Abstract
This paper investigates the multi-target tracking problem of networked heterogeneous collaborative robots with parametric uncertainties and external disturbances in the task space, where each robot can be kinematic redundant or non-redundant. The acceleration of the targets can either belong to \({\mathcal {L}}_2\) or \({\mathcal {L}}_{\infty }\) space. A uniform distributed controller–estimator algorithm is designed to solve the aforementioned problem. The sufficient conditions for both zero-error stability and Lagrange stability of the closed-loop system are derived. Finally, simulation examples are illustrated to demonstrate the effectiveness of the main results.
Similar content being viewed by others
References
Ge, M.F., Guan, Z.H., Hu, B., He, D.X., Liao, R.Q.: Distributed controller–estimator for target tracking of networked robotic systems under sampled interaction. Automatica 69, 410–417 (2016)
Yao, X.Y., Ding, H.F., Ge, M.F.: Task-space tracking control of multi-robot systems with disturbances and uncertainties rejection capability. Nonlinear Dyn. 92(4), 1649–1664 (2018)
Dong, X., Hu, G.: Time-varying formation tracking for linear multiagent systems with multiple leaders. IEEE Trans. Autom. Control 62(7), 3658–3664 (2017)
Hua, Y., Dong, X., Han, L., Li, Q., Ren, Z.: Finite-time time-varying formation tracking for high-order multiagent systems with mismatched disturbances. IEEE Trans. Syst. Man Cybern. Syst. 99, 1–9 (2018)
Wang, Y.W., Liu, X.K., Xiao, J.W., Shen, Y.: Output formation-containment of interacted heterogeneous linear systems by distributed hybrid active control. Automatica 93, 26–32 (2018)
Meng, Z., Yang, T., Shi, G., Dimarogonas, D.V., Hong, Y., Johansson, K.H.: Targeted agreement of multiple Lagrangian systems. Automatica 84, 109–116 (2017)
Zhao, X.W., Guan, Z.H., Hu, B., Liao, R.Q., Zhang, X.H., He, D.X.: Attitude-synchronization flocking of multiple 3-dimensional nonholonomic agents without position measurement. Int. J. Robust Nonlinear Control 28(6), 2369–2382 (2018)
Zhao, X.W., Guan, Z.H., Li, J., Zhang, X.H., Chen, C.Y.: Flocking of multi-agent nonholonomic systems with unknown leader dynamics and relative measurements. Int. J. Robust Nonlinear Control 27(17), 3685–3702 (2017)
Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)
Liu, Z.W., Guan, Z.H., Shen, X., Feng, G.: Consensus of multi-agent networks with aperiodic sampled communication via impulsive algorithms using position-only measurements. IEEE Trans. Autom. Control 57(10), 2639–2643 (2012)
Li, Z., Yuan, W., Chen, Y., Ke, F., Chu, X., Chen, C.P.: Neural-dynamic optimization-based model predictive control for tracking and formation of nonholonomic multirobot systems. IEEE Trans. Neural Netw. Learn. Syst. (2018). https://doi.org/10.1109/TNNLS.2018.2818127
Wang, L., Shen, Y., Zhang, G.: Synchronization of a class of switched neural networks with time-varying delays via nonlinear feedback control. IEEE Trans. Cybern. 46(10), 2300–2310 (2016)
Wang, L., Zeng, Z., Hu, J., Wang, X.: Controller design for global fixed-time synchronization of delayed neural networks with discontinuous activations. Neural Netw. 87, 122–131 (2017)
Liu, Y.C., Chopra, N.: Controlled synchronization of heterogeneous robotic manipulators in the task space. IEEE Trans. Robot. 28(1), 268–275 (2012)
Liu, Y.C.: Distributed synchronization for heterogeneous robots with uncertain kinematics and dynamics under switching topologies. J. Frankl. Inst. 352(9), 3808–3826 (2015)
Wen, G., Yu, W., Xia, Y., Yu, X., Hu, J.: Distributed tracking of nonlinear multiagent systems under directed switching topology: an observer-based protocol. IEEE Trans. Syst. Man Cybern. Syst. 47(5), 869–881 (2017)
Wen, G., Yu, W., Li, Z., Yu, X., Cao, J.: Neuro-adaptive consensus tracking of multiagent systems with a high-dimensional leader. IEEE Trans. Cybern. 47(7), 1730–1742 (2017)
