Algorithm for calculating the motion laws of working elements for CNC-controlled automated winding and laying systems


Аuthors

Abramenkov G. V.1, Gutenev A. V.2*, Marinin V. I.3**, Stradanchenko S. G.3***, Mokhov V. A.3****

1. ,
2. United Aircraft Corporation, UAC, 22-1, Ulansky pereulok, Moscow, 101000, Russia
3. Platov South-Russian State Polytechnic University (NPI), 132, Prosvesheniya str., Novocherkassk, 346428, Russia

*e-mail: a.v.gutenev@gmail.com
**e-mail: marinin_vi@npi-tu.ru
***e-mail: rektorat@npi-tu.ru
****e-mail: mokhov_v@mail.ru

Abstract

During the manufacturing preparation phase for CNC-controlled automated winding and laying systems, effective machine control requires solving the temporal parametrization problem-specifically, determining the motion laws of working elements along a predefined path geometry. Existing methods either suffer from high computational complexity or fail to ensure sufficient accuracy and trajectory smoothness, thereby reducing processing efficiency and accelerating equipment wear. A temporal parametrization algorithm is proposed that combines high accuracy with acceptable computation time by integrating the advantages of dynamic programming and a tube-based refinement method. In the initial stage, the algorithm generates a nominal trajectory using dynamic programming; subsequent stages refine it within a dynamically narrowing «tube» of allowable velocity bounds. The approach accounts for physical constraints on coordinate velocities and accelerations, as well as technological requirements, including point-wise constraints along the trajectory. Experimental validation demonstrates that the developed algorithm yields smoother motion laws and reduces trajectory generation time by 3% compared to classical dynamic programming, while maintaining a comparable computational load. The proposed approach enhances the productivity of CNC-controlled automated winding and laying systems, reduces equipment wear, and improves the quality of manufactured components.

Keywords:

temporal parametrization; dynamic programming; tube method; motion law; trajectory optimization; velocity and acceleration constraints; CNC-controlled systems

References

  1. Chumakov O.A., Snisarenko S.V. Dynamic programming method for optimizing manipulator movements. – 2022. – pp. 499-504.
  2. Marinin V.I. Optimization of the movement of executive bodies of units with software control // Control systems for technological processes: Collection of art. Novocherkassk: NPI Publishing House, 1974, Issue 1.
  3. Marinin V.I., Gorodetsky G.B. The problem of calculating optimal performance trajectories and laws of motion of executive bodies of winding machines with software control // Control systems for technological processes: Collection of art. Novocherkassk, NPI Publishing House, 1976, Issue 3.
  4. Marinin V.I. Planning optimal movements of the working bodies of winding machines // News of higher educational institutions. The North Caucasus region. Technical sciences. - 2003. – No. 3. – pp. 12-14.
  5. Marinin V.I., Knyazev D.N. Optimization of trajectories and laws of motion of working bodies of CNC winding machines. // Materials of the 4th International Scientific and Technical Conference Conference «New technologies for controlling the movement of technical facilities». Volume 3, Novocherkassk, 2002. pp.53-55.
  6. Marinin V.I., Knyazev D.N. Mitkevich A.B. Optimal trajectories and laws of motion of the working bodies of the winding machine. // Proceedings of the 4th International Conference. «Theory and practice of technologies for the production of products from composite materials and new metal alloys (TPKMM). Corporate NAO and CALS technologies in high-tech industries». Moscow: Znanie, 2006, pp. 632-536
  7. Kireev D.M., Marinin V.I. Solving the direct dynamics problem for winding machines // Student scientific spring – 2006. – Novocherkassk, – 2006. – pp. 224-225.
  8. Bertsekas D. Abstract dynamic programming. – Athena Scientific, 2022.
  9. Bobrow J.E., Dubowsky S., Gibson J.S. Time-optimal control of robotic manipulators along specified paths // The International Journal of Robotics Research. – 1985. – Vol. 4. – №3. – P. 3-17.
  10. Pham Q.C., Stasse O. Time-optimal path parameterization for redundantly actuated robots: A numerical integration approach // IEEE/ASME Transactions on Mechatronics. – 2015. – Т. 20. – №. 6. – С. 3257-3263.
  11. Haschke R., Weitnauer E., Ritter H. On-line planning of time-optimal, jerk-limited trajectories // IEEE/RSJ International Conference on Intelligent Robots and Systems. – 2008. – P. 3248-3253.
  12. Bastos Jr G., Franco E. Dynamic tube model predictive control for a class of soft manipulators with fluidic actuation // International Journal of Robust and Nonlinear Control. – 2025. – Т. 35. – №. 7. – С. 2780-2799.
  13. Luo Y. et al. Robust tube-based MPC with smooth computation for dexterous robot manipulation //Science China Information Sciences. – 2024. – Т. 67. – №. 11. – С. 1-17.
  14. Leskov A.G., Kalevatykh I.A. Experimental studies of algorithms for controlling the coupled movement of a two-armed manipulative robot // Bulletin of the Bauman Moscow State Technical University. The Instrument Engineering series. - 2012. – No. 4. – pp. 33-43.
  15. Artyomov K. Algorithms of adaptive reactive and proactive hybrid control of manipulative robots: dis. – 2022. 
  16. Golovin V.A., Yakovlev K.S. Primitives of robot movement in the task of trajectory planning with kinematic constraints // Computer Science and automation. – 2023. – Vol. 22. – No. 6. – pp. 1354-1386.
  17. Zhang T., Zhang M., Zou Y. Time-optimal and smooth trajectory planning for robot manipulators // International Journal of Control, Automation and Systems. – 2021. – Т. 19. – №. 1. – С. 521-531.
  18. Haghshenas H., Hansson A., Norrlöf M. Time-optimal path tracking for cooperative manipulators: A convex optimization approach // Control Engineering Practice. – 2023. – Т. 140. – С. 105668.
  19. Santos R.R., Rade D.A., da Fonseca I.M. A machine learning strategy for optimal path planning of space robotic manipulator in on-orbit servicing //Acta Astronautica. – 2022. – Т. 191. – С. 41-54.
  20. Bityukov Yu.I., Deniskin Yu.I. Geometric modeling of multilayer winding // Proceedings of the MAI. – 2010. – №. 37. – P. 15.
  21. Bityukov Yu. I. On one local coordinate system on a smooth surface used in computer modeling of the manufacturing process of structures from composite materials // Proceedings of MAI. – 2014. – no. 72. – P. 13.
  22. Lavrentiev M.A., Lyusternik L.A. Course of calculus of variations. Moscow: GONTI NKTP USSR, 1938, 192 p.


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