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Mathematical Problems in Engineering
Volume 2015, Article ID 690310, 14 pages
Research Article

Representation of 3D Environment Map Using B-Spline Surface with Two Mutually Perpendicular LRFs

1Department of Mechatronics Engineering, Hanyang University, Ansan, Gyeonggi-do 426-791, Republic of Korea
2Department of Robot Engineering, Hanyang University, Ansan, Gyeonggi-do 426-791, Republic of Korea

Received 19 November 2014; Revised 27 March 2015; Accepted 2 April 2015

Academic Editor: Yongsheng Ou

Copyright © 2015 Rui-Jun Yan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.