pytransform3d.transformations.adjoint_from_transform

pytransform3d.transformations.adjoint_from_transform(A2B, strict_check=True, check=True)[source]

Compute adjoint representation of a transformation matrix.

The adjoint representation of a transformation \left[Ad_{\boldsymbol{T}_{BA}}\right] from frame A to frame B translates a twist from frame A to frame B through the adjoint map

\mathcal{V}_{B}
= \left[Ad_{\boldsymbol{T}_{BA}}\right] \mathcal{V}_A

The corresponding matrix form is

\left[\mathcal{V}_{B}\right]
= \boldsymbol{T}_{BA} \left[\mathcal{V}_A\right]
\boldsymbol{T}_{BA}^{-1}

We can also use the adjoint representation to transform a wrench from frame A to frame B:

\mathcal{F}_B
= \left[ Ad_{\boldsymbol{T}_{AB}} \right]^T \mathcal{F}_A

Note that not only the adjoint is transposed but also the transformation is inverted.

Adjoint representations have the following properties:

\left[Ad_{\boldsymbol{T}_1 \boldsymbol{T}_2}\right]
= \left[Ad_{\boldsymbol{T}_1}\right]
\left[Ad_{\boldsymbol{T}_2}\right]

\left[Ad_{\boldsymbol{T}}\right]^{-1} =
\left[Ad_{\boldsymbol{T}^{-1}}\right]

Parameters
A2Barray-like, shape (4, 4)

Transform from frame A to frame B

strict_checkbool, optional (default: True)

Raise a ValueError if the transformation matrix is not numerically close enough to a real transformation matrix. Otherwise we print a warning.

checkbool, optional (default: True)

Check if transformation matrix is valid

Returns
adj_A2Barray, shape (6, 6)

Adjoint representation of transformation matrix

Examples using pytransform3d.transformations.adjoint_from_transform