Mei, J., Ren, W., Ma, G.: Distributed coordinated tracking with a dynamic leader for multiple Euler–Lagrange systems. IEEE Trans. Autom. Control 56(6), 1415–1421 (2011)
Han, G.S., Guan, Z.H., Li, J., Liao, R.Q., Cheng, X.M.: Multi-consensus of multi-agent networks via a rectangular impulsive approach. Syst. Control Lett. 76, 28–34 (2015)
Li, J., Guan, Z.H., Chen, G.: Multi-consensus of nonlinearly networked multi-agent systems. Asian J. Control 17(1), 157–164 (2015)
Han, G.S., Guan, Z.H., Li, J., He, D.X., Zheng, D.F.: Multi-tracking of second-order multi-agent systems using impulsive control. Nonlinear Dyn. 84(3), 1771–1781 (2016)
Huang, D., Jiang, H.J., Yu, Z.Y., Hu, C., Fan, X.L.: Cluster-delay consensus in MASs with layered intermittent communication: a multi-tracking approach. Nonlinear Dyn. (2018). https://doi.org/10.1007/s11071-018-4604-4
Han, T., Guan, Z.H., Chi, M., Hu, B., Li, T., Zhang, X.H.: Multi-formation control of nonlinear leader-following multi-agent systems. ISA Trans. 69, 140–147 (2017)
Ge, M.F., Guan, Z.H., Yang, C., Chen, C.Y., Zheng, D.F., Chi, M.: Task-space coordinated tracking of multiple heterogeneous manipulators via controller-estimator approaches. J. Frankl. Inst. 353(15), 3722–3738 (2016)
Meng, Z., Dimarogonas, D.V., Johansson, K.H.: Leader–follower coordinated tracking of multiple heterogeneous Lagrange systems using continuous control. IEEE Trans. Robot. 30(3), 739–745 (2014)
Wang, H.: Task-space synchronization of networked robotic systems with uncertain kinematics and dynamics. IEEE Trans. Autom. Control 58(12), 3169–3174 (2013)
Liang, X., Wang, H., Liu, Y. H., Chen, W., Xie, L.: Task-space cooperative tracking control of multi-robot systems with unknown parameters and time delays. In: IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) pp. 57–62. IEEE (2018)
Zergeroglu, E., Dawson, D. M., Walker, I., Behal, A.: Nonlinear tracking control of kinematically redundant robot manipulators. In: Proceedings of the American Control Conference, vol. 4, pp. 2513–2517. IEEE (2000)
Xu, W., Zhang, J., Liang, B., Li, B.: Singularity analysis and avoidance for robot manipulators with nonspherical wrists. IEEE Trans. Ind. Electron. 63(1), 277–290 (2016)
Jin, L., Li, S., Luo, X., Li, Y., Qin, B.: Neural dynamics for cooperative control of redundant robot manipulators. IEEE Trans. Ind. Inform. 14(9), 3812–3821 (2018)
Zhou, J., Wu, X., Liu, Z.: Distributed coordinated adaptive tracking in networked redundant robotic systems with a dynamic leader. Sci. China Technol. Sci. 57(5), 905–913 (2014)
Lozano, R., Brogliato, B., Egeland, O., Maschke, B.: Dissipative Systems Analysis and Control: Theory and Applications. Springer, Berlin (2013)
Kelly, R., Davila, V.S., Perez, J.A.L.: Control of Robot Manipulators in Joint Space. Springer, Berlin (2006)
Parks, P.C., Hahn, V.: Stability Theory. Prentice Hall, New York (1993)
Khalil, Hassan K.: Nonlinear Systems, pp. 1–5. Prentice-Hall, Upper Saddle River (1996)
Ioannou, P.A., Sun, J.: Robust Adaptive Control, vol. 1. PTR Prentice-Hall, Upper Saddle River (1996)
Hsu, P., Mauser, J., Sastry, S.: Dynamic control of redundant manipulators. J. Robot. Syst. 6(2), 133–148 (1989)
Nakamura, Y., Hanafusa, H., Yoshikawa, T.: Task-priority based redundancy control of robot manipulators. Int. J. Robot. Res. 6(2), 3–15 (1987)
Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grants 61703374, 61703377 and 61673303, the Teaching Laboratory Open Fund Project, China University of Geosciences (Wuhan), and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) under Grants CUG170656 and CUG170632.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liang, CD., Wang, L., Yao, XY. et al. Multi-target tracking of networked heterogeneous collaborative robots in task space. Nonlinear Dyn 97, 1159–1173 (2019). https://doi.org/10.1007/s11071-019-05038-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-019-05038-x