skrobot.models.kuka.Kuka¶

class skrobot.models.kuka.Kuka(*args, **kwargs)[source]¶

Kuka Robot Model.

Methods

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]])

angle_vector(av=None, return_av=None)[source]¶

Returns angle vector

If av is given, it updates angles of all joint. If given av violate min/max range, the value is modified.

assoc(child, relative_coords='world', force=False, **kwargs)[source]¶

Associate child coords to this coordinate system.

If relative_coords is None or ‘world’, the translation and rotation of childcoords in the world coordinate system do not change. If relative_coords is specified, childcoords is assoced at translation and rotation of relative_coords. By default, if child is already assoced to some other coords, raise an exception. But if force is True, you can overwrite the existing assoc relation.

Parameters:

child (CascadedCoords) – child coordinates.
relative_coords (None or Coordinates or str) – child coordinates’ relative coordinates.
force (bool) – predicate for overwriting the existing assoc-relation

Returns:

child – assoced child.

Return type:

CascadedCoords

Examples

>>> from skrobot.coordinates import CascadedCoords
>>> parent_coords = CascadedCoords(pos=[1, 0, 0])
>>> child_coords = CascadedCoords(pos=[1, 1, 0])
>>> parent_coords.assoc(child_coords)
#<CascadedCoords 0x7f1d30e29510 1.000 1.000 0.000 / 0.0 -0.0 0.0>
>>> child_coords.worldpos()
array([1., 1., 0.])
>>> child_coords.translation
array([0., 1., 0.])

None and ‘world’ have the same meaning.

>>> parent_coords = CascadedCoords(pos=[1, 0, 0])
>>> child_coords = CascadedCoords(pos=[1, 1, 0])
>>> parent_coords.assoc(child_coords, relative_coords='world')
#<CascadedCoords 0x7f1d30e29510 1.000 1.000 0.000 / 0.0 -0.0 0.0>
>>> child_coords.worldpos()
array([1., 1., 0.])

If relative_coords is ‘local’, child is associated at world translation and world rotation of child from this coordinate system.

>>> parent_coords = CascadedCoords(pos=[1, 0, 0])
>>> child_coords = CascadedCoords(pos=[1, 1, 0])
>>> parent_coords.assoc(child_coords, relative_coords='local')
>>> child_coords.worldpos()
array([2., 1., 0.])
>>> child_coords.translation
array([1., 1., 0.])

axis(ax)[source]¶

calc_inverse_jacobian(jacobi, manipulability_limit=0.1, manipulability_gain=0.001, weight=None, *args, **kwargs)[source]¶

calc_inverse_kinematics_nspace_from_link_list(link_list, avoid_nspace_gain=0.01, union_link_list=None, n_joint_dimension=None, null_space=None, additional_nspace_list=None, weight=None)[source]¶

calc_inverse_kinematics_weight_from_link_list(link_list, avoid_weight_gain=1.0, union_link_list=None, n_joint_dimension=None, weight=None, additional_weight_list=[])[source]¶: Calculate all weight from link list.

calc_jacobian_for_interlocking_joints(link_list, interlocking_joint_pairs=None)[source]¶

calc_jacobian_from_link_list(move_target, link_list=None, transform_coords=None, rotation_axis=None, translation_axis=None, col_offset=0, dim=None, jacobian=None, additional_jacobi_dimension=0, n_joint_dimension=None, *args, **kwargs)[source]¶

calc_joint_angle_from_min_max_table(index, j, av)[source]¶

calc_joint_angle_speed(union_vel, angle_speed=None, angle_speed_blending=0.5, jacobi=None, j_sharp=None, null_space=None, *args, **kwargs)[source]¶

calc_joint_angle_speed_gain(union_link_list, dav, periodic_time)[source]¶

calc_nspace_from_joint_limit(avoid_nspace_gain, union_link_list, weight)[source]¶: Calculate null-space according to joint limit.

calc_target_axis_dimension(rotation_axis, translation_axis)[source]¶: rotation-axis, translation-axis -> both list and atom OK.

calc_target_joint_dimension(link_list)[source]¶

calc_union_link_list(link_list)[source]¶

calc_vel_for_interlocking_joints(link_list, interlocking_joint_pairs=None)[source]¶

Calculate 0 velocity for keeping interlocking joint.

at the same joint angle.

calc_vel_from_pos(dif_pos, translation_axis, p_limit=100.0)[source]¶

Calculate velocity from difference position

Parameters:

dif_pos (np.ndarray) – [m] order
translation_axis (str) – see calc_dif_with_axis

Returns:

vel_p

Return type:

np.ndarray

calc_vel_from_rot(dif_rot, rotation_axis, r_limit=0.5)[source]¶

calc_weight_from_joint_limit(avoid_weight_gain, link_list, union_link_list, weight, n_joint_dimension=None)[source]¶: Calculate weight according to joint limit.

changed()[source]¶

Return False

This is used for CascadedCoords compatibility

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

close_hand(av=None)[source]¶

collision_avoidance_link_pair_from_link_list(link_list, obstacles=None)[source]¶

compute_qp_common(target_coords, move_target, dt, link_list=None, gain=0.85, weight=1.0, translation_axis=True, rotation_axis=True, dof_limit_gain=0.5)[source]¶

compute_velocity(target_coords, move_target, dt, link_list=None, gain=0.85, weight=1.0, translation_axis=True, rotation_axis=True, dof_limit_gain=0.5, fast=True, sym_proj=False, solver='cvxopt', *args, **kwargs)[source]¶

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]¶

dissoc(child)[source]¶

find_joint_angle_limit_weight_from_union_link_list(union_link_list)[source]¶

find_link_path(src_link, target_link)[source]¶

Find paths of src_link to target_link

Parameters:

src_link (skrobot.model.link.Link) – source link.
target_link (skrobot.model.link.Link) – target link.

