Dynamic Model of a Robotic Manipulator with One Degree of Freedom with Friction Component
(1) Jose A. G. Luz Junior Mail (São Paulo State University, Brazil)
(2) Jose M. Balthazar Mail (São Paulo State University, Brazil)
(3) Mauricio A. Ribeiro Mail (Federal University of Technology, Brazil)
(4) Frederic C. Janzen Mail (Federal University of Technology-Paraná (UTFPR), Brazil)
(5) * Angelo Marcelo Tusset Mail (Federal University of Technology-Paraná (UTFPR), Brazil)
*corresponding author

Abstract


This research aims to develop a dynamic model of a robotic manipulator with one degree of freedom by incorporating the LuGre friction model. The study combines a mathematical model with experimental data analysis, using the Stribeck curve and Non-linear Least Square method for Parameter Identification. The purpose of the study is to improve the accuracy of the model and enhance the performance of robotic manipulators. The LuGre model is chosen for its ability to capture the nonlinear behavior of friction, which is a significant source of error in robot control systems. The effectiveness of the proposed representation is evaluated by comparing the simulation results of the dynamic model with experimental data obtained from a prototype. The results indicate that the model accurately captures the nonlinear behavior of friction, and the proposed approach can be used to develop more accurate models for control purposes.

Keywords


Robotic Dynamics; Friction; LuGre; Parameter Identification

   

DOI

https://doi.org/10.31763/ijrcs.v3i2.984 		      

Article metrics

10.31763/ijrcs.v3i2.984 Abstract views : 909 | PDF views : 323

   

Cite

How to cite item
   

Full Text

Download

References


[1] J. Kumar, V. Kumar, and K. P. S. Rana, “Fractional-order self-tuned fuzzy PID controller for three-link robotic manipulator system,” Neural Computing and Applications, vol. 32, pp. 7235-7257, 2020, https://doi.org/10.1007/s00521-019-04215-8.

[2] M. Deng, S. Kubota, and Y. Xu, “Nonlinear Intelligent Control of Two Link Robot Arm by Considering Human Voluntary Components,” Sensors, vol. 22, pp. 1-22, 2022, https://doi.org/10.3390/s22041424.

[3] P. Lu, W. Huang, J. Xiao, F. Zhou, and W. Hu, “Adaptive Proportional Integral Robust Control of an Uncertain Robotic Manipulator Based on Deep Deterministic Policy Gradient,” Mathematics, vol. 9, pp. 1-16, 2021, https://doi.org/10.3390/math9172055.

[4] A. M. Tusset, J. J. De Lima, F. C. Janzen, P. L. Paula Filho, J. A. G. Luz Junior, J. M. Balthazar, and A. Kossoski, “Hybrid PID-LQR control applied in positioning control of robotic manipulators subject to excitation from non-ideal sources,” Mechanism and Machine Science, Springer, vol. 116, pp. 393-403, 2022, https://doi.org/10.1007/978-3-030-96603-4_2.

[5] P. Mercorelli, “A Theoretical Dynamical Noninteracting Model for General Manipulation Systems Using Axiomatic Geometric Structures,” Axioms, vol. 11, pp. 309, 2020, https://doi.org/10.3390/axioms11070309.

[6] C. Garriz and R. Domingo, “Development of trajectories through the Kalman algorithm and application to an industrial robot in the automotive industry,” IEEE Access, vol. 7, pp. 23570-23578, 2019, https://doi.org/10.1109/ACCESS.2019.2899370.

[7] U. Zakia, M. Moallem, and C. Menon, “PID-SMC controller for a 2-DOF planar robot. 2019 International Conference on Electrical,” Computer and Communication Engineering (ECCE), pp. 1-5, 2019, https://doi.org/10.1109/ECACE.2019.8679436.

[8] B. Dong, T. An, F. Zhou, K. Liu, and Y. Li, “Decentralized robust zero-sum neuro-optimal control for modular robot manipulators in contact with uncertain environments: Theory and experimental verification,” Nonlinear Dyn., vol. 97, no. 1, pp. 503-524, 2019, https://doi.org/10.1007/s11071-019-04994-8.

[9] Z. Dachang, D. Baolin, Z. Puchen, and C. Shouyan, “Constant force PID control for robotic manipulator based on fuzzy neural network algorithm,” Complexity, vol. 2020, pp. 1-11, 2020, https://doi.org/10.1155/2020/3491845.

