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Published in:
Geometric Algebra for Modeling in Robotic Physics Read chapter Read first chapter

2020 | OriginalPaper | Chapter

18. 3D Maps, Navigation, and Relocalization

Author : Eduardo Bayro-Corrochano

Published in: Geometric Algebra Applications Vol. II

Publisher: Springer International Publishing

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Abstract

This chapter presents applications of body–eye calibration algorithms using motors of the conformal geometric algebra. A scan-matching algorithm, based on such algorithm, aligns the scans by representing the scan points as lines. We show then a path-following procedure that also uses the conformal geometric algebra techniques to estimate the geometric error for a control law. The chapter extends the applications of body-sensor calibration for the case of stereo vision and laser scanner. Such sensors are used for building 3D maps and tackling the relocalization problem. For the relocalization, we resort to an approach based in the Hough transform, where the desired position is searched in the line Hough space.

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previous chapter Tracking, Grasping, and Object Manipulation
next chapter Quadrotor
Literature
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Hollerbach, J., & Nahvi, A. (1995). Total least squares in robot calibration. In 4th International Symposium on Experimental Robotics IV (pp. 274–282).
2.
Hartley, R. I., & Zissermann, A. (2003). Multiple view geometry in computer vision (2nd ed.). Cambridge: Cambridge University Press.
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Bayro-Corrochano, E. (2010). Geometric computing for wavelet transforms, robot vision, learning, control and action. London: Springer Verlag.MATH
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Nguyen, V., Gächter, S., Martinelli, A., Tomatis, N., & Siegwart, R. (2007). A comparison of line extraction algorithms using 2D range data for indoor mobile robotics. Autonomous Robots, 23(2), 97–111.CrossRef
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Bayro-Corrochano, E., Daniilidis, K., & Sommer, G. (1997). Hand-eye calibration in terms of motions of lines using geometric algebra. In 10th Scandinavian Conference on Image Analysis (Vol. I, pp. 397–404). Finland: Lappeenranta.
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Hough, P. (1962). Methods and means for recognizing complex patterns. U.S. Patent 3 069 654.
Metadata
Title
3D Maps, Navigation, and Relocalization
Author
Eduardo Bayro-Corrochano
Copyright Year
2020
Book
Geometric Algebra Applications Vol. II

Print ISBN: 978-3-030-34976-9

Electronic ISBN: 978-3-030-34978-3

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-34978-3_18

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