Design of the mathematical model of a stepper motor SCARA robot control system

Design of the mathematical model of a stepper motor SCARA robot control system

Konstantin A. Kalushev
Master's degree, Moscow Technical University of Communications and Informatics (MTUCI), 8А, Aviamotornaya ul., Moscow, 111024, Russia, This email address is being protected from spambots. You need JavaScript enabled to view it.

Liliya I. Voronova
Doctor of Physical and Mathematical Sciences, Professor, MTUCI, Head of «Intellectual systems in control and automation» Department, 8А, Aviamotornaya ul., Moscow, 111024, Russia, This email address is being protected from spambots. You need JavaScript enabled to view it.

Received March 13, 2024

Abstract
SCARA robots are simple and efficient for a vast majority of tasks. The key problem to increase the utilization of these robots is the high cost of the machines as compared to the potential economic effect when used in real operation. It is possible to decrease the cost of a robot and, thus, increase its economic efficiency by use of stepper motors in design of the robot. To solve this task a complete mathematical model of a two-link SCARA robot control should be developed covering all aspects from determining the coordinates of an object in the basic coordinate frame to calculation of the number of impulses generated by the control electronics of a stepper motor. This article reveals a complete description of mathematical essentials of a two-links stepper motor SCARA robot control system. The article includes a comprehensive solution of the direct and inverse kinematics tasks for such a robot. Given the fact that the inverse kinematics task may have multiple solutions, an algorithm to choose the only appropriate solution was developed. It provides a specificgraphical approach to determine the robot working zone considering links revolution angles specific to the robot constriction approach. The article includes mathematical aspects to control stepper motors in terms of calculation of the number of impulses based on the required angles. It considers the inevitable problem of stepper motor SCARA robot positioning error and provides for positioning optimization approaches. By applying a two-link demonstration robot designed by the author, it was practically confirmed that the described mathematical approach is correct. The inevitable stepper motor SCARA robot positioning error was experimentally confirmed. Overall, the provided results support the practical possibility to design inexpensive stepper motor SCARA robot to reach sufficient economic efficiency and, as a result, increase the spectrum of application of similar machines.

Key words
Coordinate systems transformations, SCARA robot, direct kinematics problem, reverse kinematics problem, stepper motors, positioning error, transformation matrix.

Bibliographic description
Kalushev, K.A. and Voronova, L.I. (2025), "Design of the mathematical model of a stepper motor SCARA robot control system", Robotics and Technical Cybernetics, vol. 13, no. 2, pp. 104-114, EDN: TPEXZJ. (in Russian).

EDN
TPEXZJ

UDC identifier
681.51:007.52

References

  1. Efremov, V.D. (1997), Systemy upravleniya robotami I robototechnicheskimi kompleksami [Robots and robotic complexes control systems], Voronezh State University Publ., Voronezh, Russia. (in Russian).
  2. Tyagunov, O.A. (1996), Systemy upravleniya robotami I manipulyatorami (mechanica robotov) [Robot and manipulators control systems (mechanics of robots)], Russian Technological University Publ., Moscow, Russia, ISBN 5-230-12175-0. (in Russian).
  3. Kovalchuk, A.K. (2011), “Selecting the kinematic structure and research of tree-like executive mechanism of Robo-dog”, Izvestiya vischih uchebnih zavedeniy. Mashinostroenie, no. 8, pp. 65-73. (in Russian).
  4. Podkorytov, D.D. (2022), “Application of Denavi-Hartenberg method in robot operation”, in Proceedings of X Int. scientific-practical. conf. “Innovative scientific research: humanitarian and exact sciences”, 25 November Moscow, Russia. pp. 122-128. (in Russian).
  5. Alchakov, V.V. (2019), “Design of a mathematical model of an antropomorphous robot gripper based on Denavit-Hartenberg method”, Avtomatizaciya I izmereniya v mashino I priborostroenii, no. 1(5), pp. 92-102. (in Russian).
  6. Danilov, A.V. (2018), “General approach to solving inverse kinematic task for a sequential structure manipulator using rotation and displacement”, Preprinty IPM im. M.V.Keldisha, no. 81, pp. 1-15, DOI: 10.20948/prepr-2018-81. (in Russian).
  7. Shulgin, S.K. (2023), “Modelling an daptive positioning system of a two-link kinematics chain using artificial neural network”, Socialno-economicheskiy I technicheskie sistemy: issledovanie, proektirovanie, optimizaciya, no. 2(94), pp. 122-130. (in Russian).
  8. Daniel Cagigas-Muniz (2023), “Artificial Neural Networks for inverse kinematics problem in articulated robots”, Engineering Applications of Artificial Intelligence, no.126(3), DOI: 10.1016/j.engappai.2023.107175.
  9. Marchuk, E.A. (2023), “On numerical modelling of the working zone of a hybrid cable robot”, Izvestiya Volgogradskogo gosudarstvennogo technicheskogo universiteta, no. 4(275), pp. 64-71, DOI: 10.35211/1990-5297-2023-4-275-64-71. (in Russian).
  10. Tanyrbergenova, K.I. (2020), “Kinematics of a manipulashion robot and approximation of its working area”, Vestnik Almatinskogo universiteta energetiki I svyazi, no. 3(50), pp. 54-61, DOI: 10.51775/1999-9801_2020_50_3_54. (in Russian).
  11. Malyshev, D.I., Posypkin, M.A., Rybak, L.A. and Usov, A.L. (2018), “Analysis of working area of DexTAR - dexterous twin-arm robot”, International Journal of Open Information Technologies, vol. 6, no 7, pp. 15-20. (in Russian).
  12. Chzhu Lyanlyan (2022), “Analysis of error causes and methods to increase robot positioning accuracy”, Politechnicheskiy molodezhniy zhurnal, no. 5(70), DOI: 10.18698/2541-8009-2022-5-797. (in Russian).
  13. Koltygin, D.S., Sedelnikov, I.A. and Pavlyuk, E.Yu (2016), “Determining positioning accuracy of DELTA and OMEGA manipulation robots”, Trudy Bratskogo gosudarstvennogo unizersiteta. Seriya: Estestvennie I inzhenernie nauki, vol. 2, pp. 121-126. (in Russian).
  14. Balanev, N.V. and Yanov, R.A. (2016), “Analysis of factors affecting accuracy of industrial robot positioning and methods to maintain the required accuracy”, Dostigeniya nauki i obrazovaniya, no. 1(2), pp. 11-14. (in Russian).