Abstract
This paper proposes a novel disturbance estimator-based nonsingular fast fuzzy terminal sliding-mode formation control method. The leader–follower formation control method is combined with the path planning strategy based on the artificial potential field to be collision-free and move in consensus for each AUV. An improved sliding-mode surface is incorporated into the controller, providing the system’s state with a faster convergence rate away from the stable equilibrium. The chattering problem in the controller is eliminated by designing fuzzy control rules which are derived from the Lyapunov energy function. A disturbance estimator is proposed to compensate for unknown dynamic and disturbances, which enhances the robustness and stability of the system. Simulation and comparison results are provided to show the effectiveness of the proposed method.











Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data availability
The authors confirm that the data supporting the findings of this study are available within the article.
References
Wang, N., Ahn, C.K.: Coordinated trajectory-tracking control of a marine aerial-surface heterogeneous system. IEEE-ASME Trans. Mechatron. 26(6), 3198–3210 (2021). https://doi.org/10.1109/TMECH.2021.3055450
Wang, N., Gao, Y., Zhang, X.F.: Data-driven performance-prescribed reinforcement learning control of an unmanned surface vehicle. IEEE Trans. Neural Netw. Learn. Syst. 32(12), 5456–5467 (2021). https://doi.org/10.1109/TNNLS.2021.3056444
Wang, N., Zhang, Y.H., Ahn, C.K., Xu, Q.Y.: Autonomous pilot of unmanned surface vehicles: bridging path planning and tracking. IEEE Trans. Veh. Technol. 71(3), 2358–2374 (2022). https://doi.org/10.1109/TVT.2021.3136670
Cui, R.X., Shuzhi, S.G., Bernard, V.E.H., Yoo, S.C.: Leader–follower formation control of underactuated autonomous underwater vehicles. Ocean Eng. 37(17), 1491–1502 (2010). https://doi.org/10.1016/j.oceaneng.2010.07.006
Balch, T., Arkin, R.C.: Behavior-based formation control for multirobot teams. IEEE Trans. Robot. Autom. 14(6), 926–939 (1998). https://doi.org/10.1109/70.736776
Pashna, M., Yusof, R., Ismail, Z.H., Namerikawa, T., Yazdani, S.: Autonomous multi-robot tracking system for oil spills on sea surface based on hybrid fuzzy distribution and potential field approach. Ocean Eng. 207, 107238 (2020). https://doi.org/10.1016/j.oceaneng.2020.107238
Do, K.D.: Formation control of multiple elliptical agents with limited sensing ranges. Automatica 48(7), 1330–1338 (2012). https://doi.org/10.1016/j.automatica.2012.04.005
Wang, N., Su, S.-F.: Finite-time unknown observer based interactive trajectory tracking control of asymmetric underactuated surface vehicles. IEEE Trans. Control Syst. Technol. 29(2), 794–803 (2021)
Xu, J.: Fault tolerant finite-time leader–follower formation control for autonomous surface vessels with LOS range and angle constraints. Automatica 68, 228–236 (2016). https://doi.org/10.1016/j.automatica.2016.01.064
Yang, F., Fei, L., Liu, S.R., Zhong, C.L.: Hybrid formation control of multiple mobile robots with obstacle avoidance. In: 2010 8th World Congress on Intelligent Control and Automation. pp. 1039–1044 (2010). https://doi.org/10.1109/WCICA.2010.5554820.
Barnes, L.E.: A potential field based formation control methodology for robot swarms. ProQuest Dissertations and Theses University of South Florida, USA (2008).
Yang, L., Yang, J.: Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems. Int. J. Robust Nonlinear Control. 21(16), 1865–1879 (2011). https://doi.org/10.1002/rnc.1666
Chen, M., Shi, P., Lim, C.C.: Robust constrained control for MIMO nonlinear systems based on disturbance observer. IEEE Trans. Automat. Control. 60(12), 3281–3286 (2015). https://doi.org/10.1109/TAC.2015.2450891
Qiao, L., Bowen, Y., Wu, D., Zhang, W.D.: Design of three exponentially convergent robust controllers for the trajectory tracking of autonomous underwater vehicles. Ocean Eng. (2017). https://doi.org/10.1016/j.oceaneng.2017.02.006
Van, M.: An enhanced robust fault tolerant control based on an adaptive fuzzy PID-nonsingular fast terminal sliding mode control for uncertain nonlinear systems. IEEE-ASME Trans. Mechatron. 23(3), 1362–1371 (2018). https://doi.org/10.1109/TMECH.2018.2812244
Cui, R.X., Zhang, X., Cui, D.: Adaptive sliding-mode attitude control for autonomous underwater vehicles with input nonlinearities. Ocean Eng. 123, 45–54 (2016). https://doi.org/10.1016/j.oceaneng.2016.06.041
Wang, N., Gao, Y., Zhao, H., Ahn, C.K.: Reinforcement learning-based optimal tracking control of an unknown unmanned surface vehicle. IEEE Trans. Neural Netw. Learn. Syst. 32(7), 3034–3045 (2021)
