MathematicalRobotics

What is this?

The development of robotics is always closely related to mathematics. But sometime pure mathematical expressions are boring and difficult to understand, so I hope to show the magic of mathematics through some interesting robotics demonstrations.

The goals of our project.

We want to select some widely used and practical algorithms. for each algorithm, we aim to

• Provide a readable python implementation.
• Show a detailed mathematical proof.
• To show the math behind it, minimal use of third-party libraries.

Requirements

sudo apt-get install libsuitesparse-dev
pip3 install -r requirements.txt

Demo Lists

guass_newton_method

We have developed a Gauss-Newton method library implemented in pure Python.

• Guass-newton Method Document
• Newton Method Document

We also provide some demos on Lie-Group based points matching using our library.

Lie group Document:

• SO3 group
• SE3 group

gauss newton for 2d points matching.

guass_newton_method/demo_2d.py

gauss newton for 3d points matching.

guass_newton_method/demo_3d.py

gauss newton for linear regression.

guass_newton_method/demo_line.py

Graph Optimization

We have developed a graph optimization library implemented in pure Python. In comparison to well-known graph optimization libraries like g2o, gtsam, ceres, etc., our implementation is highly readable and ideal for studying purposes.

Graph Optimization Document

2d pose graph problem

graph_optimization/demo_g2o_se2.py

dataset: sphere2500.g2o ¹

3d pose graph problem

graph_optimization/demo_g2o_se3.py

dataset: manhattanOlson3500.g2o ¹

bundle adjustment

slam/demo_bundle_adjustment.py

dataset: Venice: problem-427-310384-pre ²

geometry

point to line ICP

robot_geometry/demo_p2line_matching.py

point to plane ICP

robot_geometry/demo_p2plane_matching.py

plane cross a cube

robot_geometry/demo_plane_cross_cube.py

Footnotes

1. Datasets are available in the open source package of vertigo. ↩ ↩²

2. The datasets used in the demo are available in the project Bundle Adjustment in the Large. ↩