skrobot.coordinates.Coordinates¶

class skrobot.coordinates.Coordinates(pos=None, rot=None, name=None, hook=None, check_validity=True)[source]¶

Coordinates class to manipulate rotation and translation.

Parameters:

pos (list or numpy.ndarray or None) – shape of (3,) translation vector. or 4x4 homogeneous transformation matrix. If the homogeneous transformation matrix is given, rot will be overwritten. If this value is None, set [0, 0, 0] vector as default.
rot (list or numpy.ndarray or None) – we can take 3x3 rotation matrix or [yaw, pitch, roll] or quaternion [w, x, y, z] order If this value is None, set the identity matrix as default.
name (str or None) – name of this coordinates
check_validity (bool (optional)) – Default True. If this value is True, check whether an input rotation and an input translation are valid.

Methods

T()[source]¶

Return 4x4 homogeneous transformation matrix.

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

Examples

>>> from numpy import pi
>>> from skrobot.coordinates import make_coords
>>> c = make_coords()
>>> c.T()
array([[1., 0., 0., 0.],
       [0., 1., 0., 0.],
       [0., 0., 1., 0.],
       [0., 0., 0., 1.]])
>>> c.translate([0.1, 0.2, 0.3])
>>> c.rotate(pi / 2.0, 'y')
array([[ 2.22044605e-16,  0.00000000e+00,  1.00000000e+00,
         1.00000000e-01],
       [ 0.00000000e+00,  1.00000000e+00,  0.00000000e+00,
         2.00000000e-01],
       [-1.00000000e+00,  0.00000000e+00,  2.22044605e-16,
         3.00000000e-01],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         1.00000000e+00]])

axis(ax)[source]¶

changed()[source]¶

Return False

This is used for CascadedCoords compatibility

Returns:: False – always return False
Return type:: bool

coords()[source]¶: Return a deep copy of the Coordinates.

copy()[source]¶: Return a deep copy of the Coordinates.

copy_coords()[source]¶: Return a deep copy of the Coordinates.

copy_worldcoords()[source]¶: Return a deep copy of the Coordinates.

difference_position(coords, translation_axis=True)[source]¶

Return differences in positoin of given coords.

Parameters:

coords (skrobot.coordinates.Coordinates) – given coordinates
translation_axis (str or bool or None (optional)) – we can take ‘x’, ‘y’, ‘z’, ‘xy’, ‘yz’, ‘zx’, ‘xx’, ‘yy’, ‘zz’, True or False(None).

Returns:

dif_pos – difference position of self coordinates and coords considering translation_axis.

Return type:

numpy.ndarray

Examples

>>> from skrobot.coordinates import Coordinates
>>> from skrobot.coordinates import transform_coords
>>> from numpy import pi
>>> c1 = Coordinates().translate([0.1, 0.2, 0.3]).rotate(
...          pi / 3.0, 'x')
>>> c2 = Coordinates().translate([0.3, -0.3, 0.1]).rotate(
...          pi / 2.0, 'y')
>>> c1.difference_position(c2)
array([ 0.2       , -0.42320508,  0.3330127 ])
>>> c1 = Coordinates().translate([0.1, 0.2, 0.3]).rotate(0, 'x')
>>> c2 = Coordinates().translate([0.3, -0.3, 0.1]).rotate(
...          pi / 3.0, 'x')
>>> c1.difference_position(c2)
array([ 0.2, -0.5, -0.2])

difference_rotation(coords, rotation_axis=True)[source]¶

Return differences in rotation of given coords.

Parameters:

coords (skrobot.coordinates.Coordinates) – given coordinates
rotation_axis (str or bool or None (optional)) – we can take ‘x’, ‘y’, ‘z’, ‘xx’, ‘yy’, ‘zz’, ‘xm’, ‘ym’, ‘zm’, ‘xy’, ‘yx’, ‘yz’, ‘zy’, ‘zx’, ‘xz’, True or False(None).

Returns:

dif_rot – difference rotation of self coordinates and coords considering rotation_axis.

