Particle Swarm Optimization Based Parameter Identification Applied to a Target Tracker Robot with Flexible Joint

Document Type : Original Article


Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Shiraz, Iran


This paper focuses on parameter identification of a target tracker robot possessing flexible joints using particle swarm optimization (PSO) algorithm. Since, belt and pulley mechanisms are known as flexible joints in robotic systems, their elastic behavior affecting a tracker robot is investigated in this work. First, dynamic equations governing the robot behavior are extracted taking into account the effects of considered flexible joints. Thus, a flexible joint is modeled by a non-linear spring and damper system connecting the motor to the link. It is found that the governing dynamic equations include some unknown parameters, which must be identified in order to design the robot system. Consequently, a PSO-based identification scheme is proposed to achieve the unknown variables based on the experimental data of the open-loop system. Lastly, for validating the proposed identification scheme, the obtained results are compared to the experimental measurements as well as the results of another similar work in which the robot is modeled with rigid joints. The consequences reveal that the mathematical model of the robot with flexible joint can describe the elastic behavior of the tracker robot. Thus, a better agreement between the simulation and experimental data are found in comparison with outcomes of the robot model with rigid joints.


1.     Wang, H., and Xia, X. P. “Simulation of manipulator with flexible joint.” Applied Mechanics and Materials, Vol. 327, (2013), 999–1003.
2.     Spong, M. W. “Modeling and control of elastic joint robots.” Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, Vol. 109, No. 4, (1987), 310–319.
3.     Zhang, D. G., and Angeles, J. “Impact dynamics of flexible-joint robots.” Computers and Structures, Vol. 83, No. 1, (2005), 25–33.
4.     Ettefagh, M. H., Naraghi, M., and Towhidkhah, F. “Position Control of a Flexible Joint via Explicit Model Predictive Control: An Experimental Implementation.” Emerging Science Journal, Vol. 3, No. 3, (2019), 146–156.
5.     Chaoui, H., Gueaieb, W., Biglarbegian, M., and Yagoub, M. “Computationally Efficient Adaptive Type-2 Fuzzy Control of Flexible-Joint Manipulators.” Robotics, Vol. 2, No. 2, (2013), 66–91.
6.     Yoo, S. J., Park, J. B., and Choi, Y. H. “Adaptive dynamic surface control of flexible-joint robots using self-recurrent wavelet neural networks.” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol. 36, No. 6, (2006), 1342–1355.
7.     Nanos, K., and Papadopoulos, E. G. “On the dynamics and control of flexible joint space manipulators.” Control Engineering Practice, Vol. 45, , (2015), 230–243.
8.     Moberg, S., and Hanssen, S. “Inverse Dynamics of Robot Manipulators Using Extended Flexible Joint Models.” In Conference on Multibody Dynamics, Warsaw, Poland. Retrieved from
9.     Cruze, D., G, H., Jebadurai, S. V. S., L, S., D, T., and Christy, S. S. J. E. “A Review on the Magnetorheological Fluid, Damper and Its Applications for Seismic Mitigation.” Civil Engineering Journal, Vol. 4, No. 12, (2018), 3074.
10.   Moberg, S. Modeling and parameter estimation of robot manipulators using extended flexible joint models, Doctoral thesis, Linköping University Electronic Press, (2010).
11.   Wu, J., Wang, J., and You, Z. “An overview of dynamic parameter identification of robots.” Robotics and Computer-Integrated Manufacturing. Vol. 26, No.5, (2010), 414-419.
12.   Gu, Y., and Ding, R. “A least squares identification algorithm for a state space model with multi-state delays.” Applied Mathematics Letters, Vol. 26, No. 7, (2013), 748–753.
