Synthesis of the Robotic Tool Motion-Controlling Algorithm Using Method of Correction Dynamics and Pertubations Compensation

The task of controlling the manipulation robot movement in one direction has been considered. Such task appears at cutting, welding, painting and other similar operations, when the robot instrument performs a program motion along the working surface and at the same time, it is necessary to keep a definite distance from this instrument to the surface automatically without excessive correction. A new algorithm of controlling the linear object of the second order of the general form has been obtained by dynamics and perturbations compensation method, which takes precedence over well-known decisions. The algorithm provides a zero static error of the system regulation and movement in acquisition of external effects within the accuracy of standard filters of the second order that is convenient for practical use. The first filter indicates movements of the system during the task performing; the second one provides perturbations compensation on state variables. A step-by-step procedure of the algorithm synthesis has been represented for the second order controlled object of the general form. Formulae for calculating regulator coefficients have been obtained. The obtained equations defining processes in a closed control system allow performing the analysis of the control quality and the dynamics of control changes depending on external influences. A method of equations identification of the robot motion in conditions when we know the maximum speed of its instrument movement and a dynamic error of the robot servosystem regulating has been developed. By this method, the robot equations are brought up to the Vyshnegradskiy’s form and then on the computer model a fundamental frequency and a decay factor can be easily chosen. The application of the obtained algorithm has been reviewed to create a system of automatic regulation of the robot instrument position. It has been clarified that defining free coefficients of these filters on position of filter fundamental frequency equation and a controlled object provides the given system operation speed at moderate amplitude of controlling actions. A mathematical modeling method has shown the advantages of regulation program quality, parametric and structural robustness of the obtained control system.

1. Zhao R. Trajectory planning and control for robot manipulations. Robotics [cs.RO]: thesis — Universit@ Paul Sabatier — Toulouse III, 2015, pp. 158, available at: https://tel.archives-ouvertes.fr/tel-01285383v2/document

2. Campa R., Ramirez C., Camarillo K., Santibanez V., Soto I. Motion Control of Industrial Robots in Operational Space: Analysis and Experiments with the PA10 Arm, Advances in Robot Manipulators, Ernest Hall (Ed.), 2010, pp. 417—442.

3. Lynch K. M., Park F. C. Modern Robotics: Mechanics, Planning and Control, Cambridge U. Press, 2017, pp. 642.

4. Nemeikšis A. Trajectory modulation of 2.5 degree of freedom robot arm, Scientific researches and their practical application. Modern state and shays of development, 2014, vol. 5, no. 3, pp. 3—11, available at: https://elibrary.ru/item.asp?id=22270213

5. Yurish S. ed. Advances in Robotics and Automatic Control: Reviews, Book Series, 2018, vol. 1, 404 p.

6. Zenkevich S. L., Jushhenko A. S. Robots control. The basics of manipulating robots, Moscow, Publishing house of MGTU named after N. Je. Bauman, 2000, 400 p. (in Russian)

7. Varkov A. A., Krasil’nikjanc E. V., Tjutikov V. V. Control system of a manipulation robot with compensation of dynamic moments,Avtomatizacija v Promyshlennosti. 2011, no. 5, pp. 38—44, available at: https://avtprom.ru/sistema-upravleniya-manipulyatsionnym-ro (in Russian)

8. Zada V., Belda K. Mathematical modeling of industrial robots based of Hamiltonian mechanics, 2016, pp. 813—818, available at: https://www.researchgate.net/publication/30466-5752_Mathematical_modeling_of_industrial_robots_based_on_Hamiltonian_mechanics

9. Voronov A. A. Fundamentals of the theory of automatic control. Part I. Linear control systems of one magnitude, Moscow—Leningrad, Vysshaja shkola, 1986, 367 p., available at: http://www.studmed.ru/voronov-aa-teoriya-avtomaticheskogo-upravleniya-chast-pervaya_92e4dec0e1e.html (in Russian)

10. Aleksandrov A. G. Avtomatika i Telemehanika, 2010, no. 6, pp. 3—19, available at: URL:http://m.mathnet.ru/php/archive.phtml?wshowpaper&jrnid=at&paperid=826&option_lang=rus (in Russian)

11. Letov A. M. Avtomatika i Telemehanika, 1960, no. 4, pp. 406—411; no. 5, pp. 561—568; no. 6, pp. 661—665, available at:http://m.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=at&paperid=12522&option_lang=rus (in Russian)

12. Kalman R. E. Boletin de la Sociedad Matematica Mehicana, 1960, vol. 5, no. 1, pp. 102-119, available at: https://www.semanticscholar.org/paper/Contributions-to-the-Theory-of-OptimalControl-K%C3%A1lm%C3%A1n/4602a97c4965a9f6c41c9a7eeae f5be8333dbaef

13. Poljak B. T., Shherbakov P. S. Robust stability and control, Moscow, Nauka, 2002 (in Russian), available at: http://www.studmed.ru/polyak-bt-scherbakov-ps-robastnaya-ustoychivost-i-upravlenie_9af8562ef3e.html

14. Izerman R. Digital control systems, Moscow, Mir, 1984, available at: https://lib-bkm.ru/12325 (in Russian).

15. Pupkov K. A., Egupov N. D. Methods of classical and modern theory of automatic control. Textbook in 5 t.; V. 3. Synthesis of regulators of automatic control systems), Moscow Publishing house of MGTU named after N. Je. Bauman, 2004, 656 p. (in Russian).

16. Andreev A. Ju. Control of finite-dimensional linear objects, Moscow, Nauka, 1976, 424 p., available at: http://www.toroid.ru/andreevUN.html (in Russian).

17. Gajduk A. R., Plaksienko E. A. Mekhatronika, Avtomatizatsiya, Upravlenie, 2008, no. 4, pp. 7—12, available at: https://elibrary.ru/item.asp?id=10442093 (in Russian).

18. Filimonov A. B., Filimonov N. B. Mekhatronika, Avtomatizatsiya, Upravlenie, 2011, no. 5, pp. 9—14 (in Russian), available at: http://novtex.ru/mech/mech2011/an-not05.html#2

19. Kim D. P. Mekhatronika, Avtomatizatsiya, Upravlenie, 2011, no. 5, pp. 15—21 (in Russian).

20. Kim D. P. Algebraic methods for the synthesis of automatic control systems, Moscow, FIZMATLIT, 2014, 164 p. (in Russian).

21. Shadrin G. K. Avtomatika i Telemehanika, 2016, no. 7, pp. 1151-1162, available at: http://m.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=at&paperid=14505&option_lang=rus (in Russian).

22. Shadrin G. K., Porubov D. A., Shadrin M. G. Avtomatika i programmnaja inzhenerija, 2017, no. 4 (22), pp. 10—15, available at: http://jurnal.nips.ru/sites/default/files/AaSI-4-2017-1.pdf (in Russian).

23. Krasovskij A. A., Pospelov G. S. Fundamentals of automation and technical cybernetics, Moscow—Leningrad, Gosjenergoizdat, 1962, 600 p., available at: https://www.twirpx.com/file/840055/ (in Russian).

24. Titce U., Shenk K. Semiconductor Circuitry, Moscow, Mir, 1982, 512 pp. available at: http://lazysmart.ru/wp-content/uploads/2016/07/Tittse-U.-SHenk-K.-Poluprovodnikovaya-shemotehnika.-Tom-I-2007.pdf (in Russian).