[10] A. Carron, E. Arcari, M. Wermelinger, L. Hewing, M. Hutter, and M. N. Zeilinger, “Data-driven model predictive control for trajectory tracking with a robotic arm,” IEEE Robot. Autom. Lett., vol. 4, no. 4, pp. 3758-3765, 2019, https://doi.org/10.3929/ethz-b-000363021.

[11] Y. Mehmood, J. Aslam, N. Ullah, M. S. Chowdhury, K. Techato, and A. N. Alzaed, “Adaptive robust trajectory tracking control of multiple quad-rotor UAVs with parametric uncertainties and disturbances,” Sensors, vol. 21, no. 7, pp. 2401, 2021, https://doi.org/10.3390/s21072401.

[12] N. Ullah, I. Sami, W. Shaoping, H. Mukhtar, X. Wang, M. S. Chowdhury, and K. Techato, “A computationally efficient adaptive robust control scheme for a quad-rotor transporting cable-suspended payloads,'' J. Aerosp. Eng., pp. 1-17, 2021, https://doi.org/10.1177/09544100211013617.

[13] Y. Sun, J. Xu, H. Wu, G. Lin, and S. Mumtaz, “Deep learning based semi-supervised control for vertical security of maglev vehicle with guaranteed bounded airgap,” IEEE Trans. Intell. Transp. Syst., vol. 22, no. 7, pp. 4431-4442, 2021, https://doi.org/10.1109/TITS.2020.3045319.

[14] M. Van, X. P. Do, and M. Mavrovouniotis, “Self-tuning fuzzy PID-nonsingular fast terminal sliding mode control for robust fault tolerant control of robot manipulators,” ISA Transactions, vol. 96, pp. 60-68, 2020, https://doi.org/10.1016/j.isatra.2019.06.017.

[15] S. A. Rad, M. G. Tamizi, A. Mirfakhar, M. T. Masouleh, and A. Kalhor, “Control of a two-DOF parallel robot with unknown parameters using a novel robust adaptive approach,” ISA Transactions, vol.117, pp. 70-84, 2021, https://doi.org/10.1016/j.isatra.2021.02.001.

[16] S. Yang, J. Han, L. Xia, and Y-H Chen, “An optimal fuzzy-theoretic setting of adaptive robust control design for a lower limb exoskeleton robot system,” Mechanical Systems and Signal Processing, vol. 141, pp. 106706, 2020, https://doi.org/10.1016/j.ymssp.2020.106706.

[17] E-H. Guechi, S. Bouzoualegh, Y. Zennir, S. Blažiˇc, and “MPC Control and LQ Optimal Control of A Two-Link Robot Arm: A Comparative Study,” Machines, vol. 6, pp. 409-414, 2018, https://doi.org/10.3390/machines6030037.

[18] M. H. Korayem, M. Irani, and S. R. Nekoo, “Load maximization of flexible joint mechanical manipulator using nonlinear optimal controller,” Acta Astronautica, vol. 69, pp. 458-469, 2011, https://doi.org/10.3390/machines6030037.

[19] M. H. Korayem, M. Irani, and S. R. Nekoo, “Analysis of manipulators using SDRE: a closed loop nonlinear optimal control approach,” Scientia Iranica. Transaction B, Mechanical Engineering, vol. 17, pp. 456-467, 2010, http://scientiairanica.sharif.edu/article_3368.html.

[20] M. H. Korayem and S. R. Nekoo, “Finite-time state-dependent Riccati equation for time-varying nonaffine systems: rigid and flexible joint manipulator control,” ISA Transactions, vol. 54, pp. 125–144, 2015, https://doi.org/10.1016/j.isatra.2014.06.006.

[21] M. H. Korayem and S. R. Nekoo, “State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities,” ISA Transactions, vol. 57, pp. 117–135, 2015, https://doi.org/10.1016/j.isatra.2015.02.008.

[22] J. J. Lima, A. M. Tusset, F. C. Janzen, V. Piccirillo, C. B. Nascimento, J. M. Balthazar, and M. R. L. F. Brasil, “SDRE applied to position and vibration control of a robot manipulator with a flexible link,” Journal of Theoretical and Applied Mechanics, vol. 54, pp. 1067–1078, 2016, https://doi.org/10.1016/j.isatra.2015.02.008.

[23] J. J. Lima, J. M. Balthazar, R. T. Rocha, F. C. Janzen, D. Bernardini, G. Litak, A. M. Tusset, and D. Bassinello, “On Positioning and Vibration Control Application to Robotic Manipulators with a Nonideal Load Carrying,” Shock and Vibration, vol. 2019, pp. 5408519, 2019, https://doi.org/10.1155/2019/5408519.

