Lie

Lie#

This module provides a Lie group interface for rigid-body transforms, delegating to MuJoCo’s quaternion and rotation-matrix routines where possible (e.g., from_matrix() calls mujoco.mju_mat2Quat).

This library is heavily ported from jaxlie, swapping out JAX for Numpy and adding a few additional features.

MatrixLieGroup#

class mink.lie.base.MatrixLieGroup#

Interface definition for matrix Lie groups.

matrix_dim#

Dimension of square matrix output.

Type:

int

parameters_dim#

Dimension of underlying parameters.

Type:

int

tangent_dim#

Dimension of tangent space.

Type:

int

space_dim#

Dimension of coordinates that can be transformed.

Type:

int

abstract classmethod identity() → Self#

Returns identity element.

Return type:

Self

abstract classmethod from_matrix(matrix: ndarray) → Self#

Get group member from matrix representation.

Parameters:

matrix (ndarray)

Return type:

Self

abstract classmethod sample_uniform() → Self#

Draw a uniform sample from the group.

Return type:

Self

abstract as_matrix() → ndarray#

Get transformation as a matrix.

Return type:

ndarray

abstract parameters() → ndarray#

Get underlying representation.

Return type:

ndarray

abstract apply(target: ndarray) → ndarray#

Applies group action to a point.

Parameters:

target (ndarray)

Return type:

ndarray

abstract multiply(other: Self) → Self#

Composes this transformation with another.

Parameters:

other (Self)

Return type:

Self

abstract classmethod exp(tangent: ndarray) → Self#

Computes expm(wedge(tangent)).

Parameters:

tangent (ndarray)

Return type:

Self

abstract log() → ndarray#

Computes vee(logm(transformation matrix)).

Return type:

ndarray

abstract adjoint() → ndarray#

Computes the adjoint.

Return type:

ndarray

abstract inverse() → Self#

Computes the inverse of the transform.

Return type:

Self

abstract normalize() → Self#

Normalize/projects values and returns.

Return type:

Self

interpolate(other: Self, alpha: float = 0.5) → Self#

Interpolate between two matrix Lie groups.

Parameters:

  • other (Self) – The other Lie group, which serves as the end point of interpolation.

  • alpha (float) – The fraction of interpolation between [self, other]. This must be within [0.0, 1.0]. 0.0 = self, 1.0 = other.

Returns:

The interpolated matrix Lie group.

Return type:

Self

plus(other: ndarray) → Self#

Alias for rplus.

Parameters:

other (ndarray)

Return type:

Self

minus(other: Self) → ndarray#

Alias for rminus.

Parameters:

other (Self)

Return type:

ndarray

SO3#

class mink.lie.so3.SO3#

Bases: MatrixLieGroup

Special orthogonal group for 3D rotations.

Internal parameterization is (qw, qx, qy, qz). Tangent parameterization is (omega_x, omega_y, omega_z).

parameters() → ndarray#

Get underlying representation.

Return type:

ndarray

classmethod from_matrix(matrix: ndarray) → SO3#

Get group member from matrix representation.

Parameters:

matrix (ndarray)

Return type:

SO3

classmethod identity() → SO3#

Returns identity element.

Return type:

SO3

classmethod sample_uniform() → SO3#

Draw a uniform sample from the group.

Return type:

SO3

as_matrix() → ndarray#

Get transformation as a matrix.

Return type:

ndarray

inverse() → SO3#

Computes the inverse of the transform.

Return type:

SO3

normalize() → SO3#

Normalize/projects values and returns.

Return type:

SO3

apply(target: ndarray) → ndarray#

Applies group action to a point.

Parameters:

target (ndarray)

Return type:

ndarray

multiply(other: SO3) → SO3#

Composes this transformation with another.

Parameters:

other (SO3)

Return type:

SO3

classmethod exp(tangent: ndarray) → SO3#

Computes expm(wedge(tangent)).

Parameters:

tangent (ndarray)

Return type:

SO3

log() → ndarray#

Computes vee(logm(transformation matrix)).

Return type:

ndarray

adjoint() → ndarray#

Computes the adjoint.

Return type:

ndarray

clamp(roll_radians: tuple[float, float] = (-inf, inf), pitch_radians: tuple[float, float] = (-inf, inf), yaw_radians: tuple[float, float] = (-inf, inf)) → SO3#

Clamp a SO3 within RPY limits.

Parameters:

  • roll_radians (tuple[float, float]) – The (lower, upper) limits for the roll.

  • pitch_radians (tuple[float, float]) – The (lower, upper) limits for the pitch.

  • yaw_radians (tuple[float, float]) – The (lower, upper) limits for the yaw.

Returns:

A SO3 within the RPY limits.

Return type:

SO3

SE3#

class mink.lie.se3.SE3#

Bases: MatrixLieGroup

Special Euclidean group for proper rigid transforms in 3D.

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

parameters() → ndarray#

Get underlying representation.

Return type:

ndarray

classmethod identity() → SE3#

Returns identity element.

Return type:

SE3

classmethod from_matrix(matrix: ndarray) → SE3#

Get group member from matrix representation.

Parameters:

matrix (ndarray)

Return type:

SE3

classmethod sample_uniform() → SE3#

Draw a uniform sample from the group.

Return type:

SE3

as_matrix() → ndarray#

Get transformation as a matrix.

Return type:

ndarray

classmethod exp(tangent: ndarray) → SE3#

Computes expm(wedge(tangent)).

Parameters:

tangent (ndarray)

Return type:

SE3

inverse() → SE3#

Computes the inverse of the transform.

Return type:

SE3

normalize() → SE3#

Normalize/projects values and returns.

Return type:

SE3

apply(target: ndarray) → ndarray#

Applies group action to a point.

Parameters:

target (ndarray)

Return type:

ndarray

multiply(other: SE3) → SE3#

Composes this transformation with another.

Parameters:

other (SE3)

Return type:

SE3

log() → ndarray#

Computes vee(logm(transformation matrix)).

Return type:

ndarray

adjoint() → ndarray#

Computes the adjoint.

Return type:

ndarray

clamp(x_translation: tuple[float, float] = (-inf, inf), y_translation: tuple[float, float] = (-inf, inf), z_translation: tuple[float, float] = (-inf, inf), roll_radians: tuple[float, float] = (-inf, inf), pitch_radians: tuple[float, float] = (-inf, inf), yaw_radians: tuple[float, float] = (-inf, inf)) → SE3#

Clamp a SE3 within translation and RPY limits.

Parameters:

  • x_translation (tuple[float, float]) – The (lower, upper) limits for translation along the x axis.

  • y_translation (tuple[float, float]) – The (lower, upper) limits for translation along the y axis.

  • z_translation (tuple[float, float]) – The (lower, upper) limits for translation along the z axis.

  • roll_radians (tuple[float, float]) – The (lower, upper) limits for the roll.

  • pitch_radians (tuple[float, float]) – The (lower, upper) limits for the pitch.

  • yaw_radians (tuple[float, float]) – The (lower, upper) limits for the yaw.

Returns:

A SE3 within the translation and RPY limits.

Return type:

SE3