A Tutorial on Graph-Based SLAM笔记

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本文详细介绍了图基Simultaneous Localization And Mapping (SLAM)的基本概念，包括图结构中的节点（机器人在不同位置的姿势）、边（来自观测或运动动作的姿势间约束），以及解决SLAM问题的前后端任务。前端负责图构建，后端负责图优化，通过最小化误差来估计机器人轨迹和环境地图。此外，文章还讨论了滤波和平滑两种SLAM解决方案，以及在实际2D地图构建中的应用。

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A Tutorial on Graph-Based SLAM

Cyrill Stachniss Wolfram Burgard

A graph
- Node: The poses of the robot at different points
- Edges: Constraints between the poses. Obtained from observations or movement actions
  - a probability distribution over a relative transformations between two pose nodes
  - eg odometry measurement, aligning observations from two robot locations.
  - Include data association problem. included in front-end.
- tasks of pose graph slam
  - Graph construction (Front-end)
  - Graph optimization (Back-end)
Solutions for SLAM

Estimating the robot trajectory and the map of environment.
- Filtering: on-line state estimation of current robot position and the map
- Smoothing: estimate the full trajectory from full set of measurements.
Solving a large error minimization problem to find a configuration of the graph (trajectory) that is maximally consistent with the measurement.
$\min_{x}{\sum _{<i,j>\in C } e^T_{ij}\Omega _{ij} e_{ij}}\\$
where
$eij(xi,xj)=zij−z^ij(xi,xj) e_{ij}(x_i, x_j) = z_{ij}-\hat z_{ij}(x_i, x_j)$ and $Ωij\Omega _{ij}$ is information matrix of a virtual measurement.
- Solutions
  - Iterative local linearizations: fist order Taylor expansion around the current guess of $x$ ( for x is robot pose)
    
    Some question about sparcse construction and sparse Cholesky factorization.
    
    Summary: Gauss-Newton plus Cholesky factorization.
    
    Practical Application: 2D mapping system
  - Least Squares on a Manifold (Lie group?) ( for x is robot transfomation)
    
    Define a operator map 3D transformation to manifold.
Map:

Map can be parametrized as a set of spatially located landmarks, by dense representations like occupancy grids, surface maps, or by raw sensor measurements.
- map is different from 3d reconstruction? (3d surface map is reconstruction?)
Dynamic Bayesian Network (DBN)
- A directed graph to describe stochastic process
- observed variable nodes (like measurements)
- hidden variable nodes (like robot position state, map)
- state transition model
- observation model

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