By Andreas Nüchter
The monograph written by way of Andreas Nüchter is targeted on buying spatial versions of actual environments via cellular robots. The robot mapping challenge is usually known as SLAM (simultaneous localization and mapping). 3D maps are essential to keep away from collisions with advanced hindrances 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 wide selection of functions are presented.
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Extra info for 3D Robotic Mapping: The Simultaneous Localization and Mapping Problem with Six Degrees of Freedom
Undist u, undist v) are computed. Then the 3D coordinates in the camera coordinate system (cx, cy, cz) are given by solving c x u = αx c + cx z c y undist v = αy c + cy z c 2 r = x + cy 2 + cz 2 undist based on the distances r. This process yields a 3D point cloud. Fig. 21 3D Cameras: Left Swissranger manufactured by MESA Imaging AG. It uses technology developed by CSEM. Right: PMD (Photonic Mixer Device) Camera by PMDTechnologies GmbH. Figures courtesy of MESA Imaging and PMDTechnologies. 4 3D Cameras 27 Fig.
11). 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.
Proof. 10). Now the quaternions come into play: To ﬁnd the rotation matrix R equals ﬁnding the unit quaternion q˙ that maximizes the term N N ˙ i · (q˙ d˙ i q˙ ∗ ) = m i=1 ˙ ˙ i ) · (d˙ i q) (q˙ m i=1 ¯ i and D i are now the matrices that correspond (see Eq. 16)). Suppose M ˙ i and d˙ i as given by Eq. 15). 16) the to the quaternions m sum that has to be maximized is N ¯ i q) ˙ · (Di q) ˙ (M i=1 or N N ¯ i DT q˙ = q˙ T q˙ T M i i=1 ¯ iDT M i i=1 ˙ q. 44 4 3D Range Image Registration ¯ i and Di , a calculation yields: After writing the matrices for M ⎛ N ¯ iDT M i q˙ T i=1 ⎛ 0 ⎜ N ⎜m ⎜ ⎜ x,i q˙ = q˙ T ⎜ ⎜ ⎝ i=1 ⎝my,i mz,i ⎛ 0 ⎜d ⎜ x,i ⎜ ⎝dy,i dz,i −mx,i 0 −mz,i my,i −my,i mz,i 0 −mx,i −dx,i 0 dz,i −dy,i −dy,i −dz,i 0 dx,i ⎞ −mz,i −my,i ⎟ ⎟ ⎟ mx,i ⎠ 0 ⎞T ⎞ −dz,i ⎟ dy,i ⎟ ⎟ ⎟ ⎟ ⎟ q˙ −dx,i ⎠ ⎟ ⎠ T ˙ = q˙ N q.