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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 ...

This post explores collision loss design for end-to-end autonomous driving training, focusing on extending PLUTO’s binary occupancy map approach to handle probabilistic maps. The method enables safer autonomous driving by providing smooth, uncertainty-aware collision avoidance while maintaining computational efficiency. Using Signed Distance Map with Binary Occupancy Map How PLUTO Builds the Loss Map [2] Vehicle Model In PLUTO and other planning algorithms, the vehicle is modelded as a series of overlapping discs. ...

This post contains a state machine diagram that illustrates the typical lifecycle of an object in a tracking system. Object Tracking Management State Machine.

This post provides a technical deep dive into the Wayformer paper [1], a key publication in the field of motion forecasting. Training Overview An overview of the deep learning training pipeline, illustrating the data flow and key components involved during model training. Model Overview of the One-Stage E2E model One staged E2E model. Overview of the Two-Stage E2E model Two staged E2E model. Details of the Two-Stage E2E Model Overview of the Wayformer model. Model Structure Overview (a) (b) The left figure shows the encoder and decoder of the Wayformer model. The right figure shows the details of the encoder [1]. Feature Embedding/Feature Projection $$\mathbf{f}\in \mathbb{R}^{T \times N\times D} \to \mathbf{x}_{input} \in \mathbb{R}^{(T \cdot N) \times d}$$Where $T$ is the number of time history, $N$ is the number of entities, $D$ is the number of features, and $d=256$. ...

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 post, we will discuss the perspective-n-point (PnP) problem. We will start with the problem definition. Then, gradient-based optimization methods will be introduced. Finally, we will discuss two global optimization methods. Problem Formulation The core task of the Perspective-n-Point (PnP) problem is to determine the pose—specifically, the rotation and translation—of a calibrated camera in 3D space. This is achieved by using a set of known 3D points in the world and their corresponding 2D projections observed on the camera’s image sensor. ...

Given a starting point, starting direction, ending point, and ending direction, the goal is to generate a feasible and “natural” path that connects the two points. This path should adhere to vehicle dynamics and avoids obstacles. However, it is hard to define what is “natural”. Path Planning In this section, we review some classical path planning methods. We ignore the algorithmic details and focus on the resulting path shapes to provide an overview. The demonstration images are generated using the code repository [1]. ...

In this post, we will discuss the Kalman filters from two perspectives: classical parameter estimation and Bayesian estimation. Each perspective provides a unique way to derive the Kalman filter. Parameter estimation is more flexible as it allows you to easily add constraints, revise the transition and observation models, and derive other related smoothing and filtering methods. Meanwhile, Bayesian estimation is more intuitive and provides a clearer probabilistic interpretation, helping us understand the underlying principles better. By examining both approaches, we can gain a more comprehensive understanding of how Kalman filters work. ...

I have taken some courses related to reinforcement learning during my Ph.D. study. However, I have not touched it for a long time. Recently, I am working on end-to-end autonomous driving and the success of reinforcement learning in large language models brings me back to this topic. In this post, we will introduce the basic concepts and commonly used algorithms in reinforcement learning. More detailed information can be found in the reference book [1] and OpenAI RL page. ...