Tutorial on manifolds and lie groups

[aaron-skydio]

[LMWafer]

As examples, I suggest the following references :

• A micro Lie theory for state estimation in robotics. It explains core concepts from a robotic POV into less than 20 pages and provides references to other tutorials.
• Modern Robotics : Mechanics, Planning and Control. A book alongside videos and online courses to explain Lie groups and their applications to undergraduates.
• Lie groups for 2D and 3D transformations. Provides tools for operations, differentiation and probabilities over usual groups (SO(3), SE(3), Sim(3) etc.)
• A tutorial on SE(3) transformation parameterizations and on-manifold optimization. Similar to the previous reference, but offers a lot more insights on maths and proposes an optimization POV.
• The Banana Distribution Is Gaussian: A Localization Study with Exponential Coordinates. A research paper accessible to graduates who want to better understand probabilities one Lie groups.