scipy.spatial.transform.Rotation.as_mrp

Rotation.as_mrp()

Represent as Modified Rodrigues Parameters (MRPs).

MRPs are a 3 dimensional vector co-directional to the axis of rotation and whose magnitude is equal to tan(theta / 4), where theta is the angle of rotation (in radians) [1].

MRPs have a singuarity at 360 degrees which can be avoided by ensuring the angle of rotation does not exceed 180 degrees, i.e. switching the direction of the rotation when it is past 180 degrees. This function will always return MRPs corresponding to a rotation of less than or equal to 180 degrees.

Returns

mrpsndarray, shape (3,) or (N, 3)

Shape depends on shape of inputs used for initialization.

Notes

New in version 1.6.0.

References

1

Shuster, M. D. “A Survery of Attitude Representations”, The Journal of Astronautical Sciences, Vol. 41, No.4, 1993, pp. 475-476

Examples

>>> from scipy.spatial.transform import Rotation as R

Represent a single rotation:

>>> r = R.from_rotvec([0, 0, np.pi])
>>> r.as_mrp()
array([0.        , 0.        , 1.         ])
>>> r.as_mrp().shape
(3,)

Represent a stack with a single rotation:

>>> r = R.from_euler('xyz', [[180, 0, 0]], degrees=True)
>>> r.as_mrp()
array([[1.       , 0.        , 0.         ]])
>>> r.as_mrp().shape
(1, 3)

Represent multiple rotations:

>>> r = R.from_rotvec([[np.pi/2, 0, 0], [0, 0, np.pi/2]])
>>> r.as_mrp()
array([[0.41421356, 0.        , 0.        ],
       [0.        , 0.        , 0.41421356]])
>>> r.as_mrp().shape
(2, 3)