[24] A. M. Tusset, J. J. De Lima, F. C. Janzen, P. L. Paula Filho, J. A. G. Luz Junior, J. M. Balthazar, and A. Kossoski, “A Hybrid PID-LQR Control Applied in Positioning Control of Robotic Manipulators Subject to Excitation from Non-ideal Sources,” Mechanisms and Machine Science, pp. 393-403, 2022, https://doi.org/10.1007/978-3-030-96603-4_21.

[25] A. M. Tusset, A. E. B. Pereira, J. M. Balthazar, F. C. Janzen, C. Oliveira, M. E. K. Fuziki, and G. G. Lenzi, “Positioning Control of Robotic Manipulators Subject to Excitation from Non-Ideal Sources,” Robotics, vol. 12, pp. 51, 2023, https://doi.org/10.3390/robotics12020051.

[26] O. Saleem, F. Abbas, and J. Iqbal, “Complex Fractional-Order LQIR for Inverted-Pendulum-Type Robotic Mechanisms: Design and Experimental Validation,” Mathematics, vol. 11, pp. 913, 2023, https://doi.org/10.3390/math11040913.

[27] K. Ali, A. Mehmood, I. Muhammad, S. Razzaq, and J. Iqbal, “Control of an Anthropomorphic Manipulator using LuGre Friction Model-Design and Experimental Validation,” Journal of Mechanical Engineering, vol. 67, pp. 401-410, 2021, https://doi.org/10.5545/sv-jme.2021.7258.

[28] K. Ali, S. Ullah, A. Mehmood, H. Mostafa, M. Marey, and J. Iqbal, “Adaptive FIT-SMC Approach for an Anthropomorphic Manipulator with Robust Exact Differentiator and Neural Network-Based Friction Compensation,” IEEE Access, vol. 10, pp. 3378-3389, 2022, https://doi.org/10.1109/ACCESS.2021.3139041.

[29] A. Asghar, M. Iqbal, A. Khaliq, S. Rehman, and J. Iqbal, “Performance comparison of structured H∞ based looptune and LQR for a 4-DOF robotic manipulator,” PLOS ONE, 2022, vol. 17, no. 4, pp. e0266728, 2022, https://doi.org/10.1371/journal.pone.0266728.

[30] A. Rezoug, J. Iqbal, M. Tadjine, “Extended grey wolf optimization–based adaptive fast nonsingular terminal sliding mode control of a robotic manipulator,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 236, pp. 1738-1754, 2022, https://doi.org/10.1177/09596518221099768.

[31] S. Ullah, A. Mehmood, Q. Khan, S. Rehman, and J. Iqbal, “Robust integral sliding mode control design for stability enhancement of under-actuated quadcopter,” Int. J. Control, Autom. Syst., vol. 18, no. 7, pp. 1671-1678, 2020, https://doi.org/10.1007/s12555-019-0302-3.

[32] J. Hu, Y. Wang, L. Liu, and Z. Xie, “High-accuracy robust adaptive motion control of a torque-controlled motor servo system with friction compensation based on neural network,” Proc. Inst. Mech. Eng, C, J. Mech. Eng. Sci., vol. 233, no. 7, pp. 2318-2328, 2019, https://doi.org/10.1177/09544062187830.

[33] B. Denkena, B. Bergmann, and D. Stoppel, “Reconstruction of process forces in a five-axis milling center with a LSTM neural network in comparison to a model-based approach,” J. Manuf. Mater. Process., vol. 4, no. 3, pp. 62, 2020, https://doi.org/10.3390/jmmp4030062.

[34] S.-H. Han, M. S. Tran, and D.-T. Tran, “Adaptive sliding mode control for a robotic manipulator with unknown friction and unknown control direction,” Appl. Sci., vol. 11, no. 9, pp. 3919, 2021, https://doi.org/10.3390/app11093919.

[35] Z. Zhou and B.Wu, “Adaptive sliding mode control of manipulators based on fuzzy random vector function links for friction compensation,” Optik, vol. 227, pp. 166055, 2021, https://doi.org/10.1016/j.ijleo.2020.166055.

[36] L. Zhang, J. Wang, J. Chen, K. Chen, B. Lin, and F. Xu, “Dynamic modeling for a 6-DOF robot manipulator based on a centrosymmetric static friction model and whale genetic optimization algorithm,” Adv. Eng. Softw., vol. 135, pp. 102684, 2019, https://doi.org/10.1016/j.advengsoft.2019.05.006.