Return type:

numpy.ndarray

Examples

>>> from numpy import pi
>>> from skrobot.coordinates import Coordinates
>>> from skrobot.coordinates.math import rpy_matrix
>>> coord1 = Coordinates()
>>> coord2 = Coordinates(rot=rpy_matrix(pi / 2.0, pi / 3.0, pi / 5.0))
>>> coord1.difference_rotation(coord2)
array([-0.32855112,  1.17434985,  1.05738936])
>>> coord1.difference_rotation(coord2, rotation_axis=False)
array([0, 0, 0])
>>> coord1.difference_rotation(coord2, rotation_axis='x')
array([0.        , 1.36034952, 0.78539816])
>>> coord1.difference_rotation(coord2, rotation_axis='y')
array([0.35398131, 0.        , 0.97442695])
>>> coord1.difference_rotation(coord2, rotation_axis='z')
array([-0.88435715,  0.74192175,  0.        ])

Using mirror option [‘xm’, ‘ym’, ‘zm’], you can allow differences of mirror direction.

>>> coord1 = Coordinates()
>>> coord2 = Coordinates().rotate(pi, 'x')
>>> coord1.difference_rotation(coord2, 'xm')
array([-2.99951957e-32,  0.00000000e+00,  0.00000000e+00])
>>> coord1 = Coordinates()
>>> coord2 = Coordinates().rotate(pi / 2.0, 'x')
>>> coord1.difference_rotation(coord2, 'xm')
array([-1.57079633,  0.        ,  0.        ])

disable_hook()[source]¶

get_transform()[source]¶

Return Transform object

Returns:: transform – corrensponding Transform to this coordinates
Return type:: skrobot.coordinates.base.Transform

inverse_rotate_vector(v)[source]¶

inverse_transform_vector(vec)[source]¶

Transform vector in world coordinates to local coordinates

Parameters:: vec (numpy.ndarray) – 3d vector. We can take batch of vector like (batch_size, 3)
Returns:: transformed_point – transformed point
Return type:: numpy.ndarray

inverse_transformation(dest=None)[source]¶

Return a invese transformation of this coordinate system.

Create a new coordinate with inverse transformation of this coordinate system.

\[\begin{split}\left( \begin{array}{ccc} R^{-1} & - R^{-1} p \\ 0 & 1 \end{array} \right)\end{split}\]

Parameters:: dest (None or skrobot.coordinates.Coordinates) – If dest is given, the result of transformation is in-placed to dest.
Returns:: dest – result of inverse transformation.
Return type:: skrobot.coordinates.Coordinates

move_coords(target_coords, local_coords)[source]¶

Transform this coordinate so that local_coords to target_coords.

Parameters:

target_coords (skrobot.coordinates.Coordinates) – target coords.
local_coords (skrobot.coordinates.Coordinates) – local coords to be aligned.

Returns:

self.worldcoords() – world coordinates.

Return type:

skrobot.coordinates.Coordinates

newcoords(c, pos=None, check_validity=True)[source]¶

Update of coords is always done through newcoords.

Parameters:

c (skrobot.coordinates.Coordinates or numpy.ndarray) – If pos is None, c means new Coordinates. If pos is given, c means rotation matrix.
pos (numpy.ndarray or None) – new translation.
check_validity (bool) – If this value is True, check whether an input rotation and an input translation are valid.

orient_with_matrix(rotation_matrix, wrt='world')[source]¶

Force update this coordinate system’s rotation.

Parameters:

rotation_matrix (numpy.ndarray) – 3x3 rotation matrix.
wrt (str or skrobot.coordinates.Coordinates) – reference coordinates.

parent_orientation(v, wrt)[source]¶

rotate(theta, axis=None, wrt='local')[source]¶

Rotate this coordinate by given theta and axis.

This coordinate system is rotated relative to theta radians around the axis axis. Note that this function does not change a position of this coordinate. If you want to rotate this coordinates around with world frame, you can use transform function. Please see examples.

