10th International Congress of the Serbian Society of Mechanics (18-20. 06. 2025, Niš) [pp. 206-215]
AUTHOR(S) / АУТОР(И): Petar D. Mandić
, Mihailo P. Lazarević
, Tomislav B. Šekara 
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DOI: 10.46793/ICSSM25.206M
ABSTRACT / САЖЕТАК:
This paper addresses the problem of path following for robotic systems. Specifically, a robot manipulator with three degrees of freedom must consecutively track an elliptic curve in space while adhering to a prescribed velocity law. Given that robots are highly nonlinear mechanical systems, achieving this objective is a complex task. Therefore, the mathematical model of the robot manipulator is transformed into a more manageable linear form, based on the actuator dynamics. To achieve high-accuracy path following, a model-based resonant controller is proposed. While this type of controller is not novel within the control community, its application in robotics remains relatively unexplored. To minimize tracking error, a particle swarm optimization (PSO) algorithm is employed, with an appropriate objective function designed to achieve the desired goal. The primary contribution of this paper lies in the integration of this metaheuristic algorithm with the complex resonant controller. Extensive simulations are conducted for various velocities of the robot’s end-effector, and the results are consistent with the expected dynamic behavior.
KEYWORDS / КЉУЧНЕ РЕЧИ:
robot manipulator, resonant controller, path following, PSO algorithm
ACKNOWLEDGEMENT / ПРОЈЕКАТ:
Authors gratefully acknowledge the support of Ministry of Education, Science and Technological Development of the Republic of Serbia under the contract 451-03- 137/2025-03/200105 from 04.02.2025 (P.D.M and M.P.L.), and 451-03-137/2025-03/200103 (T.B.Š.)
REFERENCES / ЛИТЕРАТУРА:
- Siciliano, L. Sciavicco, L. Villani, G. Oriolo, Robotics, London: Springer-Verlag, 2009.
- Dawson DM, Qu Z, Lewis FL, Dorsey JF. Robust control for the tracking of robot motion. International Journal of Control 1990; 52(3):581–595.
- Alvarez-Ramirez J, Cervantes I, Kelly R. PID regulation of robot manipulators: stability and performance. Systems and Control Letters 2000; 41(2):73–83.
- Stout WL, Sawan ME. Application of H-infinity theory to robot manipulator control. Proceedings of the IEEE Conference on Control Applications, Dayton, OH, USA, 13–16 September 1992; 148–153.
- Spong MW. On the robust control of robot manipulators. IEEE Transactions on Automatic Control 1992; 37(11):1782–1786.
- Stepanenko Y, Cao Y, Su C-Y. Variable structure control of robotic manipulator with PID sliding surfaces. International Journal of Robust and Nonlinear Control 1998; 8(1):79–90.
- Lin F, Brandt RD. An optimal control approach to robust control of robot manipulators. IEEE Transactions on Robotics and Automation 1998; 14(1):69–77.
- Kolhe JP, Shaheed M, Chandar TS, Talole SE. Robust control of robot manipulators based on uncertainty and disturbance estimation. Int. J. Robust. Nonlinear Control, 23(1), 104-122,
- Lewis FL. Neural network control of robot manipulators. IEEE Expert Magazine 1996; 11(3):64–75
- Ham C, Qu Z, Johnson R. Robust fuzzy control for robot manipulators. IEE Proceedings – Control Theory and Applications 2000; 147(2):212–216.
- C. Chou and C. M. Liaw, Development of Robust Current 2-DOF Controllers for a Permanent Magnet Synchronous Motor Drive With Reaction Wheel Load, in IEEE Transactions on Power Electronics, vol. 24, no. 5, pp. 1304-1320, May 2009.
- Abdallah C, Dawson D, Dorato P, Jamshidi Survey of robust control for rigid robots. IEEE Control Systems Magazine 1991; 11(2):24–30
- B. Šekara, M.R. Mataušek, Optimization of PID Controller Based on Maximization of the Proportional Gain Under Constraints on Robustness and Sensitivity to Measurement Noise, IEEE Trans Automat Contr, vol. 54, pp. 184-189, 2009.
- B. Šekara, M.R. Mataušek, (2010). Revisiting the Ziegler-Nichols process dynamics characterization. Journal of Process Control, 20(3), 360–363.
- B. Šekara, M.R. Mataušek, (2011). Classification of dynamic processes and PID controller tuning in a parameter plane. Journal of Process Control, 21(4), 620–626.
- R. Mataušek, T.B. Šekara, (2011). PID controller frequency-domain tuning for stable, integrating and unstable processes, including dead-time. Journal of Process Control, 21(1), 17–27.
- D. Mandić, T.B. Šekara, M.P. Lazarević, Analytical design of resonant controller applied for solving robot arm tracking problem, 9th International Congress of Serbian Society of Mechanics, Vrnjacka Banja, Serbia, July 5-7, 2023.
- D. Mandić, T.B. Šekara, M.P. Lazarević, M.Č. Bošković. Dominant pole placement with fractional order PID controllers: D-decomposition approach, 67, 76-86, 2017.
- D. Mandić, M.Č. Bošković, T.B. Šekara, M.P. Lazarević, A new optimisation method of PIDC controller under constraints on robustness and sensitivity to measurement noise using amplitude optimum principle, International Journal of Control, 97(1), 36-50,2024.
- P. Lazarević, P.D. Mandić, S.Ostojić, Further results on advanced robust iterative learning control and modeling of robotic systems, Proc IMechE Part C: J Mechanical Engineering Science, pp. 1-16, 2020.
- P. Cvetković, M.P. Lazarević, P.D. Mandić, T.B. Šekara, Open closed loop PDµ/PD type ILC control of NeuroArm robotic system, 8th International Congress of Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021.
- D. Mandić, M.P. Lazarević, Z. Stokić, T.B. Šekara, Dynamic Modelling and Control Design of Seven Degrees of Freedom Robotic Arm, 6th International Congress of Serbian Society of Mechanics, Tara, Serbia, June 19-21, 2017.
- Čović, M.P. Lazarević, Robot Mechanics, Faculty of Mechanical Engineering, Belgrade, Serbia, 2009.
- D. Mandić, Advanced modeling of complex robotic systems and mechanisms and applications of modern control theory, PhD Dissertation, Faculty of Mechanical Engineering, 2019.
- D. Mandić, P. Lino, G. Maione, M.P. Lazarević, T.B. Šekara, Design of fractional order lag network and fractional order PI controller for a robotic manipulator, IFAC PapersOnLine, 53(2), 3669-3674, 2020.
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