Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-26T21:28:52.478Z Has data issue: false hasContentIssue false
  • English
  • Français

An observer-based output tracking controller for electrically driven cooperative multiple manipulators with adaptive Bernstein-type approximator

Published online by Cambridge University Press:  29 November 2021

Alireza Izadbakhsh Open the ORCID record for Alireza Izadbakhsh [Opens in a new window]
Alireza Izadbakhsh*
Affiliation:
Department of Electrical Engineering, Garmsar Branch, Islamic Azad University, Garmsar, Iran
*
*Corresponding author. E-mail: izadbakhsh_alireza@hotmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Thisarticle presents an observer-based output tracking control method for electrically actuated cooperative multiple manipulators using Bernstein-type operators as a universal approximator. This efficient mathematical tool represents lumped uncertainty, including external perturbations and unmodeled dynamics. Then, adaptive laws are derived through the stability analysis to tune the polynomial coefficients. It is confirmed that all the position and force tracking errors are uniformly ultimately bounded using the Lyapunov stability theorem. The theoretical achievements are validated by applying the proposed observer-based controller to a cooperative robotic system comprised of two manipulators transporting a rigid object. The outcomes of the introduced method are also compared to RBFNN, which is a powerful state-of-the-art approximator. The results demonstrate the efficacy of the introduced adaptive control approach in controlling the system even in the presence of disturbances and uncertainties.

Keywords

The Bernstein-type operatorcooperative manipulatorsLyapunov stabilityOutput Tracking Controller
Type
Research Article
Information
Robotica , Volume 40 , Issue 7 , July 2022 , pp. 2295 - 2319
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Gimenez, J., Gandolfo, D. C., Salinas, L. R., Rosales, C., Carelli, R., “Multi-objective control for cooperative payload transport with rotorcraft UAVs,” ISA Trans. 80, 491–502 (2018).CrossRefGoogle ScholarPubMed
Peng, X., Guo, K., Li, X. and Geng, Z., “Cooperative moving-target enclosing control for multiple nonholonomic vehicles using feedback linearization approach,” IEEE Trans. Syst. Man Cybern. Syst. 51(8), 4929–4935 (2019).CrossRefGoogle Scholar
Qian, S., Zi, B. and Ding, H., “Dynamics and trajectory tracking control of cooperative multiple mobile cranes,” Nonlinear Dyn. 83(1), 89–108 (2016).CrossRefGoogle Scholar
AzizZadeh, H., Menhaj, M. B. and Talebi, H. A., “Model-based force/position control of cooperative manipulation systems,” Automatika 60(1), 113–123 (2019).CrossRefGoogle Scholar
Miao, Z., Wang, Y. and Fierro, R., “Cooperative circumnavigation of a moving target with multiple nonholonomic robots using backstepping design,” Syst. Control Lett. 103, 58–65 (2017).10.1016/j.sysconle.2017.03.004CrossRefGoogle Scholar
He, C., Huang, K., Chen, X., Zhang, Y. and Zhao, H., “Transportation control of cooperative double-wheel inverted pendulum robots adopting Udwadia-control approach,” Nonlinear Dyn. 91(4), 2789–2802 (2018).10.1007/s11071-018-4046-zCrossRefGoogle Scholar
Pizetta, I. H. B., Brandão, A. S. and Sarcinelli-Filho, M., “Avoiding obstacles in cooperative load transportation,” ISA Trans. 91, 253–261 (2019).CrossRefGoogle ScholarPubMed
