SLAM

Occasionally, we discover that the LiDAR extrinsic parameters are inaccurate. In such cases, we aim to recalibrate the SLAM poses and maps based on the updated parameters, without the need to rerun the entire SLAM process. By doing so, we can keep the annotations and the original SLAM map, which saves human effort and computational resources. Raw Data Given LiDAR points in the LiDAR coordinate system $$\mathbf{p}^{orig} = \bigcup_{t=0:T}\{\mathbf{p}_{t,i}\}_{i=1}^{N_t}$$Where $t$ is the time index, $i$ is the point index at time $t$, and $N_t$ is the number of points at time $t$. ...

In this post, we will discuss the post-processing of LiDAR SLAM. We mainly focus on its problem formulation. The content of this post follows papers [1] and [2]. Problem Formulation Factor graph representation of bundle adjustment formulation. (Fig. 1 of [2]) With LiDAR poses, each denoted by $\mathbf{T}_j = (\mathbf{R}_j,\mathbf{t}_j)$ $(j=1,\ldots,M_p)$, the bundle adjustment refers to simultaneously determining all the LiDAR poses (denoted by $\mathbf{T} = (\mathbf{T}_1,\cdots,\mathbf{T}_{M_p})$) and feature parameters (denoted by $\boldsymbol{\pi} = (\pi_1,\cdots,\pi_{M_f})$), such that the reconstructed map agrees with the LiDAR measurements to the best extent. Denote $c(\pi_i,\mathbf{T})$ the map consistency due to the $i$-th feature; a straightforward BA formulation is ...

What is SLAM? SLAM demo. SLAM stands for Simultaneous Localization and Mapping. It is a computational problem of constructing or updating a map of an unknown environment while simultaneously keeping track of an agent's location within it. Applications Object Detection Parking Lot Annotation Lane Annotation Lane Reprojection HD Map [source] SLAM has various applications, including: ...

In this document, we provide detailed derivations complementing those presented in [2]. Details of the Derivation Discrete Model Based on the $\boxplus$ operation defined above, we can discretize the continuous model in (1) at the IMU sampling period $\Delta t$ using a zero-order holder. The resultant discrete model is $$ \mathbf{x}_{i+1} = \mathbf{x}_i \boxplus (\Delta t f(\mathbf{x}_i, \mathbf{u}_i, \mathbf{w}_i))$$where $i$ is the index of IMU measurements, and the function $f$, state $\mathbf{x}$, input $\mathbf{u}$, and noise $\mathbf{w}$ are defined below: ...

In this post, we will discuss the Iterative Closest Point (ICP) problem: from point-to-point and point-to-plane ICP to generalized ICP. Problem Formulation Let two 3D point-sets $\mathcal{X} = \{\mathbf{x}_i\}, i = 1, \ldots, N$ and $\mathcal{Y} = \{\mathbf{y}_j\}, j = 1, \ldots, M$, where $\mathbf{x}_i, \mathbf{y}_j \in \mathbb{R}^3$ are point coordinates, be the data point-set and the model point-set respectively. The goal is to estimate a rigid motion with rotation $\mathbf{R} \in SO(3)$ and translation $\mathbf{t} \in \mathbb{R}^3$ that minimizes the following $L_2$-error $E$: ...