13.   Brunot, M., Janot, A., Carrillo, F., Garnier, H., Vandanjon, P. O., and Gautier, M. “Physical parameter identification of a one-degree-of-freedom electromechanical system operating in closed loop.” IFAC-PapersOnLine, Vol. 48, No. 28, (2015), 823–828.
14.   Wang, W., Ding, F., and Dai, J. “Maximum likelihood least squares identification for systems with autoregressive moving average noise.” Applied Mathematical Modelling, Vol. 36, No. 5, (2012), 1842–1853.
15.   El-Kafafy, M., Peeters, B., Guillaume, P., and De Troyer, T. “Constrained maximum likelihood modal parameter identification applied to structural dynamics.” Mechanical Systems and Signal Processing, Vol. 72–73, (2016), 567–589.
16.   Hashemi, S. M., and Rahmani, I. “Numerical Comparison of the Performance of Genetic Algorithm and Particle Swarm Optimization in Excavations.” Civil Engineering Journal, Vol. 4, No. 9, (2018), 2186.
17.   Eberhart, R. C., and Shi, Y. “Particle swarm optimization: Developments, applications and resources.” In Proceedings of the IEEE Conference on Evolutionary Computation, ICEC (Vol. 1, pp. 81–86).
18.   Kwok, N. M., Ha, Q. P., Nguyen, T. H., Li, J., and Samali, B. “A novel hysteretic model for magnetorheological fluid dampers and parameter identification using particle swarm optimization.” Sensors and Actuators, A: Physical, Vol. 132, No. 2, (2006), 441–451.
19.   Modares, H., Alfi, A., and Fateh, M. M. “Parameter identification of chaotic dynamic systems through an improved particle swarm optimization.” Expert Systems with Applications, Vol. 37, No. 5, (2010), 3714–3720.
20.   Liu, L., Liu, W., and Cartes, D. A. “Particle swarm optimization-based parameter identification applied to permanent magnet synchronous motors.” Engineering Applications of Artificial Intelligence, Vol. 21, No. 7, (2008), 1092–1100.
21.   Zare, S., and Tavakolpour-Saleh, A. R. “Applying Particle Swarm Optimization to Study the Effect of Dominant Poles Places on Performance of a Free Piston Stirling Engine.” Arabian Journal for Science and Engineering, Vol. 44, No. 6, (2019), 5657–5669.
22.   Tavakolpour, A. R., Mat Darus, I. Z., Tokhi, O., and Mailah, M. “Genetic algorithm-based identification of transfer function parameters for a rectangular flexible plate system.” Engineering Applications of Artificial Intelligence, Vol. 23, No. 8, (2010), 1388–1397.
23.   Zare, S., and Tavakolpour-Saleh, A. R. “Frequency-based design of a free piston Stirling engine using genetic algorithm.” Energy, Vol. 109, (2016), 466–480.
24.   Zare, S., Tavakolpour-Saleh, A. R., and Sangdani, M. H. “Investigating limit cycle in a free piston Stirling engine using describing function technique and genetic algorithm.” Energy Conversion and Management, Vol. 210, (2020), 112706.
25.   Tavakolpour-Saleh, A. R., Zare, S. H., and Badjian, H. “Multi-objective Optimization of Stirling Heat Engine Using Gray Wolf Optimization Algorithm.” International Journal of Engineering, Transactions C: Aspects , Vol. 30, No. 6, (2017), 895–903.
26.   Sitarz, P., and PowaƂka, B. “Modal parameters estimation using ant colony optimisation algorithm.” Mechanical Systems and Signal Processing, Vol. 76–77, (2016), 531–554.
27.   Ding, L., Wu, H., Yao, Y., and Yang, Y. “Dynamic Model Identification for 6-DOF Industrial Robots.” Journal of Robotics, Vol. 2015, (2015), 1–9.
28.   Sangdani, M. H., Tavakolpour-Saleh, A. R., and Lotfavar, A. “Genetic algorithm-based optimal computed torque control of a vision-based tracker robot: Simulation and experiment.” Engineering Applications of Artificial Intelligence, Vol. 67, (2018), 24–38.
29.           Sangdani, M. H., and Tavakolpour-Saleh, A. R. “Robot Using Genetic Algorithm.” International Journal of Engineering, Transactions C: Aspects, Vol. 31, No. 3, (2018), 480–486.