最优控制碎碎念
欢迎来到「最优控制碎碎念」系列！本系列融合施凌老师的 协同感知、Zachary Manchester 的 最优控制、高飞老师的 轨迹规划 以及 Pieter Abbeel 的 深度强化学习 等课程精华，通过严谨的数学推导，构建一个从经典控制到现代强化学习的完整知识体系。我们将从最优感知与控制的基础理论出发，系统探讨模型预测控制、轨迹规划等核心主题，并深入解析深度强化学习在控制领域的前沿进展。
Posts
Derivation of On-Manifold IMU Preintegration
- C. Forster, L. Carlone, F. Dellaert, and D. Scaramuzza, “On-Manifold Preintegration for Real-Time Visual--Inertial Odometry,” IEEE Trans. Robot., vol. 33, no. 1, pp. 1–21, Feb. 2017, doi: 10.1109/TRO.2016.2597321.
- Z. Yang and S. Shen, “Monocular Visual–Inertial State Estimation With Online Initialization and Camera–IMU Extrinsic Calibration,” IEEE Trans. Automat. Sci. Eng., vol. 14, no. 1, pp. 39–51, Jan. 2017, doi: 10.1109/TASE.2016.2550621.
IMU preintegration is a technique in visual-inertial odometry that efficiently fuses high-frequency IMU data between keyframes. Using Lie group theory on \(SE(3)\), it handles nonlinear 3D rotations and precomputes motion constraints for optimization. This method accounts for sensor biases, noise, and is essential for real-time state estimation.
Innovations in BIM-based Localization
- H. Yin, J. M. Liew, W. L. Lee, M. H. Ang, Ker-Wei Yeoh, and Justin, “Towards BIM-based robot localization: a real-world case study,” presented at the 39th International Symposium on Automation and Robotics in Construction, Jul. 2022. doi: 10.22260/ISARC2022/0012.
- H. Yin, Z. Lin, and J. K. W. Yeoh, “Semantic localization on BIM-generated maps using a 3D LiDAR sensor,” Automation in Construction, vol. 146, p. 104641, Feb. 2023, doi: 10.1016/j.autcon.2022.104641.
- Z. Qiao et al., “Speak the Same Language: Global LiDAR Registration on BIM Using Pose Hough Transform,” IEEE Transactions on Automation Science and Engineering, pp. 1–1, 2025, doi: 10.1109/TASE.2025.3549176.
In traditional SLAM, mapping and localization occur simultaneously, with maps built incrementally. In construction, maps are created once to support long-term operations, and BIM is increasingly favored over CAD. The following studies explore BIM-based localization, semantic consistency, and geometric consistency.
Sparsity Extended Information Filter SLAM
M. R. Walter, R. M. Eustice, and J. J. Leonard, “Exactly Sparse Extended Information Filters for Feature-based SLAM,” The International Journal of Robotics Research, vol. 26, no. 4, pp. 335–359, Apr. 2007, doi: 10.1177/0278364906075026.
稀疏扩展信息滤波器（SEIF）SLAM 是一种计算高效的同时定位与地图构建（SLAM）方法。通过利用信息矩阵的稀疏性，SEIF 降低了状态估计的计算复杂度，使其适用于大规模环境。
Linear Quadratic Regulator
This is the lecture notes for 'ELEC 5650: Networked Sensing, Estimation and Control' in the 2024-25 Spring semester, delivered by Prof. Ling Shi at HKUST. In this session, we will cover Linear Quadratic Regulator (LQR) theory and its applications in control systems.
Kalman Filter in 3 Ways
This is the lecture notes for "ELEC 5650: Networked Sensing, Estimation and Control" in the 2024-25 Spring semester, delivered by Prof. Ling Shi at HKUST. In this session, we will deviate Kalman Filter from three different perspectives: Geometric, Probabilistic, and Optimization approaches.
Optimal Estimation Theory
This is the lecture notes for "ELEC 5650: Networked Sensing, Estimation and Control" in the 2024-25 Spring semester, delivered by Prof. Ling Shi at HKUST. In this session, we will explore maximum a posteriori (MAP) estimation, minimum mean squared error (MMSE) estimation, maximum likelihood (ML) estimation, weighted least squares estimation, and linear minimum mean square error (LMMSE) estimation.
Linear Algebra & System Theory
This is the lecture notes for "ELEC 5650: Networked Sensing, Estimation and Control" in the 2024-25 Spring semester, delivered by Prof. Ling Shi at HKUST. In this session, we will cover essential mathematical tools and concepts from linear algebra, matrix theory, and system theory that are fundamental to networked sensing, estimation, and control.