- 22 Sep Class — Real-time updates: (Prof is currently at 👨🏽🏫)
Note-1: Please read this note first.
This page is complete and this level of understanding is sufficient for the scope of this course. However, the way it is introduced might be a bit confusing. Therefore, it is highly suggested to go through the basics first (LINK TO BE ADDED) and understand the general formulation of any common optimization function in robotics/vision.
For interested readers, there are certain Lie Group/Lie Algebra concepts which may be given as formulae in this page. You can refer to "A micro Lie theory for state estimation in robotics" to dive into more detail.
Prof's notes on ICP-SLAM
Prof Madhav's notes on ICP-SLAM
(This Notion page link if you're viewing a PDF)
0. Need for SLAM Backend or Multiview ICP "Optimization"
In the figure:
- Blue frame $\{0\}$ 🖼️ —— $\mathrm{T}_{0}=[ \mathbf{I} | \mathbf{0}]$ is the origin.
- Blue tree 🌴—— ${\mathrm{X}}{0j}=\left[ \begin{array}{lll} x{0j} & y_{0j} & z_{0j} \end{array}\right] ^\mathrm{T}$: where $j=\{1,\dots,n\}$ are the coordinates of $n$ points in frame $\{0\}$ obtained from depth, azimuth and elevation measurements.
- Since the depth for every pont $j$ in frame $\{0\}$ is in error, hence ${\mathrm{X}}_{0j}$ is also in error.
- So is the case for ${\mathrm{X}}{1j}$ (frame 1) and hence, relative pose estimates between successive frames $\{i,i+1\}$ i.e. $\widehat{\mathrm{T}}{01}, \widehat{\mathrm{T}}{12},\dots, \widehat{\mathrm{T}}{(m-1 ,\: m)}$ are all in error.
- How to alleviate this error?
- Filtering methods: Last topic of the semester (After Vision)
- Optimization methods: Now — Pose this as "multiview optimization".
Key Insight