By Andreas Nüchter
The monograph written by way of Andreas Nüchter is concentrated on buying spatial versions of actual environments via cellular robots. The robot mapping challenge is often 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 suggestions to the 6D SLAM challenge for 3D laser scans are proposed and a large choice of functions are presented.
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Extra resources for 3D Robotic Mapping: The Simultaneous Localization and Mapping Problem with Six Degrees of Freedom
STAR 52, pp. 35–75. com © Springer-Verlag Berlin Heidelberg 2009 36 4 3D Range Image Registration Nm Nd ˆ i − (Rdˆj + t) wi,j m E(R, t) = 2 . 1) i=1 j=1 ˆ describes the same point in space as wi,j is assigned 1 if the i-th point of M ˆ Otherwise wi,j is 0. Two things have to be calculated: the j-th point of D. First, the corresponding points, and second, the transformation (R, t) that minimizes E(R, t) on the base of the corresponding points. The ICP algorithm calculates iteratively the point correspondences.
Choosing α1 = 1 and α2 = α3 = α4 = 0 the maximal value is reached and the unit quaternion is q˙ = e˙ 1 . After the computation of the rotation matrix R the translation is t = cm − Rcd . Computing the Tranformation using Dual Quaterions The transformation that minimizes Eq. 1) can be computed by an algorithm that uses so-called dual quaternions. This method was developed by Walker, Shao and Volz in 1991 . Unlike the ﬁrst three methods covered so far the transformation is found by one step.
The epipoles are known the search for corresponding pixel can be reduced to the search along the epipolar line. Camera calibration. During camera calibration the extrinsic parameters of both cameras are determined. This gives the rotation and translation 22 2 Perceiving 3D Range Data Fig. 18 Rectiﬁed stereo images allow to search for corresponding points along horizontal lines. 15 right. (R, t) between the two cameras. These parameters allow the rectiﬁcation of the images and simplify the correspondence problem: After rectiﬁcation corresponding points must lie on the scan lines of the images.