Doctoral course - Lie Theory for the Roboticist

External Teacher Name: Joan Sola
External Teach Organization: Consejo Superior de Investigaciones Científicas (CSIC)

Extent: 2 ECTS

Assesment:

Written exam.

Grading:

pass/fail.

Schedule

Day 1: Tuesday 9.4 at 13:15-16:45 in PK251

Day 2: Wednesday 10.4 at 13:15-16:45 in TL102

Day 3: Thursday 11.4 at 13:15-16:45 in TL102

About the Instructor

http://www.joansola.eu/

Preparation

[1] Sola, Joan, Jeremie Deray, and Dinesh Atchuthan. "A micro Lie theory for state estimation in robotics." arXiv preprint arXiv:1812.01537 (2018).

[2] Sola, Joan. "Quaternion kinematics for the error-state Kalman filter." arXiv preprint arXiv:1711.02508 (2017).

Learning Objectives and Contents:
This course teaches the basics of Lie Theory from the perspective of using it with robotics.
1. The Notion of Group
2. The Notion of Manifold
3. Definition of Lie Group
4. Properties of Lie Groups
5. The Tangent Space and the Lie Algebra of a Lie Group
6. The Exponential Map
7. The Adjoint
8. Derivatives on Lie Groups
9. Motion Integration on Lie Groups
10. Uncertainty Representation and Propagation on Lie Groups
11. Exercises and Examples for Robotics

Course Schedule:
Day 1:
- Lectures, sections 1-6
- Evening self-study: 2.5 hours of exercises
Day 2:
- Review of Day 1 exercises
- Lectures, sections 7-10
- Evening self-study: 2.5 hours of exercises
Day 3:
- Review of Day 2 exercises
- Lectures, section 11