Math lasts forever, even in the AI era.
The best way to attack Math is to write it down and think twice yourself.
This course is designed to cover the in-depth math knowledge essential for research in Robotics & State Estimation, with direct applications to:
- Robot perception and navigation
- Simultaneous Localization and Mapping (SLAM)
- Structure from Motion (SfM)
- Visual-Inertial Odometry (VIO)
- Multi-sensor fusion & calibration
| # | Topic | Contents | Instructor | Recording | |
|---|---|---|---|---|---|
| 1 | Basics | probability, estimator, linear system | Yulin Yang | — | |
| 2 | 3D Geometry | rotation, Lie group (SE(3), SE2(3)) | Yulin Yang | — | |
| 3 | Visual SLAM I | camera model, point / line / plane | Yulin Yang | — | |
| 4 | Visual SLAM II | information, marginalization and pipeline | Yulin Yang | — | |
| 5 | IMU | IMU model and integration | Yulin Yang | — | |
| 6 | Kalman Filter For SLAM | KF and observability analysis, KF-based VINS | Yulin Yang | — | |
| 7 | Batch Optimization For SLAM | IMU pre-integration based VINS, multi-visual-inertial | Yulin Yang | — | |
| 8 | Information Theory for Estimation | TBD | Chuchu Chen | — | — |
| 9 | System Consistency | TBD | Chuchu Chen | — | — |
| 10 | Learning-based SLAM | dense mapping | Xingxing Zuo | — | Slides |
See resources/ for the full reading list and links.
Lecture 2 — rotation, Lie groups, SE(3), quaternions
- Barfoot, State Estimation for Robotics, Cambridge Univ. Press, 2017 — Ch. 7 (matrix Lie groups): http://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser17.pdf
- Dellaert et al., Lie Groups for 2D and 3D Transformations (GTSAM): https://github.com/borglab/gtsam/blob/develop/doc/LieGroups.pdf
- Atanasov, Rotations SO(3) and Rigid-Body Motions SE(3) (ECE276A, UCSD, 2020): https://natanaso.github.io/ece276a2020/ref/ECE276A_12_SO3_SE3.pdf
- Solà, Deray & Atchuthan, A Micro Lie Theory for State Estimation in Robotics, 2018: https://arxiv.org/abs/1812.01537
- Trawny & Roumeliotis, Indirect Kalman Filter for 3D Attitude Estimation, UMN TR 2005-002 — Sec. 1: https://mediawiki.isr.tecnico.ulisboa.pt/images/d/db/Indirect_Kalman_Filter_for_3D_Attitude_Estimation.pdf
- Solà, Quaternion Kinematics for the Error-State Kalman Filter, 2017 — Sec. 1–3: https://arxiv.org/abs/1711.02508
- One lecture per week.
- Bring a pen and paper — follow along with the equation derivations.
- Video recordings and notes are shared after each lecture. Please do not redistribute (e.g., to YouTube) for now.
- Discussions and office hours are held on GitHub: https://github.com/yangyulin/rise-tutorial/discussions
Weekly on Sunday:
| Location | Local time |
|---|---|
| Seattle | 6:30 AM – 7:45 AM PDT |
| Washington DC | 9:30 AM – 10:45 AM EDT |
| Abu Dhabi | 5:30 PM – 6:45 PM |
| Beijing | 9:30 PM – 10:45 PM |