By Andreas Nüchter

ISBN-10: 3540898832

ISBN-13: 9783540898832

ISBN-10: 3540898840

ISBN-13: 9783540898849

The monograph written via Andreas Nüchter is targeted on buying spatial types of actual environments via cellular robots. The robot mapping challenge is often known as SLAM (simultaneous localization and mapping). 3D maps are essential to keep 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 suggestions to the 6D SLAM challenge for 3D laser scans are proposed and a large choice of purposes are presented.

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

Example text

The square matrix H can be decomposed into a product of an orthonormal matrix P and a positive semidefinite matrix S [62]. The matrix S is unambiguously defined. If H is not singular, then P is unique. 1 The ICP Algorithm 41 is an orthonormal matrix. 3, Lemma 12). Now we have to determine, how to compute the positive definite square root of a positive definite matrix. 3, Lemma 8): H T H = λ1 u1 uT1 + λ2 u2 uT2 + λ3 u3 uT3 . Since H T H is positive definite, the eigenvalues are positive and the root is a real number.

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. The first category consists geometric aberrations and include spherical aberration, astigmatism, distortion and coma. The second class contain the chromatic aberrations and deal with errors due to the refractive index function of the wavelength. Geometric aberrations can be handled and reduced by a combination of lenses and by software.

The perspective projection of parallel lines yields intersections. 9 shows an example of one vanishing point. 10. All rays go through the focal point o. Objects of same size that are at the same distance to o yield projections of the same size. A point p in the three-dimensional space has the coordinates (cx, c y, cz) relative to the camera center c. The point p is projected to the image point p in the image plane with the coordinates (u, v). The latter coordinates are relative to the image center c that is the intersection between the optical axis and the image plane (cf.

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3D Robotic Mapping: The Simultaneous Localization and Mapping Problem with Six Degrees of Freedom by Andreas Nüchter

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