Synthesis of Control Algorithm for Position of Six–Axis Manipulator

: pp. 118 – 126
Received: October 15, 2022
Revised: November 05, 2022
Accepted: November 14, 2022
Lviv Polytechnic National University
Lviv Polytechnic National University, Bydgoszcz University of Science and Technology

The paper formulates the inverse kinematic problem for the robotic manipulator with six degrees of freedom. For the solution if this problem, the geometric method combined with the Denavit–Hartenberg transformation was applied. The Denavit–Hartenberg method offers the advantage of reducing the number of coordinates that determine the special position of the solid body from six to four. This method provides for an accurate positioning of the working tool. The inverse kinematic problem was solved. This problem aims at calculating the rotating angle of each axis. The geometric solution of the problems for each of the axes is presented. Based on the calculation data, the algorithm of determining the rotating angles of the robotic manipulator was developed. This algorithm was implemented in the Matlab environment. The control flow chart of the algorithm is presented and its operation is described. The paper offers an example of solving the inverse kinematic problem using the developed algorithm. The calculation results were verified and shown to be consistent with the preset position, which confirms the adequacy of the developed model.

  1. V. Fedak, F. Durovsky, R. Uveges,  K. Kyslan, and M. Lacko (2015) Implementation of Robot Control Algorithms by Real-Time Control System. International Journal of Engineering Research in Africa, vol.18, 112–119.
  2. B.Siciliano, L.Sciavicco, L.Villani, G.Oriolo (2010) Robotics: Modelling, Planning and Control. Springer Science&Business Media. 632 p.
  3. Matthew T. Mason (2001) Mechanics of Robotic Manipulation. MIT Press. 272 p.
  4. Vihuro М., Malyar А. (2021) Solving the forward kinematics problem for a welding manipulator with six degrees of freedom. Electrical Power and Electromechanical Systems, no.1. 27-34.
  5. C. Smith and H. Christensen (2009) Robot manipulators. IEEE Robotics&Automation Magazine, vol.16, no.4, 75-83.
  6. G. C. Fernandez, S. M. Gutierrez, E. S. Ruiz, F. M. Perez and M. C. Gil. (2012) Robotics the New Industrial Revolution, IEEE Technology and Society Magazine, vol. 31, no. 2, 51-58.
  7. Blatnický M, Dižo J, Gerlici J, Sága M, Lack T, Kuba E. (2020) Design of a robotic manipulator for handling products of automotive industry. International Journal of Advanced Robotic Systems, no.17(1).
  8. Fu, K., Gonzalez, R., Lee, K. Robotics: Translated from English. Moscow: Mir Publishers, 1989. 624 p. (in Russian)
  9. Dmitrieva I.S, Levchenko D.O. Research of kinematic model of manipulative robot // System technology. 2015. No. 3 (98). pp. 57-62.
  10. Burdakov, S.F., Dyachenko, V.A., Timofeev, A.N. (1986) Design of industrial robotic manipulators and robotic centers. Moscow: Vysshaya Shkola Publishers. 264 p. (in Russian)
  11. Colomé A., Torras C. (2012) Redundant inverse kinematics: Experimental comparative review and two enhancements // Intelligent Robots and Systems (IROS). 2012. pp. 5333-5340.
  12. Duka A. V. (2014) Neural network based inverse kinematics solution for travel path tracking of a robotic arm. Procedia Technology, vol. 12. 20-27.
  13. K. Tokarz and S. Kieltyka (2010) Geometric approach to inverse kinematics for arm manipulator. Proceedings of International Conference on Systems, vol. II, ISSN 1792-4235, ISBN 978-960-474-214-1, 682-687
  14. Denavit J. and Hartenberg R. S. (1955) A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices. Journal of Applied Mechanics, vol. 22, 215–221.
  15. Marushchak, Ya.Yu. Kushnir, A.P. (2016) The Mathematical Model of the Mechanism of Electrodes Movement of Arc Steel-Melting Furnaces on the Basis of Denavit-Hartenberg Presentation. Electrotechnical and Computer Systems Journal, no 22 (98). 20-27.
M. Vihuro, A. Malyar. Synthesis of control algorithm for position of six–axis manipulator. Energy Engineering and Control Systems, 2022, Vol. 8, No. 2, pp. 118 – 126.