Representation of 3D environment map using B-spline surface with two mutually perpendicular LRFs
type: Item
instance of: scholarly article
title: Representation of 3D environment map using B-spline surface with two mutually perpendicular LRFs
zbMATH Open document ID: 1394.65014
DOI: 10.1155/2015/690310
author: Y. Aharonov
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: This paper proposes a map representation method of three-dimensional (3D) environment by using B-spline surfaces, which are first used to describe large environment in 3D map construction research. Initially, a 3D point cloud map is constructed based on extracted line segments with two mutually perpendicular 2D laser range finders (LRFs). Then two types of accumulated data sets are separated from the point cloud map according to different types of robot movements, continuous translation and continuous rotation. To express the environment more accurately, B-spline surface with covariance matrix is proposed to be extracted from each data set. Due to the random movements, there must be overlap between extracted B-spline surfaces. However, merging of two overlapping B-spline surfaces with different distribution directions of their control points is a complex problem, which is not well addressed by far. In our proposed method, each surface is divided into overlap and nonoverlap. Then generated sample points with propagated uncertainties from one overlap and their projection points located on the other overlap are merged using the product of Gaussian probability density functions. Based on this merged data set, a new surface is extracted to represent the environment instead of the two overlaps. Finally, proposed methods are validated by using the experimental result of an accurate representation of an indoor environment with B-spline surfaces.
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 6926997
Wikidata QID: Q59118939
describes a project that uses: MonoSLAM
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/690310
OpenAlex ID: W1858981725
cites work: CAD‐based shape optimisation with CFD using a discrete adjoint
cites work: Q2785470
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description: scientific article; zbMATH DE number 6926997