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Minimum landmarks for robot localization in orthogonal environments

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Abstract

Robot localization is one of the most fundamental problems in motion planing, with many important applications in tracking vehicles and router systems. One way for localizing the robot is trilateration, which is used in the environments without GPS antenna by using a number of signals that can be measure their distance to robot at any time. It has already been shown that \(\lfloor \frac{8n}{9}\rfloor \) landmarks are sufficient for trilaterating a simple n-side. Later, as a better result, it has been proved that \( \lfloor \frac{2n}{3}\rfloor \) landmarks are sufficient for this purpose. In this paper, we discuss the problem for orthogonal polygons and show that \(\frac{n}{2}\) landmarks suffice for trilaterating an orthogonal n-gon. This theoretical achievement is important for most evolutionary algorithms and neuro-computing techniques which need more speedup and high efficiency.

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References

  1. Annepu V, Rajesh A (2019) Implementation of self adaptive mutation factor and cross-over probability based differential evolution algorithm for node localization in wireless sensor networks. Evol Intell 12(3):469–478

    Article  Google Scholar 

  2. Le AV, Nhan NHK, Elara MR (2020) Evolutionary algorithm-based complete coverage path planning for tetriamond tiling robots. Sensors 20(445):1–14

    Google Scholar 

  3. Bigham BS, Fariba N, Salman K (2020) A polynomial time algorithm for big data in a special case of minimum constraint removal problem. Evol Intell 13(2):247–254

    Article  Google Scholar 

  4. Shamsfakhr F, Sadeghi Bigham B, Mohammadi A (2019) Indoor mobile robot localization in dynamic and cluttered environments using artificial landmarks. Eng Comput 36(2):400–419

    Article  Google Scholar 

  5. Shamsfakhr F, Sadeghi Bigham B (2020) GSR: geometrical scan registration algorithm for robust and fast robot pose estimation. Assem Autom 40(6):801–817

    Article  Google Scholar 

  6. Lee D, Arthurk L (1986) Computational complexity of art gallery problems. IEEE Trans Inf Theory 32(2):276–282

    Article  MathSciNet  Google Scholar 

  7. Bose P, De Carufel JL, Shaikhet A, Smid M (2017) Art gallery localization.’ arXiv preprint arXiv:1706.06938

  8. Dippel M, Sundaram R (2015) An upper bound on trilaterating simple polygons. 27th Canadian conference on computational geometry (CCCG), pp 1–8

  9. Bose P, De Carufel JL, Shaikhet A, Smid M (2020) Optimal art gallery localization is np-hard. Comput Geom 88(101607):1–12

    MathSciNet  MATH  Google Scholar 

  10. Bressan A, Piccoli B (2007) Introduction to the mathematical theory of control, vol 1. American Institute of Mathematical Sciences, Springfield

    MATH  Google Scholar 

  11. Rarità L, Stamova I, Tomasiello S (2021) Numerical schemes and genetic algorithms for the optimal control of a continuous model of supply chains. Appl Math Comput 388:125464

    Article  MathSciNet  Google Scholar 

  12. Rarità L et al (2010) Sensitivity analysis of permeability parameters for flows on Barcelona networks. J Differ Equ 249(12):3110–3131

    Article  MathSciNet  Google Scholar 

  13. Kahn J, Klawe M, Kleitman D (1983) Traditional galleries require fewer watchmen. SIAM J Algebraic Discrete Methods 4(2):194–206

    Article  MathSciNet  Google Scholar 

  14. Urrutia J (2000) Art gallery and illumination problems. Handbook of computational geometry. North-Holland, pp 973–1027

  15. O’Rourke J (1983) An alternate proof of the rectilinear art gallery theorem. J Geom 21(1):118–130

    Article  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Computer Science and Information Technology, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran

    B. Sadeghi Bigham & S. Dolatikalan

  2. Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran

    A. Khastan

Authors
  1. B. Sadeghi Bigham
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  2. S. Dolatikalan
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  3. A. Khastan
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Correspondence to B. Sadeghi Bigham.

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Sadeghi Bigham, B., Dolatikalan, S. & Khastan, A. Minimum landmarks for robot localization in orthogonal environments. Evol. Intel. 15, 2235–2238 (2022). https://doi.org/10.1007/s12065-021-00616-8

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  • DOI: https://doi.org/10.1007/s12065-021-00616-8

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