Chen, Y. and Lin, Y., “Combining model-based and model-free methods for stochastic control of distributed energy resources,” Appl. Energy 283, 116204 (2020).CrossRefGoogle Scholar
Pliego-Jimenez, J. and Arteaga-Perez, M., “On the adaptive control of cooperative robots with time-variant holonomic constraints,” Int. J. Adapt Control Signal Process. 31(8), 1217–1231 (2017).CrossRefGoogle Scholar
Marino, A., “Distributed adaptive control of networked cooperative mobile manipulators,” IEEE Trans. Control Syst. Technol. 26(5), 1646–1660 (2017).CrossRefGoogle Scholar
Sun, L., Huo, W. and Jiao, Z., “Robust nonlinear adaptive relative pose control for cooperative spacecraft during rendezvous and proximity operations,” IEEE Trans. Control Syst. Technol. 25(5), 1840–1847 (2016).10.1109/TCST.2016.2618907CrossRefGoogle Scholar
Shojaei, K., “An adaptive output feedback proportional-integral-derivative controller for n-link type (m, s) electrically driven mobile manipulators,” J. Dyn. Syst. Meas. Cont. 141(9), 091001 (2019).CrossRefGoogle Scholar
Arab, F., Shirazi, F. A. and Yazdi, M. R. H., “Planning and distributed control for cooperative transportation of a non-uniform slung-load by multiple quadrotors,” Aerosp. Sci. Technol. 117, 106917 (2021).CrossRefGoogle Scholar
Yang, D., Zong, G., Nguang, S. K. and Zhao, X., “Bumpless transfer H∞ anti-disturbance control of switching Markovian LPV systems under the hybrid switching,” IEEE Trans. Cybern., 1–13 (2020).Google Scholar
Zong, G., Li, Y. and Sun, H., “Composite anti-disturbance resilient control for Markovian jump nonlinear systems with general uncertain transition rate,” Sci. China Inf. Sci. 62(2), 22205 (2019).10.1007/s11432-017-9448-8CrossRefGoogle Scholar
Zong, G., Ren, H. and Karimi, H. R., “Event-triggered communication and annular finite-time H∞ filtering for networked switched systems,” IEEE Trans. Cybern. 51(1), 309–317 (2020).CrossRefGoogle ScholarPubMed
Baigzadehnoe, B., Rahmani, Z., Khosravi, A. and Rezaie, B., “On position/force tracking control problem of cooperative robot manipulators using adaptive fuzzy backstepping approach”, ISA Trans. 70, 432–446 (2017).CrossRefGoogle ScholarPubMed
Hu, B., Guan, Z. H., Lewis, F. L. and Chen, C. P., “Adaptive tracking control of cooperative robot manipulators with Markovian switched couplings,” IEEE Trans. Ind. Electron. 68(3), 2427–2436 (2020).10.1109/TIE.2020.2972451CrossRefGoogle Scholar
Thusoo, R., Jain, S. and Bangia, S., “An evaluation of UAV path following and collision avoidance using NFMGOA control algorithm,” Wirel. Pers. Commun., 1–20 (2021).Google Scholar
Khan, A. T., Li, S. and Cao, X., “Control framework for cooperative robots in smart home using bio-inspired neural network,” Measurement. 167, 108253 (2021).CrossRefGoogle Scholar
Wu, J., Jin, Z., Liu, A. and Yu, L., “Vision-based neural predictive tracking control for multi-manipulator systems with parametric uncertainty,” ISA Trans. 110, 247–257 (2020).CrossRefGoogle ScholarPubMed
Farahmandrad, M., Ganjefar, S., Talebi, H. A. and Bayati, M., “Fuzzy sliding mode controller design for a cooperative robotic system with uncertainty for handling an object,” J. Dyn. Syst. Meas. Control. 141(6), 1–8 (2019).CrossRefGoogle Scholar
Zong, G., Sun, H. and Nguang, S. K., “Decentralized adaptive neuro-output feedback saturated control for INS and its application to AUV,” IEEE Trans. Neural Netw. Learn. Syst. (2021)CrossRefGoogle Scholar
