pytransform3d.uncertainty.invert_uncertain_transform

pytransform3d.uncertainty.invert_uncertain_transform(mean, cov)[source]

Invert uncertain transform.

For the mean \boldsymbol{T}_{BA}, the inverse is simply \boldsymbol{T}_{BA}^{-1} = \boldsymbol{T}_{AB}.

For the covariance, we need the adjoint of the inverse transformation \left[Ad_{\boldsymbol{T}_{BA}^{-1}}\right]:

\boldsymbol{\Sigma}_{\boldsymbol{T}_{AB}}
=
\left[Ad_{\boldsymbol{T}_{BA}^{-1}}\right]
\boldsymbol{\Sigma}_{\boldsymbol{T}_{BA}}
\left[Ad_{\boldsymbol{T}_{BA}^{-1}}\right]^T

Parameters:
meanarray-like, shape (4, 4)

Mean of transform from frame A to frame B.

covarray, shape (6, 6)

Covariance of transform from frame A to frame B in exponential coordinate space.

Returns:
mean_invarray, shape (4, 4)

Mean of transform from frame B to frame A.

cov_invarray, shape (6, 6)

Covariance of transform from frame B to frame A in exponential coordinate space.

See also

pytransform3d.transformations.invert_transform

Invert transformation without uncertainty.

References

Mangelson, Ghaffari, Vasudevan, Eustice: Characterizing the Uncertainty of Jointly Distributed Poses in the Lie Algebra, https://arxiv.org/pdf/1906.07795.pdf

Examples using pytransform3d.uncertainty.invert_uncertain_transform

Invert Uncertain Transform

Invert Uncertain Transform

Invert Uncertain Transform