Abstract
The distributed coordinated tracking control problem for multiple robotic manipulators under intermittent communications is researched, respectively, with a stationary leader and a dynamic leader in this note. First, three auxiliary variables are introduced and a new distributed coordinated tracking controller is established with a stationary leader, and then, a multi-step design algorithm is proposed to calculate the controller gain matrix and coupling gain. The stability of the controller is further proved, and the range of communication rate is obtained by using Lyapunov stability and switching system theories. Second, with considering a dynamic leader whose joint velocity is unavailable, the distributed velocity estimator is constructed to estimate the unknown joint velocity, and then, a distributed coordinated tracking control strategy-based velocity estimator is designed, whose unknown parameters are resolved by the new multi-step design algorithm accordingly. It is proved that the stability of the controller can be achieved, and the threshold value of the communication rate obtained by utilizing Lyapunov stability theory and LMI technology. Finally, two simulation examples and quantitative comparison are provided to demonstrate the validity and correctness of the obtained methods, and the experimented results show that the distributed tracking controllers of this work can effectively solve the distributed coordinated tracking problem for multiple two-link manipulator systems under intermittent communications.
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References
Savkin, A.: Coordinated collective motion of groups of autonomous mobile robots: analysis of vicsek’s model. IEEE Trans. Autom. Control 49(6), 981–982 (2004)
Fax, J., Murray, R.M.: Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control 49(9), 1465–1476 (2004)
Chang, I., Park, S.Y., ChoiK, H.: Decentralized coordinated attitude control for satellite formation flying via the state-dependent Riccati equation technique. Int. J. Non-Linear Mech. 44(8), 891–904 (2009)
Yu, J., Wang, C., Xie, G.: Coordination of multiple robotic fish with applications to underwater robot competition. IEEE Trans. Ind. Electron. 62(2), 1280–1288 (2016)
Wang, J., Han, L., Dong, X., Li, Q.: Distributed sliding mode control for time-varying formation tracking of multi-UAV system with a dynamic leader. Aerosp. Sci. Technol. 111(1), 106549 (2021)
Zhu, Y., Zheng, W.: Observer-based control for cyber-physical systems with DoS attacks via a cyclic switching strategy. IEEE Trans. Autom. Control 65(8), 3714–3721 (2020)
Jiang, Y., Zhang, Y., Wang, S.: Distributed adaptive consensus control for networked robotic manipulators with time-varying delays under directed switching topologies. Peer Peer Netw. Appl. 12(6), 1705–1715 (2019)
Zhang, H., Lewis, F.L., Das, A.: Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback. IEEE Trans. Autom. Control 56(8), 1948–1952 (2011)
Liang, H., Zhang, H., Wang, Z.: Distributed-observer-based cooperative control for synchronization of linear discrete-time multi-agent systems. ISA Trans. 59, 72–78 (2015)
Wen, W., Wang, H., Yu, X., Yu, W.: Bipartite tracking consensus of linear multi-agent systems with a dynamic leader. IEEE Trans. Circuits Syst. II Exp. Briefs 65(9), 1204–1208 (2018)
Zhang, W., Karimi, H.R., Tang, Y.: Distributed tracking for discrete-time multiagent networks via an ultrafast control protocol. IEEE Trans. Syst. Man, Cybern. Syst 99, 1–11 (2020)
Zhang, W., Tang, Y., Kocarev, L., Wu, Z.: Cluster tracking performance analysis of linear heterogeneous multi-agent networks: a complex frequency domain approach. IEEE Trans. Circuits Syst I Reg. Papers 67(1), 259–270 (2020)
Jiang, Y., Wang, H., Wang, S.: Distributed \(H_{\infty }\) consensus control for nonlinear multi-agent systems under switching topologies via relative output feedback. Neural Comput. Appl. 31(1), 1–9 (2019)
Jia, Z., Wang, L., Yu, J., Ai, X.: Distributed adaptive neural networks leader-following formation control for quadrotors with directed switching topologies. ISA Trans. 93, 93–107 (2019)
Ai, X.: Distributed Nash equilibrium seeking for networked games of multiple high-order systems with disturbance rejection and communication delay. Nonlinear Dyn. 101(2), 961–976 (2020)
Zhu, Y., Zheng, W.: Multiple Lyapunov functions analysis approach for discrete-time switched piecewise-affine systems under dwell-time constraints. IEEE Trans. Autom. Control 65(5), 2177–2184 (2020)
Liang, H., Guo, X., Pan, Y., Huang, T.: Event-triggered fuzzy bipartite tracking control for network systems based on distributed reduced-order observers. IEEE Trans. Fuzzy Syst. 99(9), 1 (2020)
Cai, M., Xiang, Z.: Adaptive practical fast finite-time consensus protocols for multiple uncertain nonlinear mechanical systems. Int. J. Syst. Sci. 51(11), 1929–1944 (2020)
Altan, A., Hacioglu, R.: Model predictive control of three-axis gimbal system mounted on UAV for real-time target tracking under external disturbances. Mech. Syst. Signal Process. 138, 1–23 (2020)
