By Andreas Nüchter
The monograph written by means of Andreas Nüchter is concentrated on buying spatial types of actual environments via cellular robots. The robot mapping challenge is usually known as SLAM (simultaneous localization and mapping). 3D maps are essential to steer clear of collisions with advanced stumbling blocks and to self-localize in six levels of freedom
(x-, y-, z-position, roll, yaw and pitch angle). New ideas to the 6D SLAM challenge for 3D laser scans are proposed and a large choice of functions are presented.
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Additional resources for 3D Robotic Mapping: The Simultaneous Localization and Mapping Problem with Six Degrees of Freedom
2 Planar 3D Mapping Instead of using 3D scanners, which yield consistent 3D scans in the ﬁrst place, some groups have attempted to build 3D volumetric representations of environments by translating 2D laser range ﬁnders. Thrun et al. , Früh et al.  and Zhao et al.  use two 2D laser scanners for acquiring 3D data. One scanner is mounted horizontally, another vertically. The latter one grabs a vertical scan line which is transformed into 3D points based on the current 3D robot pose.
The dependence of the 3D coordinates in the camera coordinate system and the image coordinates with a focal length f is given by: u v f −c = c = c . z x y Using homogeneous coordinates the projection law can be linearized and rewritten using matrix notation. The transformation matrix for projective Fig. 3 Cameras and Camera Models 17 x1 x o u y x1 u x2 o f x2 f y z Fig. 10 The pinhole camera model Fig. 11 The camera coordinate system is ﬁxed to the camera. It is deﬁned by the optical axis and image center.
The complete algorithm was invented at the same time in 1991 by Besl and McKay , by Chen and Medioni  and by Zhang . The method is called Iterative Closest Points (ICP) algorithm. ˆ (model set, |M ˆ| = Given two independently acquired sets of 3D points, M ˆ ˆ Nm ) and D (data set, |D| = Nd ) which correspond to a single shape, we want to ﬁnd the transformation (R, t) consisting of a rotation matrix R and a translation vector t which minimizes the following cost function: A. : The Simultaneous Local.