Regression in Logmap? (v4.2a7)

[Guillaume Jacob]

Hi everyone,

After an upgrade from version 4.0.3 to 4.2a7, we've noticed a strange behavior in our unit tests which we were able to track down to back and forth conversions between AngleAxis and Rotation representations for rotations.

Here is a piece of code that generates random test data in the form of 3D vectors with a norm close to PI, applies Logmap / Expmap to each vector and compares the vectors before / after this transformation − using the same metric as Eigen::DenseBase::isApprox().

* With GTSAM 4.0.3, the error is lower than 1e-9 for angles < 3.140 rad, then increases as the angle approaches PI (as expected due to the singularity).

* With GTSAM 4.2a7, we can notice a huge jump from about 1e-12 to [1e-5, 1e-3] around ~3.110 rad and a decrease as the angle gets closer to PI.

There have been several changes in SO3::Logmap recently so we suppose a mistake might have slipped unnoticed. What do you think?

Thanks in advance,

Guillaume

[Guillaume Jacob]

I forgot to mention that with some modifications I was able to reduce the error jump from ~1e-4 down to ~1e-8 by including two additional higher order terms in the Taylor series for the scale and replacing the approximation `Q1 = 2.0 + 2.0 * Raa` by `Q1 = 1 + 2 * Raa - tr` to account for the fact that the trace of R is not exactly -1. However, we still have the discontinuity around ~ 3.110 rad.

G

[Guillaume Jacob]

Hi Fan,

I've tried with several tolerance values: 1e-4 to 1e-9, see attached figures. Pay attention to the vertical axis, as limits can change from one figure to another. Let me know if you think of additional tests I could perform.

Thanks,

Guillaume

On Sat, 25 Jun 2022 at 07:53, Jiang, Fan <fan....@gatech.edu> wrote:

Hi G,

I am pretty sure this is due to my PR https://github.com/borglab/gtsam/pull/887 for fixing the singularity. The tolerances in that PR seems a bit too loose, thanks to your observations. Could you try changing the 

if (tr + 1.0 < 1e-4) { to some higher tolerances and see the impact?

Best,

Fan

Fan Jiang

3rd year Robotics PhD
Georgia Institute of Technology

E-mail: fan....@gatech.edu

Try TeXmacs today!

On Jun 24, 2022, at 06:51:25, Guillaume Jacob <guillau...@easymile.com> wrote:

I forgot to mention that with some modifications I was able to reduce the error jump from ~1e-4 down to ~1e-8 by including two additional higher order terms in the Taylor series for the scale and replacing the approximation `Q1 = 2.0 + 2.0 * Raa` by `Q1 = 1 + 2 * Raa - tr` to account for the fact that the trace of R is not exactly -1. However, we still have the discontinuity around ~ 3.110 rad.

<Figure_4_hot+tr_s.png>

G

On Friday, 24 June 2022 at 15:37:15 UTC+2 Guillaume Jacob wrote:

Hi everyone,

After an upgrade from version 4.0.3 to 4.2a7, we've noticed a strange behavior in our unit tests which we were able to track down to back and forth conversions between AngleAxis and Rotation representations for rotations.

Here is a piece of code that generates random test data in the form of 3D vectors with a norm close to PI, applies Logmap / Expmap to each vector and compares the vectors before / after this transformation − using the same metric as Eigen::DenseBase::isApprox().

* With GTSAM 4.0.3, the error is lower than 1e-9 for angles < 3.140 rad, then increases as the angle approaches PI (as expected due to the singularity).

* With GTSAM 4.2a7, we can notice a huge jump from about 1e-12 to [1e-5, 1e-3] around ~3.110 rad and a decrease as the angle gets closer to PI.

There have been several changes in SO3::Logmap recently so we suppose a mistake might have slipped unnoticed. What do you think?

Thanks in advance,

Guillaume

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<Figure_4_hot+tr_s.png>

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[Frank Dellaert]

Thanks for the thorough investigation! I was traveling but will talk to Fan to check into it in more detail.

Is it possible to create an issue on GTSAM repo and upload these graphs?

Frank

[Fan Jiang]

Hi Guillaume,

Thanks for the new investigations! Could you open an issue on GitHub with the data, so we can keep better records?

On your test results: If you read #887 you will see that the reason #887 is introduced is to fix the axis angle for slight unnormalized matrices, hence the test case in #887. For your problem, it seems that the changes introduced have reduced tolerance when off the singularity. I am thinking about 1. reduce tolerance to like 1e-7 and 2. add a higher order term in the near-singularity case. We can tune the two halves to match at the transition.

Best,

Fan

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[Guillaume Jacob]

Frank, Fan,

Thanks for the feedback! Here's the link to the new issue: https://github.com/borglab/gtsam/issues/1233.

Regards,

Guillaume