DeepMind Robotics Transformations

Transformations is a pure python library for rigid-body transformations including velocities and forces.

The objectives for this library are simplicity and comprehensiveness across all canonical representations (euler, axis-angle, quaternion, homogeneous matrices).

Supported conversions:

• Quaternion to Rotation matrix, Axis-angle and Euler-angle
• Axis-angle to Quaternion, Rotation matrix and Euler-angle
• Rotation matrix to Quaternion, Axis-angle and Euler-angle
• Euler-angle to Quaternion, Rotation matrix and Axis-angle

Quaternions:

Quaternions are represented with the scalar part (w) first, e.g.

identity_quaternion = np.asarray([1, 0, 0, 0])  # w, i, j, k

Supported quaternion operations:

• Difference
• Distance
• Multiplication
• Inverse
• Conjugate
• Logarithm and Exponent
• Slerp (spherical linear interpolation)
• Rotation of a vector by a quaternion.

Euler-angles

All 24 from-euler orderings are supported. 7 of 24 to-euler orderings are supported.

Transforms

This library supports force and velocity transforms.

Usage Example

from dm_robotics.transformations import transformations as tr

# Convert a pose, euler angle into a homogeneous matrix (a 4x4 matrix):
hmat = tr.poseuler_to_hmat(
        np.array([x, y, z, rot_x, rot_y, rot_z]), 'XYZ')

# Convert the homogeneous matrix to a twist (a 6 vector):
twist = tr.hmat_to_twist(hmat)