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Mathematical Modeling of the Robot

  • Michał Ciszewski
  • Mariusz Giergiel
  • Tomasz Buratowski
  • Piotr MałkaEmail author
Chapter
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Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 82)

Abstract

Mathematical modeling presented in this chapter includes several aspects of control system design for the pipe inspection robot. Since the research is focused on modeling and trajectory planning for robot pedipulators that allow adaptation of the robot to different pipe shapes and sizes, forward and inverse kinematics are discussed and followed by description of an original trajectory calculation algorithm, developed for control of the closed kinematic chains. Application of the algorithm is verified numerically and visually in MATLAB software.

References

  1. 1.
    Ciszewski M, Waclawski M, Buratowski T, Giergiel M, Kurc K. Design, modelling and laboratory testing of a pipe inspection robot. Arch Mech Eng. 2015;62(3):395–408.CrossRefGoogle Scholar
  2. 2.
    Trojnacki M. Modelowanie i symulacja ruchu mobilnego robota trzykołowego z napdem na przednie koła z uwzgląednieniem poślizgu kół jezdnych. Modelowanie Inżynierskie. 2011;10(41):411–20.Google Scholar
  3. 3.
    ŻylskiW. Kinematyka i dynamikamobilnych robotów kołowych.OficynaWydawnicza Politechniki Rzeszowskiej; 1996.Google Scholar
  4. 4.
    Burdziński Z. Teoria ruchu pojazdu gaąsienicowego.Warszawa:Wydawnictwo Komunikacji i Łączności; 1972.Google Scholar
  5. 5.
    Ciszewski M, Buratowski T, Giergiel M, Kurc K, Małka P. The pipes mobile inspection robots. Diagnostyka. 2012;3(63):9–15.Google Scholar
  6. 6.
    Giergiel M, Buratowski T, Małka P, Kurc K. The mathematical description of the robot for the tank inspection. In: Mechan Mech Eng. 2011;15.4:53–62.Google Scholar
  7. 7.
    Wong JY. Terramechanics and Off-road vehicle engineering. In: Oxford: Elsevier, Butterworth-Heinemann; 2010. p. 155–76.CrossRefGoogle Scholar
  8. 8.
    Ciszewski M, Buratowski T, Giergiel M, Malka P, Kurc K. Virtual prototyping, design and analysis of an in-pipe inspection mobile robot. J Theor Appl Mech. 2014;52(2):417–29.Google Scholar
  9. 9.
    Engel Z. Giergiel J. Dynamika. Mechanika techniczna, 2nd ed. Kraków:Wydawnictwa AGH; 1998.Google Scholar
  10. 10.
    Inuktun Services Ltd. Inuktun crawler vehicles. 2015. http://www.inuktun.com/crawler-vehicles. Accessed 25 Oct 2015. Chapter 4. Mathematical modeling of the robot 68
  11. 11.
    Giergiel M, Hendzel Z, Żylski W. Modelowanie i sterowanie mobilnych robotów ko?owych. Warszawa: Wydawnictwo Naukowe PWN; 2013.Google Scholar
  12. 12.
    Frączek J, Wojtyra M. Kinematyka układów wieloczłonowych.Warszawa:Wydawnictwo Naukowo-Techniczne; 2008.Google Scholar
  13. 13.
    Kozłowski K, Dutkiewicz P, Wróblewski W. Modelowanie i sterowanie robotów. 1st ed. Warszawa: Wydawnictwo Naukowe PWN; 2012.Google Scholar
  14. 14.
    Corke P. Robotics, vision and control: fundamental algorithms inMATLAB, vol. 3. Springer Science & Business Media; 2011.Google Scholar
  15. 15.
    Sybilska AM. Porównaniemetodywykorzystującej proste i odwrotne zadanie kinematyki oraz jakobian do sterowania manipulatorem. MA thesis. PolitechnikaWarszawska; 2007.Google Scholar
  16. 16.
    Wu CH, Young KY. An efficient solution of a differential inverse kinematics problem for wrist-partitioned robots. IEEE Trans Robot Autom. 1990;6(1):117–23.MathSciNetCrossRefGoogle Scholar
  17. 17.
    Dulba I, Opałka M. A comparison of Jacobian-based methods of inverse kinematics for serial robot manipulators. Int J Appl Math Comput Sci. 2013;23(2):373–82.MathSciNetCrossRefGoogle Scholar
  18. 18.
    Buss SRS. Introduction to inverse kinematics with jacobian transpose, pseudoinverse and damped least squares methods. In: 132.4. University of California;2009. p. 1–19.Google Scholar
  19. 19.
    Spong MW, Hutchinson SM V. Robot modeling and control. In: Control 141.1, 2006. p. 419.Google Scholar
  20. 20.
    Barinka L, Berka R. Inverse kinematics—basic methods (Report). Technical report: Czech Technical University; 2002.Google Scholar
  21. 21.
    Biagiotti L, Melchiorri C. Trajectory planning for automatic machines and robots. 1st ed. Berlin, Heidelberg: Springer; 2008.Google Scholar
  22. 22.
    Maempel J. Koch T. Koehring S. Obermaier A.Witte H. Concept of a modular climbing robot. In: 2009 IEEE symposium on industrial electronics & applications 2; 2009. p. 789–94.Google Scholar
  23. 23.
    Giergiel J, Giergiel M, Buratowski T, Ciszewski M. Mechanizm pedipulatora do ustawiania pozycji modułu napdowego, zw?aszcza robota mobilnego. PL2238752016.Google Scholar
  24. 24.
    Corke P. Robotics Toolbox for MATLAB—Release 9.10 manual. 2015. http://www.petercorke.com/robot. Accessed 10 Jun 2016.
  25. 25.
    Corke P. Robotics Toolbox. 2016. http://petercorke.com/Robotics_Toolbox.html. Accessed 10 Feb 2016.

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Robotics and MechatronicsAGH University of Science and TechnologyKrakowPoland

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