type:

jax.Array

as_matrix()

Get transformation as a matrix. Homogeneous for SE groups.

Return type:

jax.Array

classmethod exp(tangent)

Computes expm(wedge(tangent)).

Parameters:

tangent (jaxlie.hints.Array) – Tangent vector to take the exponential of.

Returns:

Output.

Return type:

SE2

log()

Computes vee(logm(transformation matrix)).

Returns:

Output. Shape should be (tangent_dim,).

Return type:

jax.Array

adjoint()

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

classmethod sample_uniform(key, batch_axes=())

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

Parameters:

• key (jax.Array) – PRNG key, as returned by jax.random.PRNGKey().

• batch_axes (jax_dataclasses.Static[Tuple[int, Ellipsis]]) – Any leading batch axes for the output transforms. Each sampled transform will be different.

Returns:

Sampled group member.

Return type:

SE2