By Andreas Nüchter

ISBN-10: 3540898832

ISBN-13: 9783540898832

ISBN-10: 3540898840

ISBN-13: 9783540898849

The monograph written via Andreas Nüchter is concentrated 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 stay away from collisions with complicated stumbling blocks 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 large choice of purposes are presented.

**Read Online or Download 3D Robotic Mapping: The Simultaneous Localization and Mapping Problem with Six Degrees of Freedom PDF**

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

**Sample text**

Since the minimization of the ICP error function using the helical motion is an approximative solution, one will need more iterations for convergence of the ICP algorithm. 3 Linearized Solution of the ICP Error Function As in the last section, we linearize the rotation. Given a rotation matrix based on the Euler angles (cf. 1) ⎛ cos θy cos θz − cos θy sin θz ⎜ R = ⎝ cos θz sin θx sin θy + cos θx sin θz cos θx cos θz − sin θx sin θy sin θz sin θx sin θz − cos θx cos θz sin θy cos θz sin θx + cos θx sin θy sin θz ⎞ sin θy ⎟ − cos θy sin θx ⎠ .

1 , λ2 , λ3 , λ4 ). One can construct four eigenvectors (e˙ 1 , e˙ 2 , e˙ 3 , e˙ 4 ) corresponding to the eigenvalues, such that N e˙ i = λi e˙ i for i = 1, 2, 3, 4 holds. , they are linearly independent. Thus any quaternion q˙ is writable as linear combination q˙ = α1 e˙ 1 + α2 e˙ 2 + α3 e˙ 3 + α4 e˙ 4 . Since eigenvectors are orthogonal, we have: q˙ · q˙ = α21 + α22 + α23 + α24 . ˙ FurThis equation must equal 1, since we search for the unit quaternion q. thermore, we derive N q˙ = α1 λ1 e˙ 1 + α2 λ2 e˙ 2 + α3 λ3 e˙ 3 + α4 λ4 e˙ 4 , since e˙ 1 , e˙ 2 , e˙ 3 , e˙ 4 are eigenvectors of N .

The initial attitude (left) of two 3D scans, the attitude after three iterations (middle) and after 15 iterations (right) is presented. In all steps a rotation R and a translation t is computed in closed form and applied to the second scan. 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.

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

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