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 usually known as SLAM (simultaneous localization and mapping). 3D maps are essential to steer clear of collisions with advanced hindrances and to self-localize in six levels of freedom
(x-, y-, z-position, roll, yaw and pitch angle). New strategies to the 6D SLAM challenge for 3D laser scans are proposed and a wide selection of purposes are presented.
Read or Download 3D Robotic Mapping: The Simultaneous Localization and Mapping Problem with Six Degrees of Freedom PDF
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Additional resources for 3D Robotic Mapping: The Simultaneous Localization and Mapping Problem with Six Degrees of Freedom
With these deﬁnitions it is easy to show the equality: ¯ T s. ¯ T Qx˙ + Q ˙ Rx + t = Q Theorem 4. The transformation consisting of rotation and translation that minimized the error function Eq. 1) is the solution of the eigenvalue problem of a 4 × 4 matrix function that is built from corresponding point pairs. Proof. 2) is rewritten as: ˙ s) ˙ = E(R, t) = E(q, 1 T q˙ C 1 q˙ + N s˙ T s˙ + s˙ T C 2 q˙ + const. , N where the terms C 1 , C 2 , and const. are deﬁned using the quaternion representation M i and D i , and accordingly C mi and C di for the 3D data points mi and di (cf.
Based on these correspondences depth images are computed similarly to stereo vision . 3 Cameras and Camera Models Image acquisition is performed in two steps. First, the image is brought into focus. Cameras with autofocus use a rough distance measurement and adjust the lenses, otherwise manual adjustment is necessary. Second, the image sensor captures light using a deﬁned timing. The image sensor produces then electrical signals from the light intensities. Afterwards an analog-digital converter quantiﬁes the signal, that is transmitted to the computer.
1 shows three steps of the ICP algorithm. The computed transformation is applied to the second scan. 2 Approximate Solution of the ICP Error Function by a Helical Motion Under the assumption the transformation (R, t) that has to be calculated by the ICP algorithm is small we can approximate the solution by applying instantaneous kinematics. This solution was initially given by Hofer and Pottmann [59, 98] and ﬁrst applied to registration tasks in robotics by Rusu et al. . Instantaneous kinematics computes a displacements of a 3D point by an aﬃne transformation via a so-called helical motion .