Volume 14, Issue 1 (Journal of Control, V.14, N.1 Spring 2020)                   JoC 2020, 14(1): 93-113 | Back to browse issues page

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Abooee A, eslami M, Haeri M. Design of Robust Finite-Time Nonlinear Controllers for a 6-DOF Autonomous Underwater Vehicle for Path Tracking Objective. JoC 2020; 14 (1) :93-113
URL: http://joc.kntu.ac.ir/article-1-509-en.html
1- Yazd university
2- Department of Electrical Engineering of Sharif University of Technology
Abstract:   (7206 Views)
In this paper, kinematic and dynamic equations of a 6-DOF (Degree Of Freedom) autonomous underwater vehicle (6-DOF AUV) are introduced and described completely. By developing the nonsingular terminal sliding mode control method, three separate groups of control inputs are proposed for the autonomous underwater vehicle subjected to uncertainties including parametric uncertainties, unmodeled dynamics, and unknown disturbances from ocean. All classes of suggested inputs are able to steer the mentioned underwater vehicle to the desired path within finite times. For all of them, innovative nonlinear sliding surfaces are defined possessing several optional parameters. The global finite-time stability is proven for the closed-loop system of the aforementioned underwater vehicle injected by each class of proposed inputs. More, three applicable inequalities are derived to determine the convergence finite times related to suggested inputs. Obtained inequalities reveal that the mentioned finite times are dependent on initial conditions and optional parameters of control inputs. Finally, three suggested inputs are separately simulated on the Naval Postgraduate School Autonomous Underwater Vehicle II (NPS AUV II). Simulation results illustrate that all proposed inputs can fulfill the trajectory tracking objective for the NPS AUV II properly.
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Type of Article: Research paper | Subject: Special
Received: 2017/08/2 | Accepted: 2018/09/30 | Published: 2020/06/11

1. Y. Nasuno, E. Shimizu, M. Ito, I. Yamamoto, S. Tsukioka, and H. Yoshida, "A controller design for autonomous underwater vehicle ' MR-X1 ' using linear matrix inequalities," International Journal of Control, vol. 80, no. 7, pp. 1125-1135, 2008. [DOI:10.1080/00207170701282214]
2. [2] Y. Shen, K. Shao, W. Ren, and Y. Liu, "Diving control of autonomous underwater vehicle based on improved active disturbance rejection control approach," Neurocomputing, vol. 173, no. 3, pp. 1377-1385, 2016. [DOI:10.1016/j.neucom.2015.09.010]
3. [3] D. Maalouf, I. Tamanaja, E. Campos, A. Chemori, V. Creuze, J. Torres, and R. Lozano, "From PD to nonlinear adaptive depth-control of a tethered autonomous underwater vehicle," IFAC Proceedings Volumes, vol. 46, no. 2, pp. 743-748, 2013. [DOI:10.3182/20130204-3-FR-2033.00085]
4. [4] F. Repoulias and E. Papadopoulos, "Planar trajectory planning and tracking control design for underactuated AUVs," Ocean Engineering, vol. 34, no. 11-12, pp. 1650-1667, 2007. [DOI:10.1016/j.oceaneng.2006.11.007]
5. [5] Y. Li, C. Wei, Q. Wu, P. Chen, Y. Jiang, and Y. Li, "Study of 3 dimension trajectory tracking of underactuated autonomous underwater vehicle," Ocean Engineering, vol. 105, no. 1, pp. 270-274, 2015. [DOI:10.1016/j.oceaneng.2015.06.034]
6. [6] S. Liu, D. Wang, and E. Poh, "Nonlinear output feedback tracking control for AUVs in shallow wave disturbance condition," International Journal of Control, vol. 81, no. 11, pp. 1806-1823, 2008. [DOI:10.1080/00207170801898885]
7. [7] B. Subudhi, K. Mukherjee, and S. Ghosh, "A static output feedback control design for path following of autonomous underwater vehicle in vertical plane," Ocean Engineering, vol. 63, no. 1, pp. 72-76, 2013. [DOI:10.1016/j.oceaneng.2013.01.029]
8. [8] I. Yang, S. Byun, B. Seo, D. Lee, and D. S. Han, "Robust dynamic inversion based on sliding mode control for autonomous underwater vehicles," IFAC Proceedings Volumes, vol. 46, no. 10, pp. 79-84, 2013. [DOI:10.3182/20130626-3-AU-2035.00074]
