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3D Robotic Mapping: The Simultaneous Localization and by Andreas Nüchter

By Andreas Nüchter

The monograph written by means of Andreas Nüchter is targeted 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 stay away from collisions with complicated hindrances and to self-localize in six levels of freedom
(x-, y-, z-position, roll, yaw and pitch angle). New recommendations to the 6D SLAM challenge for 3D laser scans are proposed and a wide selection of purposes are presented.

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Additional info for 3D Robotic Mapping: The Simultaneous Localization and Mapping Problem with Six Degrees of Freedom

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After a transformation some data points that did not have a closest point within this limit might have one and therefore the value of the error function might increase. Finally, the algorithm minimizes Eq. 1) and maximizes the number of corresponding points. 1 Direct Solutions of the ICP Error Function In every iteration the optimal transformation (R, t) for minimizing the error function E(R, t) in Eq. 1) has to be computed. There exist different strategies to find the minimum that can be divided into direct and indirect methods.

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.

Besides the intrinsic parameters there are extrinsic camera parameters, that represent the pose (position and orientation) of the 3D camera coordinate system with respect to a 3D world coordinate system. The extrinsic parameters are given by a rotation matrix R and a translation vector t. It holds: ⎛ w ⎞ ⎛ c ⎞ x x ⎜ ⎟ ⎜ cy ⎟ w R t ⎜ y ⎟ ⎟ ⎜ ⎜ w ⎟. 13) and the formulas given so far are applicable. This simplification does not regard aberrations that occur due to the use of lenses. , deviations from the ideal pinhole model, can be divided into two categories.

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