[原創]NDT方法在SLAM中的應用

NDT概念

正態分佈變換（Normal Distribution Transformation , NDT）
機率密度函數（ Probability Density Function, PDF）
First proposed for two dimensional scan data registration by Biber & Strasser in 2003.
An NDT is described as a set of PDFs.
The first step of the algorithm is to subdivide the space occupied by the scan into a grid of cells (squares in the 2D case, or cubes in 3D).
A PDF is computed for each cell, based on the point distribution within the cell.

NDT及其改進

將二維空間劃分爲固定大小網格，每一個網格至少包括3個點（通常5個）
計算網格中點集的均值𝜇 
計算網格中點集的協方差矩陣Σ
網格中的觀測到點𝑥 的機率𝑝(𝑥 )服從正態分佈𝑁(𝜇 ,Σ)
The PDF in each cell can be interpreted as a generative process for surface points 𝑥 ⃗ within the cell. In other words, it is assumed that the location of 𝑥 ⃗ has been generated by drawing from this distribution. Assuming that the locations of the reference scan surface points were generated by a D-dimensional normal random process, the likelihood of having measured 𝑥 is

標準的NDT方法

 

 多尺度NDT

 

NDT tree

 聚類NDT/區域生長NDT

 

Spatial Representation Models

其它

NDT interpolation
　　NDT格網劃分後，每一個方格或者體素中的點用正態分佈描述，整幀掃描的分佈並不連續。經過重疊NDT和內插NDT能夠必定程度解決此問題。
NDT Occupancy Maps (NDT-OMs)
　　相似於佔用機率地圖，用NDT分佈網格表達整幅地圖。
Color-NDT
　　利用圖像的顏色信息進行NDT匹配。
NDT-MCL
　　NDT匹配爲蒙特卡洛方法提供初值。

 

基於NDT的掃描匹配

 

 

參考文獻

[1] Peter Biber and Wolfgang Straßer. The normal distributions transform:A new approach to laser scan matching. In Proceedings of the IEEE International Conference on Intelligent Robots and Systems (IROS), pages 2743–2748, Las Vegas, USA, October 2003.

[2]Stoyanov, T. and M. Magnusson (2011). "On the Accuracy of the 3D Normal Distributions Transform as a Tool for Spatial Representation."

[3]Stoyanov, T.D., Reliable Autonomous Navigation in Semi-Structured Environments using the Three-Dimensional Normal Distributions Transform (3D-NDT). 2012.