9. [9] M. Kim, H. Joe, J. Kim, and S. Yu, "Integral sliding mode controller for precise maneuvering of autonomous underwater vehicle in the presence of unknown environmental disturbances," International Journal of Control, vol. 88, no. 10, pp. 2055-2065, 2015. [DOI:10.1080/00207179.2015.1031182]
10. [10] H. Joe, M. Kim, and S. Yu, "Second-order sliding-mode controller for autonomous underwater vehicle in the presence of unknown disturbances," Nonlinear Dynamics, vol. 78, no. 1, pp. 183-196, 2014. [DOI:10.1007/s11071-014-1431-0]
11. [11] G. Bartolini and A. Pisano, "Black-box position and attitude tracking for underwater vehicles by second-order sliding-mode technique," International Journal of Robust and Nonlinear Control, vol. 20, no. 14, pp. 1594-1609, 2010. [DOI:10.1002/rnc.1532]
12. [12] J. Guo, "A waypoint-tracking controller for a biomimetic autonomous underwater vehicle," Ocean Engineering, vol. 33, no. 17-18, pp. 2369-2380, 2006. [DOI:10.1016/j.oceaneng.2005.11.012]
13. [13] F. Y. Bi., Y. J. Wei, J. Z. Zhang, and W. Cao, "Position-tracking control of underactuated autonomous underwater vehicles in the presence of unknown ocean currents," IET Control Theory & Applications, vol. 14, no. 11, pp. 2369-2380, 2010. [DOI:10.1049/iet-cta.2009.0265]
14. [14] K. Mukherjee, I. N. Kar, and R. K. P. Bhatt, "Region tracking based control of an autonomous underwater vehicle with input delay," Ocean Engineering, vol. 99, no. 1, pp. 107-114, 2015. [DOI:10.1016/j.oceaneng.2015.02.006]
15. [15] X. Qi, "Adaptive coordinated tracking control of multiple autonomous underwater vehicles," Ocean Engineering, vol. 91, no. 1, pp. 84-90, 2014. [DOI:10.1016/j.oceaneng.2014.08.019]
16. [16] G. Antonelli, S. Chiaverini, N. Sarkar, and M. West, "Adaptive control of an autonomous underwater vehicle: Experimental results on ODIN," IEEE Transactions On Control Systems Technology, vol. 9, no. 5, pp. 756-765, 2001. [DOI:10.1109/87.944470]
17. [17] J. Guo, F. Chiu, and C. Huang, "Design of a sliding mode fuzzy controller for the guidance and control of an autonomous underwater vehicle," Ocean Engineering, vol. 30, no. 16, pp. 2137-2155, 2003. [DOI:10.1016/S0029-8018(03)00048-9]
18. [18] Y. C. Liu, S. Y. Liu, and N. Wang, "Fully-tuned fuzzy neural network based robust adaptive tracking control of unmanned underwater vehicle with thruster dynamics," Neurocomputing, vol. 196, no. 1, pp. 1-13, 2016. [DOI:10.1016/j.neucom.2016.02.042]
19. [19] Y. Chen, R. Zhang, X. Zhao, and J. Gao, "Adaptive fuzzy inverse trajectory tracking control of underactuated underwater vehicle with uncertainties," Ocean Engineering, vol. 121, no. 1, pp. 123-133, 2016. [DOI:10.1016/j.oceaneng.2016.05.034]
20. [20] K. Shojaei, "Neural network formation control of underactuated autonomous underwater vehicles with saturating actuators," Neurocomputing, vol. 194, no. 1, pp. 372-384, 2016. [DOI:10.1016/j.neucom.2016.02.041]
21. [21] B. Miao, T. Li, and W. Luo, "A DSC and MLP based robust adaptive NN tracking control for underwater vehicle," Neurocomputing, vol. 111, no. 1, pp. 184-189, 2013. [DOI:10.1016/j.neucom.2012.12.026]
22. [22] A. Bagheri and J. J. Moghaddam, "Simulation and tracking control based on neural-network strategy and sliding-mode control for underwater remotely operated vehicle," Neurocomputing, vol. 72, no. 7, pp. 1934-1950, 2009. [DOI:10.1016/j.neucom.2008.06.008]
23. [23] J. Yang, J. Feng, D. Qi, and Y. Li, "Longitudinal motion control of underwater vehicle based on fast smooth second order sliding mode," Optik - International Journal for Light and Electron Optics, vol. 127, no. 20, pp. 9118-9130, 2016. [DOI:10.1016/j.ijleo.2016.06.124]
24. [24] J. Ghommam and M. Saad, "Backstepping-based cooperative and adaptive tracking control design for a group of underactuated AUVs in horizontal plane," International Journal of Control, vol. 87, no. 5, pp. 1076-1093, 2014. [DOI:10.1080/00207179.2013.868605]
