Synthesis of the Coordinated Control Algorithms for a Biaxial Manipulator

  • Valeriy LyubichEmail author
  • Aron Kurmashev
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 95)


Objectives of this work were to synthesize a coordinated control algorithm and a reduced coordinated control algorithm for the biaxial manipulator and for a typical (straight line and circular arc) and non-typical (parabola) trajectories. The authors synthesized the coordinated control algorithm (CCA) based on A.D. Kurmashev algorithm and proposed the reduced coordinated control algorithm (RCCA) for a biaxial manipulator model. Two synthesized algorithms and an uncoupled system on different trajectories and different contour speeds were compared using mathematical modeling. Utilizing the coordinated control algorithms leads to an increase in the minimal quality factor and may lead to a decrease in the contour speed error in comparison to the uncoupled system. The synthesized algorithms for the manipulator moving along the typical and non-typical trajectories eliminate contour and contour speed errors better than the uncoupled system. The RCCA allows to control manipulator by using information only from position and speed sensors. Therefore, it is possible to implement the RCCA on existing equipment without any significant modification of it like adding additional sensors, loops, etc.


Coordinated control algorithm Biaxial manipulator Mathematical modelling Synthesized algorithm 


  1. 1.
    Beliaev, A.N., Kurmashev, A.D., Sokolov, O.A.: Zamknutye sistemy CHPU robotami [CNC coupled systems for robots], Voronezhskii Politech. Institut, Voronezh (1989). (in Russian)Google Scholar
  2. 2.
    Shapovalov, A.A., Kurmashev, A.D.: Contouring system of coordinated control of an industrial robot, TUSUR, 1(25), part 2 (2012)Google Scholar
  3. 3.
    Tang, L., Landers, R.G.: Multiaxis contour control – the state of the art. Proc. IEEE Trans. Control Syst. Technol. (2012).
  4. 4.
    Huo, F., Poo, A.: Precision contouring control of machine tools. Int. J. Adv. Manuf. Technol. (2013).
  5. 5.
    Huan, J.: Bahnregelung zur Bahnerzeugung an numerisch gesteuerten Werkzeugmaschinen. Dr.-Ing dissertation, Stuttgart Universitaet (1982).
  6. 6.
    Chen, J., Tsai, H.: A path algorithm for robotic machining. Robot. Comput. Integr. Manuf. 10(3) (1993).
  7. 7.
    Chin, J., Lin, S.: The path precompensation method for flexible arm robot. Robot. Comput.-Integr. Manuf. 13(3) (1997).
  8. 8.
    Koren, Y.: Cross-coupled biaxial computer control for manufacturing systems. ASME J. Dyn. Syst. Meas. Control 112(2) (1990).
  9. 9.
    Chin, J., Cheng, Y., Lin, J.: Improving contour accuracy by Fuzzy-logic enhanced cross-coupled precompensation method. Robot. Comput.-Integr. Manuf. 20 (1) (2004).
  10. 10.
    Li, P.Y., Horowitz, R.: Passive velocity field control (PVFC): part II—application to contour following. IEEE Trans. Autom. Control 46(9) (2001).
  11. 11.
    Chen, C., Cheng, M., Wu, J., Su, K.: Passivity-based contour following control design with virtual plant disturbance compensation. In: Proceedings of the 11th IEEE International Workshop on Advanced Motion Control (2010).
  12. 12.
    Lyubich, V.K., Kurmashev, A.D.: Soglasovannoe upravlenie programmnym dvizheniem manipulyatora po traektorii, zadannoj kubicheskim splajnom [The coordinated control of the manipulator program movement along a cubic spline trajectory]. In: Proceedings of the Week of Science 2017, ICST, St. Petersburg (2017). (in Russian)Google Scholar
  13. 13.
    Zeng, D., Gao, Y., Hu, Y., Liu, J.: Optimization control for the coordinated system of an ultra-supercritical unit based on stair-like predictive control algorithm. Control Eng. Pract. 82 (2019).
  14. 14.
    Boichuk, L.M.: Metody strukturnogo sinteza nelineinyh sistem avtomaticheskogo upravleniya [Structure synthesis methods for nonlinear control systems], Energia, Moscow (1971). (in Russian)Google Scholar
  15. 15.
    Galiullin, A.S.: Postroenie sistem programmnogo dvizheniya [Synthesis of program movement systems], Nauka, Moscow (1971). (in Russian)Google Scholar
  16. 16.
    Spur, G., Duelen, G., Wendt, W.: Improvement of the dynamic accuracy of the continuous control paths. Robot. Comput.-Integr. Manuf. 1(1) (1984).
  17. 17.
    Kurmashev, A.D.: Povyshenie tochnosti i skorosti vosproizvedeniya programmnyh dvizhenij promyshlennymi robotami [An industrial robot program movement accuracy increase], Dissertation, Leningrad Polytechnic Institute, Leningrad (1990). (in Russian)Google Scholar
  18. 18.
    Chen, S., Wu, K.: Contouring control of smooth paths for multiaxis motion systems based on equivalent errors. IEEE Trans. Control Syst. Technol. 15(6) (2007).
  19. 19.
    Lyubich, V.K.: Razrabotka algoritmov programmnogo upravleniya elektroprivodami dvuhzvennogo manipulyatora s uprugimi swyazyami [Synthesis of a program control for the flexible biaxial manipulator], Master thesis, SPbTU, St. Petersburg (2016). (in Russian)Google Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Peter the Great St. Petersburg Polytechnic UniversitySaint PetersburgRussia

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