Li, Y., Yang, C., Yan, W., Cui, R. and Annamalai, A., “Admittance-based adaptive cooperative control for multiple manipulators with output constraints,” IEEE Trans. Netw, Neural. Syst, Learn . 30(12), 3621–3632 (2019).Google ScholarPubMed
Yu, Z., Zhang, Y., Jiang, B., Su, C. Y., Fu, J., Jin, Y. and Chai, T., “Fractional order PID-based adaptive fault-tolerant cooperative control of networked unmanned aerial vehicles against actuator faults and wind effects with hardware-in-the-loop experimental validation,” Cont. Eng. Pract. 114, 104861 (2021).CrossRefGoogle Scholar
Ortega, R., Perez, J. A. L., Nicklasson, P. J. and Sira-Ramirez, H. J., Passivity-Based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications (Springer Science & Business Media, 2013).Google Scholar
Shojaei, K., “Neural adaptive PID formation control of car-like mobile robots without velocity measurements,” Adv. Robot. 31(18), 947–964 (2017).CrossRefGoogle Scholar
Zhang, Z., Song, Y. and Zhao, K., “Neuroadaptive cooperative control without velocity measurement for multiple humanoid robots under full-state constraints,” IEEE Trans. Ind. Electron. 66(4), 2956–2964 (2018). https://doi.org/10.1109/TIE.2018.2844791 CrossRefGoogle Scholar
Li, X., Xu, Z., Li, S., Wu, H. and Zhou, X., “Cooperative kinematic control for multiple redundant manipulators under partially known information using recurrent neural network,” IEEE Access 8, 40029–40038 (2020). https://doi.org/10.1109/ACCESS.2020.2974248 CrossRefGoogle Scholar
Izadbakhsh, A., Zamani, I. and Khorashadizadeh, S., “Szász–Mirakyan-based adaptive controller design for chaotic synchronization,” Int. J. Rob. Nonlinear Cont. 31(5), 1689–1703 (2021). https://doi.org/10.1002/rnc.5380 CrossRefGoogle Scholar
Izadbakhsh, A. and Khorashadizadeh, S., “Robust adaptive control of robot manipulators using Bernstein polynomials as universal approximator,” Int. J. Rob. Nonlinear Cont. 30(7), 2719–2735 (2020). https://doi.org/10.1002/rnc.4913 CrossRefGoogle Scholar
Izadbakhsh, A., Khorashadizadeh, S. and Kheirkhahan, P., “Real-time fuzzy fractional-order control of electrically driven flexible-joint robots,” AUT J. Model. Simul. 52(1), 2–2 (2018). https://doi.org/10.22060/MISCJ.2018.13523.5075 CrossRefGoogle Scholar
Izadbakhsh, A., “FAT-based robust adaptive control of electrically driven robots without velocity measurements,” Nonlinear Dyn. 89(1), 289–304 (2017). https://doi.org/10.1007/s11071-017-3454-9 CrossRefGoogle Scholar
Izadbakhsh, A. and Khorashadizadeh, S., “Robust task-space control of robot manipulators using differential equations for uncertainty estimation,” Robotica 35(9), 1923 (2017). https://doi.org/10.1017/S0263574716000588 CrossRefGoogle Scholar
Zarei, R. and Khorashadizadeh, S., “Direct adaptive model-free control of a class of uncertain nonlinear systems using Legendre polynomials,” Trans. Inst. Meas. Cont. 41(11), 3081–3091 (2019).CrossRefGoogle Scholar
Izadbakhsh, A. and Nikdel, N., “Chaos synchronization using differential equations as extended state observer,” Chaos Solitons & Fractals 153(Part 1), 111433 (2021), https://doi.org/10.1016/j.chaos.2021.111433.CrossRefGoogle Scholar
Izadbakhsh, A. and Khorashadizadeh, S., “Robust impedance control of robot manipulators using differential equations as universal approximator,” Int. J. Cont. 91(10), 2170–2186 (2018).CrossRefGoogle Scholar