Parameters:

theta (float) – relartive rotation angle in radian.
axis (str or None or numpy.ndarray) – axis of rotation. The value of axis is represented as wrt frame.
wrt (str or skrobot.coordinates.Coordinates) –

Returns:

self

Return type:

skrobot.coordinates.Coordinates

Examples

>>> from skrobot.coordinates import Coordinates
>>> from numpy import pi
>>> c = Coordinates()
>>> c.translate((1.0, 0, 0))
>>> c.rotate(pi / 2.0, 'z', wrt='local')
>>> c.translation
array([1., 0., 0.])

>>> c.transform(Coordinates().rotate(np.pi / 2.0, 'z'), wrt='world')
>>> c.translation
array([0., 1., 0.])

rotate_vector(v)[source]¶

Rotate 3-dimensional vector using rotation of this coordinate

Parameters:: v (numpy.ndarray) – vector shape of (3,)
Returns:: np.matmul(self.rotation, v) – rotated vector
Return type:: numpy.ndarray

Examples

>>> from skrobot.coordinates import Coordinates
>>> from numpy import pi
>>> c = Coordinates().rotate(pi, 'z')
>>> c.rotate_vector([1, 2, 3])
array([-1., -2.,  3.])

rotate_with_matrix(mat, wrt='local')[source]¶

Rotate this coordinate by given rotation matrix.

This is a subroutine of self.rotate function.

Parameters:

mat (numpy.ndarray) – rotation matrix shape of (3, 3)
wrt (str or skrobot.coordinates.Coordinates) – with respect to.

Returns:

self

Return type:

skrobot.coordinates.Coordinates

rpy_angle()[source]¶

Return a pair of rpy angles of this coordinates.

Returns:: rpy_angle(self.rotation) – a pair of rpy angles. See also skrobot.coordinates.math.rpy_angle
Return type:: tuple(numpy.ndarray, numpy.ndarray)

Examples

>>> import numpy as np
>>> from skrobot.coordinates import Coordinates
>>> c = Coordinates().rotate(np.pi / 2.0, 'x').rotate(np.pi / 3.0, 'z')
>>> r.rpy_angle()
(array([ 3.84592537e-16, -1.04719755e+00,  1.57079633e+00]),
array([ 3.14159265, -2.0943951 , -1.57079633]))

transform(c, wrt='local', out=None)[source]¶

Transform this coordinates by coords based on wrt

Note that this function changes this coordinates translation and rotation. If you would like not to change this coordinates, Please use copy_worldcoords() or give out.

Parameters:

c (skrobot.coordinates.Coordinates) – coordinate
wrt (str or skrobot.coordinates.Coordinates) – If wrt is ‘local’ or self, multiply c from the right. If wrt is ‘world’ or ‘parent’ or self.parent, transform c with respect to worldcoord. If wrt is Coordinates, transform c with respect to c.
out (None or skrobot.coordinates.Coordinates) – If the out is specified, set new coordinates to out. Note that if the out is given, these coordinates don’t change.

Returns:

self – return this coordinate

Return type:

skrobot.coordinates.Coordinates

Examples

transform_vector(v)[source]¶

“Return vector represented at world frame.

Vector v given in the local coords is converted to world representation.

Parameters:: v (numpy.ndarray) – 3d vector. We can take batch of vector like (batch_size, 3)
Returns:: transformed_point – transformed point
Return type:: numpy.ndarray

transformation(c2, wrt='local')[source]¶

translate(vec, wrt='local')[source]¶

Translate this coordinates.

Note that this function changes this coordinates self. So if you don’t want to change this class, use copy_worldcoords()

Parameters:

vec (list or numpy.ndarray) – shape of (3,) translation vector. unit is [m] order.
wrt (str or Coordinates (optional)) – translate with respect to wrt.