[37] A. Khurram, A. Mehmood, I. Muhammad, S. Razzaq, and J. Iqbal, “Control of an Anthropomorphic Manipulator using LuGre Friction Model - Design and Experimental Validation,” Journal of Mechanical Engineering, vol. 67, pp. 401-410, 2021, https://doi.org/10.5545/sv-jme.2021.7258.

[38] K. Ali, S. Ullah, A. Mehmood, H. Mostafa, M. Marey, and J. Iqbal, “Adaptive FIT-SMC Approach for an Anthropomorphic Manipulator with Robust Exact Differentiator and Neural Network-Based Friction Compensation,” IEEE Access, vol. 10, pp. 3378-3389, 2022, https://doi.org/10.1109/ACCESS.2021.3139041.

[39] X. Tu, Y. Zhou, P. Zhao, and X. Cheng, “Modeling the Static Friction in a Robot Joint by Genetically Optimized BP Neural Network,” J. Intell. Robot. Syst, vol. 94, pp. 29–41, 2019, https://doi.org/10.1007/s10846-018-0796-6.

[40] A. C. Bitterncourt, E. Wernholt, S. Sander-Tavallaey, and T. Brogardh, “An Extended Friction Model to Capture Load and Temperature Effects in Robot Joints,” IEEE Int. Conf. Intell. Robots Syst, pp. 6161-6167, 2010, https://doi.org/10.1109/IROS.2010.5650358.

[41] Y. Zhang, “Design and Synthesis of Mechanical systems with Coupled Units,” Mechanical Engineering, Rennes, 2019, https://theses.hal.science/tel-02307221/document.

[42] D. R. Dentler, “Design, Control and Implementation of a Three Link Articulated Robot Arm,” Thesis, Faculty of The University of Akron, 2008, https://etd.ohiolink.edu/apexprod/rws_olink/r/1501/10?clear=10&p10_accession_num=akron1217208877.

[43] C. C.-De-Wit and P. Lischinsky, “Adaptive Friction Compensation with Partially Know Dynamic Friction Model,” Int J Adapt Control Signal Process, vol. 11, pp. 65-80, 1997, https://doi.org/10.1002/(SICI)1099-1115(199702)11:1%3C65::AID-ACS395%3E3.0.CO;2-3.

[44] B. Li, Y. Zhang, L. Yuan, and X. Xi, “Study on the Low Velocity Stability of a Prostate Seed Implantation Robot’s Rotatory Joint,” Electronics, vol. 9, pp. 284, 2020, https://doi.org/10.3390/electronics9020284.

[45] J. L. P. Felix, J. M. Balthazar, R. M. Brasil, and B. R. Pontes Jr, “On lugre friction model to mitigate nonideal vibrations,” J. Comput. Nonlinear Dyn, vol. 4, pp. 034503, 2009, https://doi.org/10.1115/1.3124783.

[46] V. Piccirillo, A. M. Tusset, and J. M. Balthazar, “Chaos control and impact suppression in rotor-bearing system using magnetorheological fluid,” The European Physical Journal. Special Topics, vol. 224, pp. 3023-3040, 2015, https://doi.org/10.1140/epjst/e2015-02604-7.

[47] A. M. Tusset, V. Piccirillo, J. M. Balthazar, and M. R. L. F. Brasil, “On suppression of chaotic motions of a portal frame structure under non-ideal loading using a magneto-rheological damper,” Journal of Theoretical and Applied Mechanics (Warsaw), vol. 53, pp. 653-664, 2015, https://doi.org/10.15632/jtam-pl.53.3.653.

[48] L. Simoni, M. Beschi, A. Visioli, and K. J. Åström, “Inclusion of the dwell time effect in the LuGre friction model,” Mechatronics, vol. 66, pp. 102345, 2020, https://doi.org/10.1016/j.mechatronics.2020.102345.

[49] A. Tusset, F. Janzen, V. Piccirillo, R. T. Rocha, J. M. Balthazar, and G. Litak, “On nonlinear dynamics of a parametrically excited pendulum using both active control and passive rotational (MR) damper,” Journal of Vibration and Control, vol. 24, pp. 1587-1599, 2018, https://doi.org/10.1177/1077546317714882.

[50] D. A. Haessig and B. Friedland, “On the Modeling and Simulation of Friction,” J Dyn Syst Meas Control, vol. 114, pp. 354-362, 1991, https://doi.org/10.1115/1.2896418.

