`pytransform3d.uncertainty`.concat_globally_uncertain_transforms¶

pytransform3d.uncertainty.concat_globally_uncertain_transforms(mean_A2B, cov_A2B, mean_B2C, cov_B2C)[source]¶

Concatenate two independent globally uncertain transformations.

We assume that the two distributions are independent.

Each of the two transformations is globally uncertain (not in the local / body frame), that is, samples are generated through

$\boldsymbol{T} = Exp(\boldsymbol{\xi}) \overline{\boldsymbol{T}},$

where $\boldsymbol{T} \in SE(3)$ is a sampled transformation matrix, $\overline{\boldsymbol{T}} \in SE(3)$ is the mean transformation, and $\boldsymbol{\xi} \in \mathbb{R}^6$ are exponential coordinates of transformations and are distributed according to a Gaussian distribution with zero mean and covariance $\boldsymbol{\Sigma} \in \mathbb{R}^{6 \times 6}$ , that is, $\boldsymbol{\xi} \sim \mathcal{N}(\boldsymbol{0}, \boldsymbol{\Sigma})$ .

The concatenation order is the same as in concat(), that is, the transformation B2C is left-multiplied to A2B. Note that the order of arguments is different from concat_locally_uncertain_transforms().

Hence, the full model is

$Exp(_C\boldsymbol{\xi'}) \overline{\boldsymbol{T}}_{CA} = Exp(_C\boldsymbol{\xi}) \overline{\boldsymbol{T}}_{CB} Exp(_B\boldsymbol{\xi}) \overline{\boldsymbol{T}}_{BA},$

where $_B\boldsymbol{\xi} \sim \mathcal{N}(\boldsymbol{0}, \boldsymbol{\Sigma}_{BA})$ , $_C\boldsymbol{\xi} \sim \mathcal{N}(\boldsymbol{0}, \boldsymbol{\Sigma}_{CB})$ , and $_C\boldsymbol{\xi'} \sim \mathcal{N}(\boldsymbol{0}, \boldsymbol{\Sigma}_{CA})$ .

This version of Barfoot and Furgale approximates the covariance up to 4th-order terms. Note that it is still an approximation of the covariance after concatenation of the two transforms.

Parameters:

mean_A2Barray, shape (4, 4): Mean of transform from A to B.
cov_A2Barray, shape (6, 6): Covariance of transform from A to B. Models uncertainty in frame B.
mean_B2Carray, shape (4, 4): Mean of transform from B to C.
cov_B2Carray, shape (6, 6): Covariance of transform from B to C. Models uncertainty in frame C.

Returns:

mean_A2Carray, shape (4, 4): Mean of new pose.
cov_A2Carray, shape (6, 6): Covariance of new pose. Models uncertainty in frame C.

Examples using `pytransform3d.uncertainty.concat_globally_uncertain_transforms`¶

Concatenate Uncertain Transforms

pytransform3d.uncertainty.concat_globally_uncertain_transforms¶

Examples using pytransform3d.uncertainty.concat_globally_uncertain_transforms¶

`pytransform3d.uncertainty`.concat_globally_uncertain_transforms¶

Examples using `pytransform3d.uncertainty.concat_globally_uncertain_transforms`¶