skrobot.coordinates.quaternion.Quaternion¶

class skrobot.coordinates.quaternion.Quaternion(w=1.0, x=0.0, y=0.0, z=0.0, q=None)[source]¶

Class for handling Quaternion.

Parameters:

w (float or numpy.ndarray) –
x (float) –
y (float) –
z (float) –
q (None or numpy.ndarray) – if q is not specified, use w, x, y, z.

Examples

>>> from skrobot.coordinates.quaternion import Quaternion
>>> q = Quaternion()
>>> q
#<Quaternion 0x1283bde48 w: 1.0 x: 0.0 y: 0.0 z: 0.0>
>>> q = Quaternion([1, 2, 3, 4])
>>> q
#<Quaternion 0x1283cad68 w: 1.0 x: 2.0 y: 3.0 z: 4.0>
>>> q = Quaternion(q=[1, 2, 3, 4])
>>> q
#<Quaternion 0x1283bd438 w: 1.0 x: 2.0 y: 3.0 z: 4.0>
>>> q = Quaternion(1, 2, 3, 4)
>>> q
#<Quaternion 0x128400198 w: 1.0 x: 2.0 y: 3.0 z: 4.0>
>>> q = Quaternion(w=0.0, x=1.0, y=0.0, z=0.0)
>>> q
#<Quaternion 0x1283cc2e8 w: 0.0 x: 1.0 y: 0.0 z: 0.0>

Methods

T()[source]¶

Return 4x4 homogeneous transformation matrix.

Returns:: matrix – homogeneous transformation matrix shape of (4, 4)
Return type:: numpy.ndarray

Examples

>>> from skrobot.coordinates.quaternion import Quaternion
>>> q = Quaternion()
>>> q.T()
array([[1., 0., 0., 0.],
       [0., 1., 0., 0.],
       [0., 0., 1., 0.],
       [0., 0., 0., 1.]])
>>> q.q = [1, 2, 3, 4]
>>> q.T()
array([[-0.66666667,  0.13333333,  0.73333333,  0.        ],
       [ 0.66666667, -0.33333333,  0.66666667,  0.        ],
       [ 0.33333333,  0.93333333,  0.13333333,  0.        ],
       [ 0.        ,  0.        ,  0.        ,  1.        ]])

copy()[source]¶

Return copy of this Quaternion

Returns:: Quaternion(q=self.q.copy()) – copy of this quaternion
Return type:: skrobot.coordinates.quaternion.Quaternion

normalize()[source]¶

Normalize this quaternion.

Note that this function changes wxyz property.

Examples

>>> from skrobot.coordinates.quaternion import Quaternion
>>> q = Quaternion([1, 2, 3, 4])
>>> q.q
array([1., 2., 3., 4.])
>>> q.normalize()
>>> q.q
array([0.18257419, 0.36514837, 0.54772256, 0.73029674])

__eq__(value, /)¶: Return self==value.

__ne__(value, /)¶: Return self!=value.

__lt__(value, /)¶: Return self<value.

__le__(value, /)¶: Return self<=value.

__gt__(value, /)¶: Return self>value.

__ge__(value, /)¶: Return self>=value.

__neg__()[source]¶

__add__(cls)[source]¶

__sub__(cls)[source]¶

__mul__(cls)[source]¶

__rmul__(cls)[source]¶

__div__(cls)[source]¶

__truediv__(cls)[source]¶

Attributes

angle¶

Return rotation angle of this quaternion

Returns:: theta – rotation angle with respect to self.axis
Return type:: float

axis¶

Return axis of this quaternion.

Note that this property return normalized axis.

Returns:: axis – normalized axis vector
Return type:: numpy.ndarray

conjugate¶

Return conjugate of this quaternion

Returns:: Quaternion – new Quaternion class has this quaternion’s conjugate
Return type:: skrobot.coordinates.quaternion.Quaternion

Examples

>>> from skrobot.coordinates.quaternion import Quaternion
>>> q = Quaternion()
>>> q.conjugate
#<Quaternion 0x12f2dfb38 w: 1.0 x: -0.0 y: -0.0 z: -0.0>
>>> q.q = [0, 1, 0, 0]
>>> q.conjugate
#<Quaternion 0x12f303c88 w: 0.0 x: -1.0 y: -0.0 z: -0.0>

inverse¶

Return inverse of this quaternion

Returns:: q – new Quaternion class has inverse of this quaternion
Return type:: skrobot.coordinates.quaternion.Quaternion

Examples

>>> from skrobot.coordinates.quaternion import Quaternion
>>> q = Quaternion()
>>> q
#<Quaternion 0x127e6da58 w: 1.0 x: 0.0 y: 0.0 z: 0.0>
>>> q.inverse
#<Quaternion 0x1281bbda0 w: 1.0 x: -0.0 y: -0.0 z: -0.0>
>>> q.q = [0, 1, 0, 0]
>>> q.inverse
#<Quaternion 0x1282b0cc0 w: 0.0 x: -1.0 y: -0.0 z: -0.0>

norm¶

Return norm of this quaternion

Returns:: quaternion_norm(self.q) – norm of this quaternion
Return type:: float

Examples

>>> from skrobot.coordinates.quaternion import Quaternion
>>> q = Quaternion()
>>> q.norm
1.0
>>> q = Quaternion([1, 2, 3, 4])
>>> q.norm
5.477225575051661
>>> q.normalized.norm
0.9999999999999999

normalized¶

Return Normalized quaternion.

Returns:: normalized quaternion – return quaternion which is norm == 1.0.
Return type:: skrobot.coordinates.quaternion.Quaternion

Examples

>>> from skrobot.coordinates.quaternion import Quaternion
>>> q = Quaternion([1, 2, 3, 4])
>>> normalized_q = q.normalized
>>> normalized_q.q
array([0.18257419, 0.36514837, 0.54772256, 0.73029674])
>>> q.q
array([1., 2., 3., 4.])

q¶

Return quaternion

Returns:: self._q – [w, x, y, z] quaternion
Return type:: numpy.ndarray

Examples

>>> from skrobot.coordinates.quaternion import Quaternion
>>> q = Quaternion()
>>> q.q
array([1., 0., 0., 0.])
>>> q = Quaternion(w=0.0, x=1.0, y=0.0, z=0.0)
>>> q.q
array([0., 1., 0., 0.])

rotation¶

Return rotation matrix.

Note that this property internally normalizes quaternion.

Returns:: quaternion2matrix(self.q) – 3x3 rotation matrix
Return type:: numpy.ndarray

Examples

>>> from skrobot.coordinates.quaternion import Quaternion
>>> q = Quaternion()
>>> q
#<Quaternion 0x12f1aa6a0 w: 1.0 x: 0.0 y: 0.0 z: 0.0>
>>> q.rotation
array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]])
>>> q.q = [0, 1, 0, 0]
>>> q
#<Quaternion 0x12f1aa6a0 w: 0.0 x: 1.0 y: 0.0 z: 0.0>
>>> q.rotation
array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0., -1.]])
>>> q.q = [1, 2, 3, 4]
>>> q
#<Quaternion 0x12f1aa6a0 w: 1.0 x: 2.0 y: 3.0 z: 4.0>
>>> q.rotation
array([[-0.66666667,  0.13333333,  0.73333333],
       [ 0.66666667, -0.33333333,  0.66666667],
       [ 0.33333333,  0.93333333,  0.13333333]])