[51] Q. Chen, L. Tao, Y. Nan, and X. Ren, “Adaptative Nonlinear Sliding Mode Control of Mechanical Servo System with LuGre Friction Compensation,” J. Comput. Nonlinear Dyn. Control, vol. 138, no. 138, pp. 021003, 2016, https://doi.org/10.1115/1.4032068.

[52] L. Gao, J. Yan, Z. Han, S. Wang, and N. Wang, “A Friction Model with Velocity, Temperature and Load Torque Effects for Collaborative Industrial Robot Joint,” IEEE Int. Conf. Intell. Robots Syst., pp. 24-27, 2017, https://doi.org/10.1109/IROS.2017.8206141.

[53] M. R. Kermani, R. V. Patel, and M. Moallem, “Friction Identification and Compensation in Robot Manipulators,” IEEE Trans. Instrum. Meas, vol. 6, pp. 56-68, 2007, https://doi.org/10.1109/TIM.2007.907957.

[54] P. Lischinsky, C. Canudas-de-Wit, and G. Morel, “Friction Compensation for an Industrial Hydraulic Robot,” IEEE Control Systems, vol. 19, pp. 25-32, 1999, https://doi.org/10.1109/37.745763.

[55] X. Wang, S. Lin, and S. Wang, “Dynamic Friction Parameter Identification Method with LuGre Model for Direct-Drive Rotary Torque Motor,” Math. Prob. Eng., vol. 2016, pp. 6929457, 2016, https://doi.org/10.1155/2016/6929457.

[56] J. Piasek, R. Patelski, D. Pazderski, and K. Krzyszrof, “Identification of a Dynamic Friction Model and its Application in a Precise Tracking Control,” ACTA Polytech Hung, vol 16, pp. 93-99, 2019, https://doi.org/10.12700/APH.16.10.2019.10.6.

[57] Y. Sun, T. Chen, and C. Shafai, “Parameter Identification of LuGre Friction Model: Experimental Set-up Design and Measurement,” Int Mech. Eng. Congress. Expo., vol 11, pp. 1319, 2015, https://doi.org/10.1115/IMECE2015-51255.

[58] L. Simoni, E. Villagrossi, M. Beschi, A. Marini, N. Pedrocchi, L. M. Tosatti, G. Legnani, and A. Visioli, “On the use of a temperature based friction model for a virtual force sensor in industrial robot manipulators,” 22nd IEEE International Conference on Emerging Technologies and Factory Automation (ETFA), pp. 1-6, 2017, https://doi.org/10.1109/ETFA.2017.8247655.

[59] F. C. Janzen, “Position and Vibration Control of a Flexible Structure in Slewing Motion by Applying Shape Memory Alloys,” Dissertation, Mechanical Engineering, Sao Paulo State University, 2016, https://repositorio.unesp.br/handle/11449/144649.

[60] S. Nithya B., Mythile A., Pavithra S., and Nivetha N., “Parameter Identification of a DC Motor,” International Journal of Science & Technology Research, vol. 9, no. 2, 2020, http://www.ijstr.org/final-print/feb2020/Parameter-Identification-Of-A-Dc-Motor.pdf.

[61] W. S. Chaves, E. H. Kaneko, M. F. Mollon, L. Niro, A. N. Vargas, and M. A. F. Montezuma, “Parameters Identification of a Direct Current Motor Using the Trust Region Algorithm,” International Journal of Advanced Engineering Research and Science, vol. 4, no. 12, 2017, https://doi.org/10.22161/ijaers.4.12.24.


Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 Jose A. G. Luz Junior, Jose M. Balthazar, Mauricio A. Ribeiro, Frederic C. Janzen, Angelo Marcelo Tusset

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

 

About the JournalJournal PoliciesAuthor Information

International Journal of Robotics and Control Systems
e-ISSN: 2775-2658
Website: https://pubs2.ascee.org/index.php/IJRCS
Email: ijrcs@ascee.org
Organized by: Association for Scientific Computing Electronics and Engineering (ASCEE), Peneliti Teknologi Teknik Indonesia, Department of Electrical Engineering, Universitas Ahmad Dahlan and Kuliah Teknik Elektro
Published by: Association for Scientific Computing Electronics and Engineering (ASCEE)
Office: Jalan Janti, Karangjambe 130B, Banguntapan, Bantul, Daerah Istimewa Yogyakarta, Indonesia