Abstract
The paper deals with the issue of autonomous navigation for the movement of a robot in a tube. The solution is to determine the center of a given conic section using three operations in the Geometric Algebra for Conic Sections (GAC). The article describes an engine that renders given conic sections through basic operations in the GAC. At the end of the work, an algorithm is described that calculates the axis of the tube based on the points that are located in the space from the image, where we place the center of the ellipse obtained by the image filter and fitting algorithm.
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References
Artin E.: Affine and Projective Geometry (1988), [cit. 2021-05-05]. https://doi.org/10.1002/9781118164518.ch2
Ayoub, A.B.: The Central Conic Sections Revisited, pp. 322–325, Taylor & Francis (1993). [cit.2021-04-28]. https://doi.org/10.1080/0025570X.1993.11996157
Dorst, L., Fontijne, D., Mann, S.: Geometric Algebra for Computer Science (Revised Edition). Morgan Kaufmann Publishers (2007). ISBN 978-0-12-374942-0
Herman, I.: Projective Geometry and Computer Graphics. In: Hewitt, W. T., Grave, M., Roch, M. (eds.) Advances in Computer Graphics IV. EurographicSeminars, pp. 28–61. Springer, Berlin, Heidelberg (1991). ISBN 978-3-642-84060-9. https://doi.org/10.1007/978-3-642-84060-9_2
Hildenbrand, D.: Foundantions of Geometric Algebra Computing. Springer, Berlin, Heidelberg (2013). ISBN 978-3-642-31794-1. https://doi.org/10.1007/978-3-642-31794-1
Hrdina, J., Návrat, A., Vašík, P.: Conic fitting in geometric algebra setting. Adv. Appl. Clifford Algebras 29(4), 1–13 (2019). https://doi.org/10.1007/s00006-019-0989-5
Hrdina, J., Návrat, A., Vašík, P.: Geometric algebra for conics. Adv. Appl. Clifford Algebras 28(3), 1–21 (2018). https://doi.org/10.1007/s00006-018-0879-2
3D Graphics with OpenGL, Internet site. [cit. 2021-05-05]
Machálek, L.: Korekce obrazových vad pomocí CGA [cit. 2021-04-08]. https://www.vutbr.cz/studenti/zav-prace/detail/109029
Machálek, L.: Geometric Algebra Applications. Brno (2021). MASTER’S THESIS. BRNO UNIVERSITY OF TECHNOLOGY. Vedoucí práce doc. Mgr. Petr Vašík, Ph.D.
Perwass, C.: Geometric Algebra with Applications in Engineering. Springer, Berlin (2009). ISBN 354089067X. https://doi.org/10.1007/978-1-4612-0159-5
Richter-Gebert, J.: Perspectives on Projective Geometry. Springer Publishing Company, Berlin, Heidelberg (2011). Incorporated. ISBN 978-3-642-17285-4. https://doi.org/10.1007/978-3-642-17286-1
Smith, C.: On Vertex-Vertex Systems and Their Use in Geometric and Biological Modelling, University of Calgary (2006). ISBN 9780494195741
Solomon, C.J., Breckon, T.P.: Fundamentals of Digital Image Processing: A Practical Approach with Examples in Matlab, Wiley-Blackwell, Hoboken (2010). ISBN 978-0470844731
Young, C.Y.: Precalculus; Chapter 9. John Wiley and Sons, Hoboken (2010). ISBN 978-0-471-75684-2
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Konecky, S., Machalek, L. (2023). Autonomous Navigation for the Movement of the Robot in the Tube. In: Mazal, J., et al. Modelling and Simulation for Autonomous Systems. MESAS 2022. Lecture Notes in Computer Science, vol 13866. Springer, Cham. https://doi.org/10.1007/978-3-031-31268-7_5
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DOI: https://doi.org/10.1007/978-3-031-31268-7_5
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