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_transformInvert transformation without uncertainty.
References
[1]Mangelson, G., Vasudevan, E. (2019). Characterizing the Uncertainty of Jointly Distributed Poses in the Lie Algebra, https://arxiv.org/pdf/1906.07795.pdf