Peng, Z.H., Wang, J.: Output-feedback path-following control of autonomous underwater vehicles based on an extended state observer and projection neural networks. IEEE Trans. Syst. Man Cybern. Syst. 48(4), 535–544 (2018). https://doi.org/10.1109/TSMC.2017.2697447
Van, M.: An enhanced tracking control of marine surface vessels based on adaptive integral sliding mode control and disturbance observer. ISA Trans. 90, 30–40 (2019). https://doi.org/10.1016/j.isatra.2018.12.047
Lee, J.Y., Chang, P.H., Jin, M.L.: Adaptive integral sliding mode control with time-delay estimation for robot manipulators. IEEE Trans. Ind. Electron. 64(8), 6796–6804 (2017). https://doi.org/10.1109/TIE.2017.2698416
Cui, R.X., Chen, L.P., Yang, C.G., Chen, M.: Extended state observer-based integral sliding mode control for an underwater robot with unknown disturbances and uncertain nonlinearities. IEEE Trans. Ind. Electron. 64(8), 6785–6795 (2017). https://doi.org/10.1109/TIE.2017.2694410
Kim, J.K., Joe, H., Yu, S.C., Lee, J.S., Kim, M.: Time-delay controller design for position control of autonomous underwater vehicle under disturbances. IEEE Trans. Ind. Electron. 63(2), 1052–1061 (2016). https://doi.org/10.1109/TIE.2015.2477270
Patre, B.M., Londhe, P.S., Nagarale, R.M.: Fuzzy sliding mode control for spatial control of large nuclear reactor. IEEE Trans. Nucl. Sci. 62(5), 2255–2265 (2015). https://doi.org/10.1109/TNS.2015.2464677
Kaynak, O., Erbatur, K., Ertugnrl, M.: The fusion of computationally intelligent methodologies and sliding-mode control-a survey. IEEE Trans. Ind. Electron. 48(1), 4–17 (2001). https://doi.org/10.1109/41.904539
Shahraz, A., Boozarjomehry, R.B.: A fuzzy sliding mode control approach for nonlinear chemical processes. Control Eng. Practice. 17(5), 541–550 (2009). https://doi.org/10.1016/j.conengprac.2008.10.011
Bessa, W.M., Dutra, M.S., Kreuzer, E.: Depth control of remotely operated underwater vehicles using an adaptive fuzzy sliding mode controller. Robot. Auton. Syst. 56(8), 670–677 (2008). https://doi.org/10.1016/j.robot.2007.11.004
Bessa, W.M., Dutra, M.S., Kreuzer, E.: An adaptive fuzzy sliding mode controller for remotely operated underwater vehicles. Robot. Auton. Syst. 58(1), 16–26 (2010). https://doi.org/10.1016/j.robot.2009.09.001
Song, X., Zou, Z.J.: A fuzzy sliding mode controller with adaptive disturbance approximation for underwater robot. In: 2010 2nd International Asia Conference on Informatics in Control, Automation and Robotics (CAR 2010). pp. 50–53 (2010). https://doi.org/10.1109/CAR.2010.5456607.
Lakhekar, G.V., Waghmare, L.M., Londhe, P.S.: Enhanced dynamic fuzzy sliding mode controller for autonomous underwater vehicles. In: 2015 IEEE Underwater Technology (UT). (2015). https://doi.org/10.1109/UT.2015.7108283.
Wang, N., Sun, Z., Yin, J.C., Zou, Z.J., Su, S.F.: Fuzzy unknown observer-based robust adaptive path following control of underactuated surface vehicles subject to multiple unknowns. Ocean Eng. 176, 57–64 (2019). https://doi.org/10.1016/j.oceaneng.2019.02.017
Wang, N., Gao, Y., Sun, Z., Zheng, Z.J.: Nussbaum-based adaptive fuzzy tracking control of unmanned surface vehicles with fully unknown dynamics and complex input nonlinearities. Int. J. Fuzzy Syst. 20(1), 259–268 (2017). https://doi.org/10.1007/s40815-017-0387-x
Zuo, Z.Y.: Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica 54, 305–309 (2015). https://doi.org/10.1016/j.automatica.2015.01.021
Zhang, Y.: Corrections: adaptive terminal angle constraint interception against maneuvering targets with fast fixed-time convergence. Int. J. Robust Nonlinear Control. (2020). https://doi.org/10.1002/rnc.4067
Cao, L., Xiao, B., Golestani, M., Ran, D.C.: Faster fixed-time control of flexible spacecraft attitude stabilization. IEEE Trans. Ind. Inform. 16(2), 1281–1290 (2020). https://doi.org/10.1109/TII.2019.2949588
Wang, N., Zhu, Z.B., Qin, H.D., Deng, Z.C., Sun, Y.C.: Finite-time extended state observer-based exact tracking control of an unmanned surface vehicle. Int. J. Robust Nonlinear Control. 31(5), 1704–1719 (2021). https://doi.org/10.1002/rnc.5369
Dian, S.Y., Han, J.X., Guo, R., Li, S.C., Zhao, T., Hu, Y., Wu, Q.: Double closed-loop general type-2 fuzzy sliding model control for trajectory tracking of wheeled mobile robots. Int. J. Fuzzy Syst. 21, 2032–2042 (2019). https://doi.org/10.1007/s40815-019-00685-z
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant Nos. 52025111, 51939003).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Qin, H., Si, J., Wang, N. et al. Disturbance Estimator-Based Nonsingular Fast Fuzzy Terminal Sliding-Mode Formation Control of Autonomous Underwater Vehicles. Int. J. Fuzzy Syst. 25, 395–406 (2023). https://doi.org/10.1007/s40815-022-01444-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40815-022-01444-3