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Fuzzy Matrix Contractor Based Approach for Localization of Robots

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Recent Advances in Applications of Computational and Fuzzy Mathematics

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Abstract

Localization consists of finding the pose of some robots with respect to its position and orientation. In case of localization of a group of robots over a planar surface, each robot is linked with other robots using constraints that may be considered in term of matrix equations. As such, this chapter deals with the localization of group of robots using angle and distance constraints associated with fuzzy matrix contractors. Matrix contractors based on azimuth–distance and bearing-distance constraints help efficient propagation of fuzzy uncertainties through a group of robots for localization purpose when no absolute frame is present. Finally, various groups of robots have been considered for the verification of proposed contractors viz. azimuth, distance, azimuth–distance, and bearing-distance contractors using Gaussian fuzzy uncertainty.

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Acknowledgements

The first author is thankful for the support by Raman-Charpak Fellowship 2016, Indo-French Center for the Promotion of Advanced Research, New Delhi, India, for a part of the work done in France.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, 769008, Odisha, India

    N. R. Mahato & Snehashish Chakraverty

  2. CNRS 6285, LabSTICC, ENSTA-Bretagne, 2 rue François Verny, 29806, Brest, France

    L. Jaulin

Authors
  1. N. R. Mahato
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  2. Snehashish Chakraverty
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  3. L. Jaulin
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Correspondence to N. R. Mahato .

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Editors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, India

    Snehashish Chakraverty

  2. Research & Development Centre for Mathematical Modeling, Faculty of Science, University of Colombo, Colombo, Sri Lanka

    Sanjeewa Perera

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Mahato, N.R., Chakraverty, S., Jaulin, L. (2018). Fuzzy Matrix Contractor Based Approach for Localization of Robots. In: Chakraverty, S., Perera, S. (eds) Recent Advances in Applications of Computational and Fuzzy Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-13-1153-6_3

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  • DOI: https://doi.org/10.1007/978-981-13-1153-6_3

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-1152-9

  • Online ISBN: 978-981-13-1153-6

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