Autors: Panov, V. K., Ivanova, M. J., Mitrev, R. P.
Title: Mathematical modeling of the longitudinal motion of a robotic construction manipulator with a freely suspended payload
Keywords: mathematical model, dynamic model

Abstract: The paper develops a mathematical model of the horizontal longitudinal motion of a robotic construction manipulator with a Cartesian kinematic structure. A dynamic model with four degrees of freedom of the manipulator with a freely suspended load has been developed. The real-world system with distributed mass was idealized and presented as concentrated masses. The mathematical models will be used to develop an automatic control system for the longitudinal motion to reduce the vibrations of the metal structure and achieve preassigned kinematic characteristics of the longitudinal motion. For the derivation of the differential equations of motion of the manipulator, the Lagrange equations of the second kind are used. To obtain the kinematic relations homogeneous transformation matrices were used with subsequent differentiation of the obtained expressions. The nonlinear differential equations are used for a numerical study of the dynamic system behaviour under different driving motor law.


  1. . A. Bulgakov and V. Vorobyov, Industrial robots. Kinematics, Dynamics, Control and Management, (Solon- Press, Moscow, Russia, 2012).
  2. E. Budny, M. Chlosta and W. Gutkowski, “Load-independent control of a hydraulic excavator”, Autom. Constr. 12, pp. 245–254 (2003).
  3. N. Pavlov and D. Dacova, “A multibody model of a wheel loader with pneumatic boom suspension and proving ground testing”, IOP Conf. Ser.: Mater. Sci. Eng. 1031, 012009, pp. 1–8 (2021).
  4. A. Koivo, M. Thoma, and E. Kocaog-lan, “Modeling and control of excavator dynamics during digging operation”, J. Aerosp. Eng. 9, pp. 10–18 (1996).
  5. J. Zhang and B. Khoshnevis, Optimal machine operation planning for construction by Contour Crafting, Autom. Constr 29, pp. 50–67 (2013).
  6. G. Petkov, J. Hlebarov, M. Prodanov, P. Karaivanov and H. Hristov, Dynamics of Stacker Cranes. Methods for Calculations, Report ???? 445/72, Technical University of Sofia (1974), (In Bulgarian).
  7. N. Qie, W.-F. Houa, and J.-H. He, “The fastest insight into the large amplitude vibration of a string”, Reports in Mechanical Engineering 2, pp. 1–5 (2021).
  8. J.-H. He and A. García, “The simplest amplitude-period formula for non-conservative oscillators”, Reports in Mechanical Engineering 2, pp. 143–148(2021).
  9. S. Kalinkov, Research on Electronic Power Supply and Control Systems of Automated Storage and Retrieval Machines, PhD thesis, Technical University of Sofia, 2011, (In Bulgarian).
  10. S. Kalinkov, R. Mitrev, and G. Ruzhekov, “Simulation modelling and study of elevating transfer vehicle with controlled electric motor of the travel mechanism”, Mechanics of Machines 82, pp. 71–78(2009), (In Bulgarian).
  11. A. Krasteva, S. Kalinkov, G. Ruzhekov, and R. Mitrev, Automated Storage and Retrieval Systems – AS/RS. Development of Models of the Mechanical and the Electronic Systems, Report ???? 4122????-03/2007, Technical University of Sofia (2008), (In Bulgarian).
  12. R. Mitrev, S. Kalinkov, and G. Ruzhekov, “Mechano-mathematical modeling of the horizontal motion of elevating transfer vehicle with uncontrolled electric motor of the travel mechanism”, Bulgarian Journal for Engineering Design 1, pp. 127–133 (2008), (In Bulgarian).
  13. M. Ivanova, “Mathematical modelling of a construction manipulator performing horizontal rectilinear motion”, CAx technologies 6, pp. 11–25 (2018), (In Bulgarian).
  14. R. Mitrev, M. Ivanova, and I. Ivanov, “Linearized mathematical model of a construction manipulator performing a horizontal rectilinear motion”, CAx technologies 6, pp. 33–42 (2018), (In Bulgarian).
  15. S. Hajdu, Mast Vibration Reduction of Single-mast Stacker Cranes via Modern Control Methods, PhD thesis, Budapest University of Technology and Economics, Budapest, 2016.
  16. M. Takahashi, S. Kinoshita, H. Kato, Y. Kawasaki and Z. Iwai, “Positioning control of a stacker crane using a robust simple adaptive control method”, IFAC Proceedings Volumes 37, pp.161–166 (2004).
  17. J. Kim, Y. Lee, S. Shin, H. Lee, D. Jo, “Dynamic Characteristics Analysis of Stacker Crane for Automatic Warehouse”, Proceedings of the KSME Conference, (Korea, 2001), pp. 436–441.
  18. L. Biagiotti and C. Melchiorri, Trajectory Planning of Automatic Machines and Robots, (Springer, 2008).
  19. J. Craig, Introduction to Robotics. Mechanics and Control, (Pearson, 2005).
  20. C. De Silva, Vibration: Fundamentals and Practice, (CRC Press, 2000).
  21. L. Sciavicco and B. Siciliano, Modelling and Control of Robot Manipulators, (Springer-Verlag, London, 2000).
  22. S. Chapra, R. Canale, Numerical Methods for Engineers, (McGraw-Hill, 2010).
  23. R. Mitrev, V. Panov, and M. Ivanova, “Mathematical modeling of longitudinal motion of robotic construction manipulator”, Mechanics of Machines 125, pp. 67–74 (2021), (In Bulgarian).
  24. A. Abe, “An effective trajectory planning method for simultaneously suppressing residual vibration and energy consumption of flexible structures”, Case Studies in Mechanical Systems and Signal Processing 4, pp. 19–27 (2016).


13TH INTERNATIONAL SCIENTIFIC CONFERENCE ON AERONAUTICS, AUTOMOTIVE AND RAILWAY ENGINEERING AND TECHNOLOGIES (BulTrans-2021), vol. 1, issue 2557, pp. 040003-1 - 040003-11, 2022, Bulgaria, AIP Conference Proceedings, ISBN 978-0-7354-4386-0

Copyright AIP Publishing LLC

Вид: публикация в международен форум, публикация в реферирано издание, индексирана в Scopus и Web of Science