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Article

Task-Space Cooperative Tracking Control for Networked Uncalibrated Multiple Euler–Lagrange Systems

by 1,2, 1 and 3,*
1
School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
2
School of Mechanical Engineering, Tianjin Sino-German University of Applied Sciences, Tianjin 300350, China
3
School of Electrical Engineering and Automation, Tianjin University of Technology, Tianjin 300384, China
*
Author to whom correspondence should be addressed.
Academic Editor: Juan M. Corchado
Electronics 2022, 11(15), 2449; https://doi.org/10.3390/electronics11152449
Received: 23 June 2022 / Revised: 28 July 2022 / Accepted: 2 August 2022 / Published: 6 August 2022
(This article belongs to the Special Issue Real-Time Control of Embedded Systems)
Task-space cooperative tracking control of the networked multiple Euler–Lagrange systems is studied in this paper. On the basis of establishing kinematic and dynamic modeling of a Euler–Lagrange system, an innovative task-space coordination controller is designed to deal with the time-varying communicating delays and uncertainties. First, in order to weaken the influence of the uncertainty of kinematic and dynamic parameters on the control error of the system, the product of the Jacobian matrix and the generalized spatial velocity are linearly parameterized; thus, the unknown parameters are separated from known parameters. The online estimation of uncertain parameters is realized by designing parameters and by proposing new adaptive laws for the dynamic and kinematic parameters. Furthermore, to describe the transmission of time-varying delay errors among networked agents, a new error term is introduced, obtained by adding the observation error and tracking error, and the coefficient of the network mutual coupling term related to the time-varying delay rate is added with reference to the generalized space velocity and task-space velocity of the Lagrange systems. In the end, the influence of the time-varying delay on the cooperative tracking control error of the networked multiple Euler–Lagrange systems is eliminated. With the help of Lyapunov stability theory, the tracking errors and synchronization errors of this system are calculated by introducing the Lyapunov–Krasovskii functional; the asymptotic convergence results rigorously prove the stability of the adaptive cooperative control systems. The simulation results verify the excellent performance of the controller. View Full-Text
Keywords: cooperative tracking control; parameter adaptive law; time-varying delay; networked multiple Euler–Lagrange systems; task-space velocity cooperative tracking control; parameter adaptive law; time-varying delay; networked multiple Euler–Lagrange systems; task-space velocity
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MDPI and ACS Style

Zhao, Z.; Wang, J.; Zhao, H. Task-Space Cooperative Tracking Control for Networked Uncalibrated Multiple Euler–Lagrange Systems. Electronics 2022, 11, 2449. https://doi.org/10.3390/electronics11152449

AMA Style

Zhao Z, Wang J, Zhao H. Task-Space Cooperative Tracking Control for Networked Uncalibrated Multiple Euler–Lagrange Systems. Electronics. 2022; 11(15):2449. https://doi.org/10.3390/electronics11152449

Chicago/Turabian Style

Zhao, Zhuoqun, Jiang Wang, and Hui Zhao. 2022. "Task-Space Cooperative Tracking Control for Networked Uncalibrated Multiple Euler–Lagrange Systems" Electronics 11, no. 15: 2449. https://doi.org/10.3390/electronics11152449

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