Kheirkhahan, P. and Izadbakhsh, A., “Observer-based adaptive fractional-order control of flexible-joint robots using the Fourier series expansion: Theory and experiment,” J. Braz. Soc. Mech. Sci. & Eng. 42(10), 1–10 (2020).CrossRefGoogle Scholar
Deylami, A. and Izadbakhsh, A., “FAT-based robust adaptive control of cooperative multiple manipulators without velocity measurement,” Robotica, 1–31 (2021). doi: 10.1017/S0263574721001338.CrossRefGoogle Scholar
Izadbakhsh, A. and Nikdel, N., “Robust adaptive controller–observer scheme for robot manipulators: A Bernstein–Stancu approach,” Robotica, 1–17 (2021). doi: 10.1017/S0263574721001120 CrossRefGoogle Scholar
Izadbakhsh, A., Khorashadizadeh, S. and Ghandali, S., “Robust adaptive impedance control of robot manipulators using Szász–Mirakyan operator as universal approximator,” ISA Trans. 106, 1–11 (2020).CrossRefGoogle ScholarPubMed
Izadbakhsh, A. and Kheirkhahan, P., “Adaptive fractional-order control of electrical flexible-joint robots: Theory and experiment,” Proc. Inst. Mech. Eng. Pt. I: J. Syst. Contr. Eng. 233(9), 1136–1145 (2019).Google Scholar
Izadbakhsh, A., Akbarzadeh Kalat, A. and Khorashadizadeh, S., “Observer-based adaptive control for HIV infection therapy using the Baskakov operator," Biomed. Sig. Process. Cont. 65, 102343 (2021).Google Scholar
Izadbakhsh, A. and Khorashadizadeh, S., “Polynomial-based robust adaptive impedance control of electrically driven robots,” Robotica, 1–21 (2020). doi: 10.1017/S0263574720001009 CrossRefGoogle Scholar
Bleimann, G., Butzer, P. l. and Hahn, L., “A Bernstein-type operator approximating continuous functions on the semi-axis,” Indag. Math. 83(3), 255–262 (1980).CrossRefGoogle Scholar
Jean, J.-H. and Fu, L.-C., “An adaptive control scheme for coordinated multi manipulator systems,” IEEE Trans. Automat, Robot . 9, 226–231 (1993).Google Scholar
Song, G. and Cai, L., “A Smooth Robust Control Approach to Cooperation of Multiple Robot Manipulators,” Proceedings of American Control Conference, Seattle, WA (1995) pp. 1382–1386.Google Scholar
Spong, M. W. and Vidyasagar, M., Robot Dynamics and Control (Wiley, New York, 1989).Google Scholar
Izadbakhsh, A., Akbarzadeh Kalat, A., Fateh, M. M. and Rafiei, S. M. R., “A robust anti-windup control design for electrically driven robots – Theory and experiment,” Int. J. Cont. Automat. Syst. 9(5), 1005–1012 (2011).CrossRefGoogle Scholar
Yao, B. and Tomizuka, M., “Adaptive Coordinated Control of Multiple Manipulators Handling a Constrained Object,” Proceedings of International Conference on Robotics and Automation Atlanta, GA (1993) pp. 624–629.Google Scholar
Huang, A.-C. and Chien, M.-C., Adaptive Control of Robot Manipulators: A Unified Regressor-free Approach (World Scientific, 2010).CrossRefGoogle Scholar
Berghuis, H. and Nijmeijer, H., “Robust control of robots via linear estimated state feedback,” IEEE Trans. Automat. Cont. 39, 2159–2162 (1994).CrossRefGoogle Scholar
Uchiyama, M. and Dauchez, P., “A Symmetric Hybrid Position/Force Control Scheme for the Coordination of Two Robots,” Proceedings of International Conference on Robotics and Automation (1988) pp. 350–356.Google Scholar
Liu, Z., Chen, C., Zhang, Y. and Chen, C. L. P., “Adaptive neural control for dual-arm coordination of humanoid robot with unknown nonlinearities in output mechanism,” IEEE Trans. Cybern. 45(3), 521–532 (2015).Google ScholarPubMed