Uncertainty

[AlexanderFabisch]

Features

• pytransform3d.rotations
  • Add left Jacobian of SO(3) and its inverse
• pytransform3d.transformations
  • Add Jacobian of SE(3) and its inverse
  • Add function to generate random exponential coordinates
  • Extend function to generate random transformation matrices by mean and covariance argument
• Add new module pytransform3d.uncertainty with the following functions:
  • estimate_gaussian_transform_from_samples
  • invert_uncertain_transform
  • concat_uncertain_transforms
  • pose_fusion
  • to_ellipsoid
  • to_projected_ellipsoid
  • plot_projected_ellipsoid

TODO

• [x] features
  • [x] compare exponential coordinate representations
  • [x] pose fusion
  • [x] concatenation of transformations
  • [x] sampling
  • [x] Gaussian estimation
    • [x] compare to http://www.roboticsproceedings.org/rss08/p34.pdf, Eq. 26, 27
  • [x] inversion
    • [x] check covariance of position terms in example plots
  • [x] cross-terms in covariances (https://arxiv.org/pdf/1906.07795.pdf, https://bitbucket.org/jmangelson/lie)
  • [x] projected ellipsoid surface
• [x] unify notation
• [x] examples
  • [x] make pose composition 3D
• [x] refactoring
  • [x] move Jacobian of SE(3) to transformations
  • [x] remove swap operations in 4th order terms
• [x] unit tests
  • [x] Jacobians of SO(3)
  • [x] Jacobians of SE(3) -> also extreme cases (theta = 0); series representation
  • [x] uncertainty module
  • [x] compare pose fusion with Matlab code of B/F
  • [x] compare pose composition with B/F
• [x] API doc
• [x] type hints

Literature

• http://ncfrn.mcgill.ca/members/pubs/barfoot_tro14.pdf
• https://arxiv.org/pdf/1906.07795.pdf, https://bitbucket.org/jmangelson/lie/src/master/
• https://gtsam.org/2021/02/23/uncertainties-part1.html
• https://gtsam.org/2021/02/23/uncertainties-part2.html
• https://gtsam.org/2021/02/23/uncertainties-part3.html

[codecov-commenter]

Codecov Report

Patch coverage: 100.00% and no project coverage change.

Comparison is base (a695633) 100.00% compared to head (47b970e) 100.00%.

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Additional details and impacted files

```diff @@ Coverage Diff @@ ## develop-3 #229 +/- ## ============================================ Coverage 100.00% 100.00% ============================================ Files 22 25 +3 Lines 2155 2348 +193 Branches 250 264 +14 ============================================ + Hits 2155 2348 +193 ``` | [Impacted Files](https://codecov.io/gh/dfki-ric/pytransform3d/pull/229?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=dfki-ric) | Coverage Δ | | |---|---|---| | [...ansform3d/transformations/\_transform\_operations.py](https://codecov.io/gh/dfki-ric/pytransform3d/pull/229?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=dfki-ric#diff-cHl0cmFuc2Zvcm0zZC90cmFuc2Zvcm1hdGlvbnMvX3RyYW5zZm9ybV9vcGVyYXRpb25zLnB5) | `100.00% <ø> (ø)` | | | [pytransform3d/rotations/\_\_init\_\_.py](https://codecov.io/gh/dfki-ric/pytransform3d/pull/229?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=dfki-ric#diff-cHl0cmFuc2Zvcm0zZC9yb3RhdGlvbnMvX19pbml0X18ucHk=) | `100.00% <100.00%> (ø)` | | | [pytransform3d/rotations/\_conversions.py](https://codecov.io/gh/dfki-ric/pytransform3d/pull/229?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=dfki-ric#diff-cHl0cmFuc2Zvcm0zZC9yb3RhdGlvbnMvX2NvbnZlcnNpb25zLnB5) | `100.00% <100.00%> (ø)` | | | [pytransform3d/rotations/\_jacobians.py](https://codecov.io/gh/dfki-ric/pytransform3d/pull/229?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=dfki-ric#diff-cHl0cmFuc2Zvcm0zZC9yb3RhdGlvbnMvX2phY29iaWFucy5weQ==) | `100.00% <100.00%> (ø)` | | | [pytransform3d/transformations/\_\_init\_\_.py](https://codecov.io/gh/dfki-ric/pytransform3d/pull/229?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=dfki-ric#diff-cHl0cmFuc2Zvcm0zZC90cmFuc2Zvcm1hdGlvbnMvX19pbml0X18ucHk=) | `100.00% <100.00%> (ø)` | | | [pytransform3d/transformations/\_conversions.py](https://codecov.io/gh/dfki-ric/pytransform3d/pull/229?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=dfki-ric#diff-cHl0cmFuc2Zvcm0zZC90cmFuc2Zvcm1hdGlvbnMvX2NvbnZlcnNpb25zLnB5) | `100.00% <100.00%> (ø)` | | | [pytransform3d/transformations/\_jacobians.py](https://codecov.io/gh/dfki-ric/pytransform3d/pull/229?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=dfki-ric#diff-cHl0cmFuc2Zvcm0zZC90cmFuc2Zvcm1hdGlvbnMvX2phY29iaWFucy5weQ==) | `100.00% <100.00%> (ø)` | | | [pytransform3d/transformations/\_random.py](https://codecov.io/gh/dfki-ric/pytransform3d/pull/229?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=dfki-ric#diff-cHl0cmFuc2Zvcm0zZC90cmFuc2Zvcm1hdGlvbnMvX3JhbmRvbS5weQ==) | `100.00% <100.00%> (ø)` | | | [pytransform3d/uncertainty.py](https://codecov.io/gh/dfki-ric/pytransform3d/pull/229?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=dfki-ric#diff-cHl0cmFuc2Zvcm0zZC91bmNlcnRhaW50eS5weQ==) | `100.00% <100.00%> (ø)` | | Help us with your feedback. Take ten seconds to tell us [how you rate us](https://about.codecov.io/nps?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=dfki-ric). Have a feature suggestion? [Share it here.](https://app.codecov.io/gh/feedback/?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=dfki-ric)

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