adam.core.spatial_math

adam.core.spatial_math#

Classes#

`ArrayLike`	Abstract class for a generic Array wrapper. Every method should be implemented for every data type.
`ArrayLikeFactory`	Abstract class for a generic Array wrapper. Every method should be implemented for every data type.
`SpatialMath`	Class implementing the main geometric functions used for computing rigid-body algorithm

Module Contents#

class adam.core.spatial_math.ArrayLike[source]#

Bases: abc.ABC

Abstract class for a generic Array wrapper. Every method should be implemented for every data type.

abstractmethod __add__(other)[source]#

abstractmethod __radd__(other)[source]#

abstractmethod __sub__(other)[source]#

abstractmethod __rsub__(other)[source]#

abstractmethod __mul__(other)[source]#

abstractmethod __rmul__(other)[source]#

abstractmethod __matmul__(other)[source]#

abstractmethod __rmatmul__(other)[source]#

abstractmethod __neg__()[source]#

abstractmethod __getitem__(item)[source]#

abstractmethod __setitem__(key, value)[source]#

abstractmethod __truediv__(other)[source]#

abstract property T[source]#

Transpose of the array

Type:: Returns

class adam.core.spatial_math.ArrayLikeFactory[source]#

Bases: abc.ABC

Abstract class for a generic Array wrapper. Every method should be implemented for every data type.

abstractmethod zeros(x: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: x (npt.ArrayLike) – matrix dimension
Returns:: zero matrix of dimension x
Return type:: npt.ArrayLike

abstractmethod eye(x: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: x (npt.ArrayLike) – matrix dimension
Returns:: identity matrix of dimension x
Return type:: npt.ArrayLike

class adam.core.spatial_math.SpatialMath(factory: ArrayLikeFactory)[source]#

Class implementing the main geometric functions used for computing rigid-body algorithm

Parameters:: ArrayLike – abstract class describing a generic Array wrapper. It needs to be implemented for every data type

_factory[source]#

property factory: ArrayLikeFactory[source]#

abstractmethod vertcat(x: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: x (npt.ArrayLike) – elements
Returns:: vertical concatenation of elements x
Return type:: npt.ArrayLike

abstractmethod horzcat(x: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: x (npt.ArrayLike) – elements
Returns:: horizontal concatenation of elements x
Return type:: npt.ArrayLike

abstractmethod mtimes(x: numpy.typing.ArrayLike, y: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

abstractmethod sin(x: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: x (npt.ArrayLike) – angle value
Returns:: sin value of x
Return type:: npt.ArrayLike

abstractmethod cos(x: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: x (npt.ArrayLike) – angle value
Returns:: cos value of angle x
Return type:: npt.ArrayLike

abstractmethod skew(x)[source]#

R_from_axis_angle(axis: numpy.typing.ArrayLike, q: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

axis (npt.ArrayLike) – axis vector
q (npt.ArrayLike) – angle value

Returns:

rotation matrix from axis-angle representation

Return type:

npt.ArrayLike

Rx(q: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: q (npt.ArrayLike) – angle value
Returns:: rotation matrix around x axis
Return type:: npt.ArrayLike

Ry(q: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: q (npt.ArrayLike) – angle value
Returns:: rotation matrix around y axis
Return type:: npt.ArrayLike

Rz(q: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: q (npt.ArrayLike) – angle value
Returns:: rotation matrix around z axis
Return type:: npt.ArrayLike

H_revolute_joint(xyz: numpy.typing.ArrayLike, rpy: numpy.typing.ArrayLike, axis: numpy.typing.ArrayLike, q: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

xyz (npt.ArrayLike) – joint origin in the urdf
rpy (npt.ArrayLike) – joint orientation in the urdf
axis (npt.ArrayLike) – joint axis in the urdf
q (npt.ArrayLike) – joint angle value

Returns:

Homogeneous transform

Return type:

npt.ArrayLike

H_prismatic_joint(xyz: numpy.typing.ArrayLike, rpy: numpy.typing.ArrayLike, axis: numpy.typing.ArrayLike, q: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

xyz (npt.ArrayLike) – joint origin in the urdf
rpy (npt.ArrayLike) – joint orientation in the urdf
axis (npt.ArrayLike) – joint axis in the urdf
q (npt.ArrayLike) – joint angle value

Returns:

Homogeneous transform

Return type:

npt.ArrayLike

H_from_Pos_RPY(xyz: numpy.typing.ArrayLike, rpy: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

xyz (npt.ArrayLike) – translation vector
rpy (npt.ArrayLike) – rotation as rpy angles

Returns:

Homegeneous transform

Return type:

npt.ArrayLike

R_from_RPY(rpy: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: rpy (npt.ArrayLike) – rotation as rpy angles
Returns:: Rotation matrix
Return type:: npt.ArrayLike

