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Algorithm for the Numerical Solution of Optimal Control Problems in Robotic Systems

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Optimization and Applications (OPTIMA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13078))

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Abstract

The paper discusses the algorithm for the numerical solution of applied optimal control problems in robotics. The proposed algorithm is the Powell method modification, which uses the combined one-dimensional nonlocal search algorithm developed by the authors based on the Strongin and parabolas methods as an auxiliary one. The developed algorithm is implemented in C language and integrated within a single software package. The obtained using the proposed algorithm solutions of two problems are presented: the problem of the optimal control of the mobile robot and the task of the industrial robot arm control. All the obtained solutions found a meaningful interpretation.

Supported by Russian Foundation for Basic Research, No 19-37-90065.

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References

  1. Betts, J.: Practical methods for optimal control and estimation using nonlinear programming. SIAM, Philadelphia (2010)

    Book  Google Scholar 

  2. Blatt, M., Schittkowski, K.: Pdecon: A fortran code for solving control problems based on ordinary, algebraic and partial differential equations. In: Technical report, Department of Mathematics, University of Bayreuth, Bayreuth (1997)

    Google Scholar 

  3. Bulatov, V., Hamisov, O.: Cut-off method in e(n+1) for solving global optimization problems on one class of functions. Comput. Math Math. phys. 47(11), 1830–1842 (2007)

    Article  MathSciNet  Google Scholar 

  4. Chernousko, F., Banichuk, V.: Variational Problems of Mechanics and Control. Nauka, Moscow (1973)

    Google Scholar 

  5. Cruz, I.: Efficient Evolutionary Algorithms for Optimal Control. Wageningen University, Wageningen (2002)

    Google Scholar 

  6. Denardo, E.: Dynamic Programming: Models and Applications. Courier Corporation, Chelmsford (2012)

    MATH  Google Scholar 

  7. Diveev, A., Konstantinov, S.: The study of evolutionary algorithms for solving the optimal control problem. Proceedings of the Moscow Inst. Phys. Technol. 9(3), 76–85 (2017)

    Google Scholar 

  8. Evtushenko, Y.: Methods for solving extremal problems and their application in optimization systems. Nauka, Moscow (1982)

    Google Scholar 

  9. Fedorenko, R.: Approximate Solution of Optimal Control Problems. Nauka, Moscow (1978)

    MATH  Google Scholar 

  10. Gornov, A.: Computational Technologies for Solving Optimal Control Problems. Nauka, Novosibirsk (2009)

    Google Scholar 

  11. Gornov, A., Zarodnyuk, T.: Optimal control problem: heuristic algorithm for global minimum. In: Proceedings of the Second International Conference on Optimization and Control, pp. 27–28. National University of Mongolia, Ulanbaatar (2007)

    Google Scholar 

  12. Gornov, A., Zarodnyuk, T.: The “curvilinear search” method of global extremum in optimal control problems. Modern techniques. System analysis. Simulation 1(3), 19–26 (2009)

    Google Scholar 

  13. Gornov, A., Zarodnyuk, T.: Method of stochastic coverings for the optimal control problem. Comput. Technol. 17(2), 31–42 (2012)

    Google Scholar 

  14. Gurman, V., Baturin, V., Rasina, I.: Approximate methods of optimal control. Irkutsk University, Irkutsk (1983)

    Google Scholar 

  15. Himmelblau, D.: Applied Nonlinear Programming. McGraw-Hill, New York (1972)

    MATH  Google Scholar 

  16. Kamien, M., Schwartz, N.: Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management. Courier Corporation, Chelmsford (2012)

    MATH  Google Scholar 

  17. Krotov, V.: Global Methods in Optimal Control Theory. CRC Press, Boca Raton (1995)

    Google Scholar 

  18. Pesterev, A.V.: A linearizing feedback for stabilizing a car-like robot following a curvilinear path. J. Comput. Syst. Sci. Int. 52(5), 819–830 (2013). https://doi.org/10.1134/S1064230713050109

    Article  MathSciNet  MATH  Google Scholar 

  19. Rapoport, L.: Estimation of attraction domains in wheeled robot control. Automation and Remote Control 1(9), 69–89 (2006)

    MATH  Google Scholar 

  20. Schwartz, A., Polak, E.: Consistent approximations for optimal control problems based on runge-kutta integration. SIAM J. Control and Optim. 34(4), 1235–1269 (1996)

    Article  MathSciNet  Google Scholar 

  21. Strongin, R.: Numerical Methods in Multiextremal Problems. Nauka, Moscow (1978)

    Google Scholar 

  22. Stryk, O.V.: Numerical solution of optimal control problems by direct collocation. Optim. Control 1(111), 129–143 (1993)

    Article  MathSciNet  Google Scholar 

  23. Teo, K., Goh, C., Wong, K.: A Unified Computational Approach to Optimal Control Problems. John Wiley and Sons, New York (1991)

    MATH  Google Scholar 

  24. Tolstonogov, A.: Differential Inclusions in a Banach Space. Springer Science and Business Media, Luxembourg (2012)

    MATH  Google Scholar 

  25. Tyatyushkin, A.: Numerical Methods and Software for Optimizing managed Systems. Nauka, Novosibirsk (1992)

    Google Scholar 

  26. Xing, B., Gao, W.: Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms. Springer, Cham (2014)

    Book  Google Scholar 

  27. Zarodnyuk, T., Gornov, A.: Global extremum search technology in the optimal control problem. Modern techniques. System analysis. Simulation 1(3), 70–76 (2008)

    Google Scholar 

  28. Zhiglyavsky, A.: Mathematical theory of random global search. Leningrad University Publishing Department, Leningrad (1985)

    Google Scholar 

  29. Zhigljavsky, A., Zilinskas, A.: Stochastic global optimization. Springer, Luxembourg (2008)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory of SB RAS, Lermontov Street, 134, 664033, Irkutsk, Russia

    Pavel Sorokovikov & Alexander Gornov

  2. Irkutsk National Research Technical University, Lermontov Street, 83, 664074, Irkutsk, Russia

    Alexander Strelnikov

Authors
  1. Pavel Sorokovikov
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  2. Alexander Gornov
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  3. Alexander Strelnikov
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Corresponding author

Correspondence to Pavel Sorokovikov .

Editor information

Editors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Nicholas N. Olenev

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Yuri G. Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  4. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  5. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Sorokovikov, P., Gornov, A., Strelnikov, A. (2021). Algorithm for the Numerical Solution of Optimal Control Problems in Robotic Systems. In: Olenev, N.N., Evtushenko, Y.G., Jaćimović, M., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2021. Lecture Notes in Computer Science(), vol 13078. Springer, Cham. https://doi.org/10.1007/978-3-030-91059-4_15

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  • DOI: https://doi.org/10.1007/978-3-030-91059-4_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-91058-7

  • Online ISBN: 978-3-030-91059-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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