Examples

>>> import numpy as np
>>> from skrobot.coordinates import Coordinates
>>> c = Coordinates()
>>> c.translation
array([0., 0., 0.], dtype=float32)
>>> c.translate([0.1, 0.2, 0.3])
>>> c.translation
array([0.1, 0.2, 0.3], dtype=float32)

>>> c = Coordinates()
>>> c.copy_worldcoords().translate([0.1, 0.2, 0.3])
>>> c.translation
array([0., 0., 0.], dtype=float32)

>>> c = Coordinates().rotate(np.pi / 2.0, 'y')
>>> c.translate([0.1, 0.2, 0.3])
>>> c.translation
array([ 0.3,  0.2, -0.1])
>>> c = Coordinates().rotate(np.pi / 2.0, 'y')
>>> c.translate([0.1, 0.2, 0.3], 'world')
>>> c.translation
array([0.1, 0.2, 0.3])

worldcoords()[source]¶: Return thisself

worldpos()[source]¶

Return translation of this coordinate

See also skrobot.coordinates.Coordinates.translation

Returns:: self.translation – translation of this coordinate
Return type:: numpy.ndarray

worldrot()[source]¶

Return rotation of this coordinate

See also skrobot.coordinates.Coordinates.rotation

Returns:: self.rotation – rotation matrix of this coordinate
Return type:: numpy.ndarray

__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.

__mul__(other_c)[source]¶

Return Transformed Coordinates.

Note that this function creates new Coordinates and does not change translation and rotation, unlike transform function.

Parameters:: other_c (skrobot.coordinates.Coordinates) – input coordinates.
Returns:: out – transformed coordinates multiplied other_c from the right. T = T_{self} T_{other_c}.
Return type:: skrobot.coordinates.Coordinates

__pow__(exponent)[source]¶

Return exponential homogeneous matrix.

If exponent equals -1, return inverse transformation of this coords.

Parameters:: exponent (numbers.Number) – exponent value. If exponent equals -1, return inverse transformation of this coords. In current, support only -1 case.
Returns:: out – output.
Return type:: skrobot.coordinates.Coordinates

Attributes

dimension¶

Return dimension of this coordinate

Returns:: len(self.translation) – dimension of this coordinate
Return type:: int

dual_quaternion¶

Property of DualQuaternion

Return DualQuaternion representation of this coordinate.

Returns:: DualQuaternion – DualQuaternion representation of this coordinate
Return type:: skrobot.coordinates.dual_quaternion.DualQuaternion

name¶

Return this coordinate’s name

Returns:: self._name – name of this coordinate
Return type:: str

quaternion¶

Property of quaternion

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

Examples

>>> from numpy import pi
>>> from skrobot.coordinates import make_coords
>>> c = make_coords()
>>> c.quaternion
array([1., 0., 0., 0.])
>>> c.rotate(pi / 3, 'y').rotate(pi / 5, 'z')
>>> c.quaternion
array([0.8236391 , 0.1545085 , 0.47552826, 0.26761657])

rotation¶

Return rotation matrix of this coordinates.

Returns:: self._rotation – 3x3 rotation matrix
Return type:: numpy.ndarray

Examples

>>> import numpy as np
>>> from skrobot.coordinates import Coordinates
>>> c = Coordinates()
>>> c.rotation
array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]])
>>> c.rotate(np.pi / 2.0, 'y')
>>> c.rotation
array([[ 2.22044605e-16,  0.00000000e+00,  1.00000000e+00],
       [ 0.00000000e+00,  1.00000000e+00,  0.00000000e+00],
       [-1.00000000e+00,  0.00000000e+00,  2.22044605e-16]])

translation¶

Return translation of this coordinates.

Returns:: self._translation – vector shape of (3, ). unit is [m]
Return type:: numpy.ndarray

Examples

>>> from skrobot.coordinates import Coordinates
>>> c = Coordinates()
>>> c.translation
array([0., 0., 0.])
>>> c.translate([0.1, 0.2, 0.3])
>>> c.translation
array([0.1, 0.2, 0.3])

x_axis¶

Return x axis vector of this coordinates.

Returns:: axis – x axis.
Return type:: numpy.ndarray

y_axis¶

Return y axis vector of this coordinates.

Returns:: axis – y axis.
Return type:: numpy.ndarray

z_axis¶

Return z axis vector of this coordinates.

Returns:: axis – z axis.
Return type:: numpy.ndarray