Altan, A., Aslan, Ö., Hacioglu, R.: Real-time control based on NARX neural network of hexarotor UAV with load transporting system for path tracking. In: International Conference on Control Engineering and Information Technology. Istanbul, Turkey (2020)
Altan, A., Hacioglu, R.: Hammerstein model performance of three axes gimbal system on Unmanned Aerial Vehicle (UAV) for route tracking. In: Signal processing and communications applications conference. Cesme, Izmir (2018)
Altan, A., Hacioglu, R.: The controller of the camera used in target tracking for unmanned vehicle with model predictive controller. In: Signal processing and communications applications conference, pp. 1686-1689. Trabzon, Turkey (2014)
Altan, A.: Performance of metaheuristic optimization algorithms based on swarm intelligence in attitude and altitude control of unmanned aerial vehicle for path following. In: International symposium on multidisciplinary studies and innovative technologies. Zonguldak, Turkey (2020)
Altan, A., Parlak, A.: Adaptive control of a 3D printer using whale optimization algorithm for bio-printing of artificial tissues and organs. In: Innovations in intelligent systems and applications. Istanbul, Turkey, Conference (2020)
Endo, T., Matsuno, F., Jia, Y.: Boundary cooperative control by flexible Timoshenko arms. Automatica 81, 377–389 (2017)
Meng, Z., Ren, W., You, Z.: Distributed finite-time attitude containment control for multiple rigid bodies. Automatica 46(12), 2092–2099 (2010)
Basic, D., Malrait, F., Rouchon, P.: Euler-Lagrange models with complex currents of three-phase electrical machines and observability issues. IEEE Trans. Autom. Control 55(1), 212–217 (2010)
Ai, X., Yu, J.: Fixed-time trajectory tracking for a quadrotor with external disturbances: a flatness-based sliding mode control approach. Aerosp. Sci. Technol. 89, 58–76 (2019)
Shah, U., Karkoub, M., Kerimoglu, D., Wang, H.: Dynamic analysis of the UVMS: effect of disturbances, coupling, and joint-flexibility on end-effector positioning. Robotica (2021). https://doi.org/10.1017/S0263574721000072
Ren, W.: Distributed leaderless consensus algorithms for networked Euler-Lagrange systems. Int. J. Control 82(11), 2137–2149 (2009)
Mei, J., Mei, W., Ma, G.: Distributed coordinated tracking with a dynamic leader for multiple Euler-Lagrange systems. IEEE Trans. Autom. Control 5(6), 1415–1421 (2011)
Nuno, E., Ortega, R., Basanez, L., Hill, D.: Synchronization of networks of nonidentical Euler-Lagrange systems with uncertain parameters and communication delays. IEEE Trans. Autom. Control 56(4), 935–941 (2011)
Sun, Y., Dong, D., Qin, H., Wang, W.: Distributed tracking control for multiple Euler-Lagrange systems with communication delays and input saturation. ISA Trans. 96, 245–254 (2020)
Hu, H., Wen, G., Yu, W., Cao, J., Huang, T.: Finite-time coordination behavior of multiple Euler-Lagrange systems in cooperation-competition networks. IEEE Trans. Cybern. 49(8), 2967–2979 (2019)
Gao, Y., Liu, B., Yu, J., Ma, J., Jiang, T.: Consensus of first-order multi-agent systems with intermittent interaction. Neurocomputing 129, 273–278 (2014)
Wen, G., Yu, X., Liu, Z., Yu, W.: Adaptive consensus-based robust strategy for economic dispatch of smart grids subject to communication uncertainties. IEEE Trans. Ind. Inform. 14(6), 2484–2496 (2018)
Wen, G., Duan, Z., Ren, W.: Distributed consensus of multi-agent systems with general linear node dynamics and intermittent communications. Int. J. Robust Nonlinear Control 24(16), 2438–2457 (2015)
Song, Q., Liu, F., Wen, G., Cao, J., Yang, X.: Distributed position-based consensus of second-order multiagent systems with continuous/intermittent communication. IEEE Trans. Cybern. 47(8), 1860–1871 (2017)
Liu, Y., Xie, D., Shi, L.: Consensus of general linear multi-agent systems with intermittent communications. Int. J. Syst. Sci. 51(12), 2293–2305 (2020)
Wang, Y., Liu, X., Xiao, J., Lin, X.: Output formation-containment of coupled heterogeneous linear systems under intermittent communication. J. Frankl. Inst. 354(1), 392–414 (2017)
Ortega, R.: Passivity-based Control Of Euler-lagrange Systems: Mechanical, Electrical And Electromechanical Applications. Springer, Berlin (1998)
Spong, M.W., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control. Wiley, New York (2006)
Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (2012)
Funding
This study was funded by the National Natural Science Foundation of China (61503045 and 61806079), the Key Science and Technology Projects of Jilin Province (20200401075GX), the Research Project on the Science and Technology of Education Department of Jilin Province (JJKH20210743KJ) and the China Postdoctoral Science Foundation (2018M641939).
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Zhang, Y., Jiang, Y., Zhang, W. et al. Distributed coordinated tracking control for multi-manipulator systems under intermittent communications. Nonlinear Dyn 107, 3573–3591 (2022). https://doi.org/10.1007/s11071-021-07159-8
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DOI: https://doi.org/10.1007/s11071-021-07159-8