Add Graph SLAM documentation and SE(2) example

[JeffLIrion]

This is a work in progress.

The Jupyter notebook doesn't render correctly on GitHub, so I moved the write-up into a LaTeX file and included both the .tex source and the generated PDF. I'll probably remove it altogether from the Jupyter notebook.

TODO: Add code and example problem

Related issue: #296

[AtsushiSakai]

@JeffLIrion Your doc looks great!!. Please keep working it : ).

[lgtm-com]

This pull request introduces 1 alert when merging 4e2d7a8 into 869650f - view on LGTM.com

new alerts:

• 1 for Unused import

[lgtm-com]

This pull request introduces 1 alert when merging a12b675 into 869650f - view on LGTM.com

new alerts:

• 1 for Unused import

[lgtm-com]

This pull request introduces 1 alert when merging 6ebdb42 into 869650f - view on LGTM.com

new alerts:

• 1 for Unused local variable

[JeffLIrion]

Current status

• Add a few citations to the write-up
• Add code for loading, optimizing, and plotting SE(2) datasets
• Add an example problem with figures
• Clean up the Jupyter notebook

Any other tasks that you'd like to see completed?

[AtsushiSakai]

Thank you for your hard work!!. That is OK. Please let me know when you are ready to start to review.

[JeffLIrion]

This is ready to start the review process!

[AtsushiSakai]

Thank you for your big work. I have several questions.

1. This repo already have graph_based_slam.py. is your code using same algorithm?
2. Do you want to keep latex codes and pdf? is it impossible to use jupyter notebook to describe math?
3. You added images in the image dir. Are these impossible to embedded a jupyter notebook?

[JeffLIrion]

1. This repo already have graph_based_slam.py. is your code using same algorithm?

   • It looks to be the same algorithm: compute b and H, solve the linear system H dx = -b, and update the poses. What the included package contributes is a Graph SLAM solver that:

     • uses a standard data format (.g2o files) for importing and exporting data
     • has been validated against results from g2o, which is arguably the de facto Graph SLAM solver

   • If the code in graph_based_slam.py could be used to achieve these same results, then I would agree that the code is redundant.

2. Do you want to keep latex codes and pdf? is it impossible to use jupyter notebook to describe math?

   • Yes, I definitely think that both the LaTeX source and the PDF should be kept. That way, it is easy to make a correction or contribution to the write-up.
   • I originally tried to put the LaTeX code in the Jupyter notebook, but the formatting was really bad and I couldn't make it work. For example: https://github.com/JeffLIrion/PythonRobotics/blob/20fec7d60f9ca6063a58430be65c96f33beded28/SLAM/GraphBasedSLAM/graphSLAM_formulation.ipynb

3. You added images in the image dir. Are these impossible to embedded a jupyter notebook?

   • I can embed them in a Jupyter notebook. I also meant to make a .gif out of them. I'll do that now.
   • Follow-up: I created the .gif image and embedded it in the Jupyter notebook. Let me know if you'd like me to delete the .png images.

[JeffLIrion]

For my own reference:

convert -background white -alpha remove -alpha off -delay 200 -loop 0 iteration*.png Graph_SLAM_optimization.gif

[AtsushiSakai]

If the code in graph_based_slam.py could be used to achieve these same results, then I would agree that the code is redundant.

Do you think it is possible for you to update the graph_based_slam.py using your solver?

[AtsushiSakai]

Yes, I definitely think that both the LaTeX source and the PDF should be kept.

OK. I got it.

[AtsushiSakai]

Let me know if you'd like me to delete the .png images.

Oh. great. Please remove the pngs. I want to keep the PR as simple as possible.

[JeffLIrion]

Let me know if you'd like me to delete the .png images.

Oh. great. Please remove the pngs. I want to keep the PR as simple as possible.

Done. I left only the .gif image.

[JeffLIrion]

If the code in graph_based_slam.py could be used to achieve these same results, then I would agree that the code is redundant.

Do you think it is possible for you to update the graph_based_slam.py using your solver?

I'm sure it's possible, but my wife and I just had a baby, so I simply don't have the time to do that right now. Sorry.

[AtsushiSakai]

OK. Thank you so much.

I simply don't have the time to do that right now. Sorry.

No problem. Is it ok to merge this PR now? Maybe I can do it later.

[JeffLIrion]

No problem. Is it ok to merge this PR now? Maybe I can do it later.

I'll squash my commits and then it will be ready.

[JeffLIrion]

I squashed the commits, so this is ready to be merged.

[AtsushiSakai]

@JeffLIrion Thank you so much for your great work. More PRs are always welcome!!