X_revolute_joint(xyz: numpy.typing.ArrayLike, rpy: numpy.typing.ArrayLike, axis: numpy.typing.ArrayLike, q: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

xyz (npt.ArrayLike) – joint origin in the urdf
rpy (npt.ArrayLike) – joint orientation in the urdf
axis (npt.ArrayLike) – joint axis in the urdf
q (npt.ArrayLike) – joint angle value

Returns:

Spatial transform of a revolute joint given its rotation angle

Return type:

npt.ArrayLike

X_prismatic_joint(xyz: numpy.typing.ArrayLike, rpy: numpy.typing.ArrayLike, axis: numpy.typing.ArrayLike, q: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

xyz (npt.ArrayLike) – joint origin in the urdf
rpy (npt.ArrayLike) – joint orientation in the urdf
axis (npt.ArrayLike) – joint axis in the urdf
q (npt.ArrayLike) – joint angle value

Returns:

Spatial transform of a prismatic joint given its increment

Return type:

npt.ArrayLike

X_fixed_joint(xyz: numpy.typing.ArrayLike, rpy: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

xyz (npt.ArrayLike) – joint origin in the urdf
rpy (npt.ArrayLike) – joint orientation in the urdf

Returns:

Spatial transform of a fixed joint

Return type:

npt.ArrayLike

spatial_transform(R: numpy.typing.ArrayLike, p: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

R (npt.ArrayLike) – Rotation matrix
p (npt.ArrayLike) – translation vector

Returns:

spatial transform

Return type:

npt.ArrayLike

spatial_inertia(I: numpy.typing.ArrayLike, mass: numpy.typing.ArrayLike, c: numpy.typing.ArrayLike, rpy: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

I (npt.ArrayLike) – inertia values from urdf
mass (npt.ArrayLike) – mass value from urdf
c (npt.ArrayLike) – origin of the link from urdf
rpy (npt.ArrayLike) – orientation of the link from the urdf

Returns:

the 6x6 inertia matrix expressed at the origin of the link (with rotation)

Return type:

npt.ArrayLike

spatial_inertial_with_parameters(I, mass, c, rpy)[source]#

Parameters:

I (npt.ArrayLike) – inertia values parametric
mass (npt.ArrayLike) – mass value parametric
c (npt.ArrayLike) – origin of the link parametric
rpy (npt.ArrayLike) – orientation of the link from urdf

Returns:

the 6x6 inertia matrix parametric expressed at the origin of the link (with rotation)

Return type:

npt.ArrayLike

spatial_skew(v: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: v (npt.ArrayLike) – 6D vector
Returns:: spatial skew matrix
Return type:: npt.ArrayLike

spatial_skew_star(v: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: v (npt.ArrayLike) – 6D vector
Returns:: negative spatial skew matrix traspose
Return type:: npt.ArrayLike

adjoint(H: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: H (npt.ArrayLike) – Homogeneous transform
Returns:: adjoint matrix
Return type:: npt.ArrayLike

adjoint_derivative(H: numpy.typing.ArrayLike, v: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

H (npt.ArrayLike) – Homogeneous transform
v (npt.ArrayLike) – 6D twist

Returns:

adjoint matrix derivative

Return type:

npt.ArrayLike

adjoint_inverse(H: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: H (npt.ArrayLike) – Homogeneous transform
Returns:: adjoint matrix
Return type:: npt.ArrayLike

adjoint_inverse_derivative(H: numpy.typing.ArrayLike, v: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

H (npt.ArrayLike) – Homogeneous transform
v (npt.ArrayLike) – 6D twist

Returns:

adjoint matrix derivative

Return type:

npt.ArrayLike

adjoint_mixed(H: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: H (npt.ArrayLike) – Homogeneous transform
Returns:: adjoint matrix
Return type:: npt.ArrayLike

adjoint_mixed_inverse(H: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: H (npt.ArrayLike) – Homogeneous transform
Returns:: adjoint matrix
Return type:: npt.ArrayLike

adjoint_mixed_derivative(H: numpy.typing.ArrayLike, v: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

H (npt.ArrayLike) – Homogeneous transform
v (npt.ArrayLike) – 6D twist

Returns:

adjoint matrix derivative

Return type:

npt.ArrayLike

adjoint_mixed_inverse_derivative(H: numpy.typing.ArrayLike, v: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:

H (npt.ArrayLike) – Homogeneous transform
v (npt.ArrayLike) – 6D twist

Returns:

adjoint matrix derivative

Return type:

npt.ArrayLike

homogeneous_inverse(H: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Parameters:: H (npt.ArrayLike) – Homogeneous transform
Returns:: inverse of the homogeneous transform
Return type:: npt.ArrayLike