Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Larkin E. V., Akimenko T. A., Bogomolov A. V. Modeling the reliability of the onboard equipment of a mobile robot. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, vol. 21, iss. 3, pp. 390-399. DOI: 10.18500/1816-9791-2021-21-3-390-399, EDN: GUSCGX

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.08.2021
Full text:
(downloads: 1364)
Language: 
English
Heading: 
Article type: 
Article
UDC: 
631.353.3
EDN: 
GUSCGX

Modeling the reliability of the onboard equipment of a mobile robot

Autors: 
Larkin Eugene V., Tula State University
Akimenko Tatiana A., Tula State University, Russia
Bogomolov Aleksey Valer'evich, St. Petersburg Federal Research Center of the Russian Academy of Science
Abstract: 

Mobile robots with complex onboard equipment are investigated in this article. It is shown that their onboard equipment, for providing the required reliability parameters, must have fault-tolerant properties. For designing such equipment it is necessary to have an adequate model of reliability parameters evaluation. The approach, linked to the creation of the model, based on parallel semi-Markov process apparatus, is considered. At the first stage of modeling, the lifetime of the single block in a complex fault-recovery cycle is determined. Dependences for the calculation of time intervals and probabilities of wandering through ordinary semi-Markov processes for a common case are obtained. At the second stage, ordinary processes are included in the parallel one, which simulates the lifetime of the equipment lifetime as a whole. To simplify calculations, a digital model of faults with the use of the procedure of histogram sampling is proposed.  It is shown that the number of samples permits to control both the accuracy and the computational complexity of  the procedure for calculating the reliability parameters.

Acknowledgments: 
This work was supported by a grant from the President of the Russian Federation for state support of leading scientific schools of the Russian Federation (NSh2553.2020.8).
References: 
  1. Tzafestas S. G. Introduction to Mobile Robot Control. Elsevier, 2014. 750 p. https://doi.org/10.1016/C2013-0-01365-5
  2. Landau I. D., Zito G. Digital Control Systems: Design, Identification and Implementation. Springer-Verlag London, 2006. 484 p. https://doi.org/10.1007/978-1-84628-056-6
  3. Astr om J., Wittenmark B. Computer-Controlled Systems: Theory and Design. (Dover Books on Electrical Engineering). Third Edition. Dover Publ., 2011. 576 p.
  4. Rousand M. Reliability of Safety-Critical Systems: Theory and Applications. John Wiley & Sons, 2014. 466 p.
  5. Sanchez-Silva M., Klutke G.-A. Reliability and Life-Cycle Analysis of Deteriorating Systems. (Springer Series in Reliability Engineering). Switzerland, Springer International Publishing, 2016. 356 p. https://doi.org/10.1007/978-3-319-20946-3
  6. O’Conner P., Kleyner A. Practical Reliability Engineering. John Willey & Sons, 2012. 512 p.
  7. Koren I., Krishna C. Fault Tolerant Systems. San Francisco, CA, Morgan Kaufmann Publ., 2007. 400 p.
  8. Dubrova E. Fault-Tolerant Design. Springer-Verlag New York, Springer Science+Business Media New York. 2013. 185 p. https://doi.org/10.1007/978-1-4614-2113-9
  9. Zhang Y., Jiang J. Bibliographical review on reconfigurable fault-tolerant control systems. Annual Reviews in Control, 2008, vol. 32, iss. 2, pp. 229–252. https://doi.org/10.1016/j.arcontrol.2008.03.008
  10. Bielecki T. R., Jakubowski J., Nieweglowski M. Conditional Markov chains: Properties, construction and structured dependence. Stochastic Processes and their Applications, 2017, vol. 127, iss. 4, pp. 1125–1170. https://doi.org/10.1016/j.spa.2016.07.010
  11. Ching W. K., Huang X., Ng M. K., Siu T. K. Markov Chains: Models, Algorithms and Applications. (International Series in Operations Research & Management Science, vol. 189). Springer Science+Business Media New York, 2013. 241 p.
  12. Howard R. A. Dynamic Probabilistic Systems. Vol. 1: Markov Models. (Dover Books on Mathematics). Dover Publ., 2007. 608 p.
  13. Howard R. A. Dynamic Probabilistic Systems. Vol. II: Semi-Markov and Decision Processes. (Dover Books on Mathematics). Dover Publ., 2007. 576 p.
  14. Janssen J., Manca R. Applied Semi-Markov Processes. Springer US, 2006. 310 p. https://doi.org/10.1007/0-387-29548-8
  15. Larkin E., Ivutin A., Malikov A. Petri-Markov model of fault-tolerant computer systems. 2017 4th International Conference on Control, Decision and Information Technologies (CoDIT), 2017, pp. 0416–0420. https://doi.org/10.1109/CoDIT.2017.8102627
  16. Naess A., Leira B. J., Batsevich O. System reliability analysis by enhanced Monte Carlo simulation. Structural Safety, 2009, vol. 31, iss. 5, pp. 349–355. https://doi.org/10.1016/j.strusafe.2009.02.004
  17. Sudret B. Global sensitivity analysis using polinomial chaos expansion. Reliability Engineering & System Safety, 2009, vol. 93, iss. 7, pp. 964–979. https://doi.org/10.1016/j.ress.2007.04.002
  18. Zaghami S. A., Gunavan I., Shultmann F. Exact reliability evaluation of infrastructure networks using draph theory. Quality and Reliability Engineering International, 2020, vol. 36, iss. 2, pp. 498–510. https://doi.org/10.1002/qre.2574
  19. Finkelstain M. Failure Rate Modelling for Reliability and Risk. (Springer Series in Reliability Engineering). London, Springer, 2008. 290 p. https://doi.org/10.1007/978-1-84800- 986-8
  20. Ivutin A. N., Larkin E. V. Simulation of concurrent games. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2015, vol. 8, no. 2, pp. 43–54. https://doi.org/10.14529/mmp150204
  21. Larkin E. V., Ivutin A. N. “Сoncurrency” in M-L-parallel semi-Markov process. MATEC Web of Conferences, 2017, vol. 108, article ID 05003. https://doi.org/10.1051/matecconf/ 201710805003
  22. Petersen P. Linear Algebra. (Undergraduate Texts in Mathematics). New York, SpringerVerlag, 2012. 390 p. https://doi.org/10.1007/978-1-4614-3612-6
  23. Bauer H. Probability Theory. Berlin, New York, de Gruyter Publ., 1996. 540 p.
Received: 
04.11.2019
Accepted: 
16.01.2021
Published: 
31.08.2021