Returns:

ret – If the links are connected, return Link list. Otherwise, return an empty list.

Return type:

List[skrobot.model.link.Link]

find_link_route(to, frm=None)[source]¶

fix_leg_to_coords(fix_coords, leg='both', mid=0.5)[source]¶

Fix robot’s legs to a coords

In the Following codes, leged robot is assumed.

Parameters:

fix_coords (Coordinates) – target coordinate
leg (string) – [‘both’, ‘rleg’, ‘rleg’, ‘left’, ‘right’]
mid (float) – ratio of legs coord.

get_transform()[source]¶

Return Transform object

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

ik_convergence_check(dif_pos, dif_rot, rotation_axis, translation_axis, thre, rthre, centroid_thre=None, target_centroid_pos=None, centroid_offset_func=None, cog_translation_axis=None, update_mass_properties=True)[source]¶

check ik convergence.

Parameters:

dif_pos (list of np.ndarray) –
dif_rot (list of np.ndarray) –
translation_axis (list of axis) –
rotation_axis (list of axis) – see _wrap_axis

init_pose()[source]¶

inverse_kinematics(target_coords, move_target=None, link_list=None, **kwargs)[source]¶

Solve inverse kinematics.

solve inverse kinematics, move move-target to target-coords look-at- target suppots t, nil, float-vector, coords, list of float-vector, list of coords link-list is set by default based on move-target -> root link link-list.

inverse_kinematics_args(union_link_list=None, rotation_axis=None, translation_axis=None, additional_jacobi_dimension=0, **kwargs)[source]¶

inverse_kinematics_loop(dif_pos, dif_rot, move_target, link_list=None, target_coords=None, **kwargs)[source]¶

move move_target using dif_pos and dif_rot.

Parameters:: TODO –
Return type:: TODO

inverse_kinematics_loop_for_look_at(move_target, look_at, link_list, rotation_axis='z', translation_axis=False, rthre=0.001, **kwargs)[source]¶

Solve look at inverse kinematics

Parameters:: look_at (list or np.ndarray or Coordinates) –

inverse_kinematics_optimization(target_coords, move_target=None, link_list=None, regularization_parameter=None, init_angle_vector=None, translation_axis=True, rotation_axis=True, stop=100, dt=0.005, inverse_kinematics_hook=[], thre=0.001, rthre=0.017453292519943295, *args, **kwargs)[source]¶

inverse_rotate_vector(v)[source]¶

inverse_transform_vector(v)[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

link_lists(to, frm=None)[source]¶: Find link list from to link to frm link.

load_urdf(urdf)[source]¶

load_urdf_file(file_obj)[source]¶

look_at_hand(coords)[source]¶

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

move_end_pos(pos, wrt='local', *args, **kwargs)[source]¶

move_end_rot(angle, axis, wrt='local', *args, **kwargs)[source]¶

move_joints(union_vel, union_link_list=None, periodic_time=0.05, joint_args=None, move_joints_hook=None, *args, **kwargs)[source]¶

move_joints_avoidance(union_vel, union_link_list=None, link_list=None, n_joint_dimension=None, weight=None, null_space=None, avoid_nspace_gain=0.01, avoid_weight_gain=1.0, avoid_collision_distance=200, avoid_collision_null_gain=1.0, avoid_collision_joint_gain=1.0, collision_avoidance_link_pair=None, cog_gain=0.0, target_centroid_pos=None, centroid_offset_func=None, cog_translation_axis='z', cog_null_space=False, additional_weight_list=None, additional_nspace_list=None, jacobi=None, obstacles=None, *args, **kwargs)[source]¶

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

Update this coordinates.

This function records that this CascadedCoords has changed and recursively records the change to descendants of this CascadedCoords.

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.

open_hand(default_angle=0.17453292519943295, av=None)[source]¶

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]¶

parentcoords()[source]¶

reset_joint_angle_limit_weight(union_link_list)[source]¶

reset_manip_pose()[source]¶

reset_pose()[source]¶

rotate(theta, axis, wrt='local')[source]¶

Rotate this coordinate.

Rotate this coordinate relative to axis by theta radians with respect to wrt.

Parameters:

theta (float) – radian
axis (str or numpy.ndarray) – ‘x’, ‘y’, ‘z’ or vector
wrt (str or Coordinates) –

Return type:

self

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(matrix, wrt)[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]))

self_collision_check()[source]¶

Return collision link pair

Returns:

is_collision (bool) – True if a collision occurred between any pair of objects and False otherwise
names (set of 2-tuple) – The set of pairwise collisions. Each tuple contains two names in alphabetical order indicating that the two corresponding objects are in collision.

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

Transform this coordinates

Parameters:

c (skrobot.coordinates.Coordinates) – coordinates
wrt (str or skrobot.coordinates.Coordinates) – transform this coordinates with respect to wrt. If wrt is ‘local’ or self, multiply c from the right. If wrt is ‘parent’ or self.parent, transform c with respect to parentcoords. (multiply c from the left.) 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 self

Return type:

skrobot.coordinates.CascadedCoords

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])

update(force=False)[source]¶

worldcoords()[source]¶: Calculate rotation and position in the world.

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

default_urdf_path¶

descendants¶

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

interlocking_joint_pairs¶

Interlocking joint pairs.

pairs are [(joint0, joint1), …] If users want to use interlocking joints, please overwrite this method.

joint_max_angles¶

joint_min_angles¶

larm¶

lleg¶

name¶

Return this coordinate’s name

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

parent¶

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])

rarm¶

rleg¶

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