25. [25] F. Rezazadegan, K. Shojaei, F. Sheikholeslam, and A. Chatraei, "A novel approach to 6-DOF adaptive trajectory tracking control of an AUV in the presence of parameter uncertainties," Ocean Engineering, vol. 107, no. 1, pp. 246-258, 2015. [DOI:10.1016/j.oceaneng.2015.07.040]
26. [26] J. Xu, M. Wang, and L. Qiao, "Dynamical sliding mode control for the trajectory tracking of underactuated unmanned underwater vehicles," Ocean Engineering, vol. 105, no. 1, pp. 54-63, 2015. [DOI:10.1016/j.oceaneng.2015.06.022]
27. [27] Z. H. Ismail, M. B. M. Mokhar, V. W. E. Putranti, and M. W. Dunnigan, "A robust dynamic region-based control scheme for an autonomous underwater vehicle," Ocean Engineering, vol. 111, no. 1, pp. 155-165, 2016. [DOI:10.1016/j.oceaneng.2015.10.052]
28. [28] S. Li and X. Wang, "Finite-time consensus and collision avoidance control algorithms for multiple AUVs," Automatica, vol. 49, no. 11, pp. 3359-3367, 2013. [DOI:10.1016/j.automatica.2013.08.003]
29. [29] Z. Peng, D. Wang, G. Sun, and H. Wang, "Formation tracking control of multiple marine surface vehicles over a directed network : A cooperative dynamic surface control design," IFAC Proceedings Volumes, vol. 46, no. 20, pp. 707-712, 2013. [DOI:10.3182/20130902-3-CN-3020.00118]
30. [30] S. Li, X. Wang, and L. Zhang, "Finite-time output feedback tracking control for autonomous underwater vehicles," IEEE Journal of Oceanic Engineering, vol. 40, no. 3, pp. 727-751, 2015. [DOI:10.1109/JOE.2014.2330958]
31. [31] S. P. Bhat and D. S. Bernstein, "Finite-time stability of continuous autonomous systems," SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751-766, 2000. [DOI:10.1137/S0363012997321358]
32. [32] M. Galicki, "Finite-time control of robotic manipulators," Automatica, vol. 51, no. 1, pp. 49-54, 2015. [DOI:10.1016/j.automatica.2014.10.089]
33. [33] M.R. Mokhtari and B. Cherki, "A new robust control for minirotorcraft unmanned aerial vehicles," ISA Transactions, vol. 56, no. 1, pp. 86-101, 2015. [DOI:10.1016/j.isatra.2014.12.003]
34. [34] M. Jiang, S. Wang, J. Mei, and Y. Shen, "Finite-time synchronization control of a class of memristor-based recurrent neural networks," Neural Networks, vol. 63, no. 1, pp. 133-140, 2015. [DOI:10.1016/j.neunet.2014.11.005]
35. [35] M. Galicki, "Finite-time trajectory tracking control in a task space of robotic manipulator ," Automatica, vol. 67, no. 1, pp. 165-170, 2016. [DOI:10.1016/j.automatica.2016.01.025]
36. [36] S. P. Bhat and D. S. Bernstein, "Continuous finite-time stabilization of the translational and rotational double integrators," IEEE Transactions on Automatic Control, vol. 43, no. 5, pp. 678-682, 1998. [DOI:10.1109/9.668834]
37. [37] Y. Hong, J. Huang, and Y. Xu, "On an output feedback finite-time stabilization problem," IEEE Transactions on Automatic Control, vol. 46, no. 2, pp. 305-309, 2001. [DOI:10.1109/9.905699]
38. [38] Z. Zuo and L. Tie, "A new class of finite-time nonlinear consensus protocols for multi-agent systems," International Journal of Control, vol. 87, no. 2, pp. 363-370, 2016. [DOI:10.1080/00207179.2013.834484]
39. [39] A. Polyakov, D. Efimov, and W. Perruquetti, "Finite-time and fixed-time stabilization: Implicit Lyapunov function approach," Automatica, vol. 51, no. 1, pp. 332-340, 2015. [DOI:10.1016/j.automatica.2014.10.082]
40. [40] X. H. Zhang, K. Zhang, and X. J. Xie, "Finite-time output feedback stabilization of nonlinear high-order feed forward systems," International Journal of Robust and Nonlinear Control, vol. 26, no. 8, pp. 1794-1814, 2016. [DOI:10.1002/rnc.3384]
41. [41] Z. Zuo, "Nonsingular fixed-time consensus tracking for second-order multi-agent networks," Automatica, vol. 54, no. 1, pp. 305-309, 2015. [DOI:10.1016/j.automatica.2015.01.021]
42. [42] H. B. Oza, Y. V. Orlov, and S. K. Spurgeon, "Finite time stabilization of a perturbed double integrator with unilateral constraints," Mathematics and Computers in Simulation, vol. 95, no. 1, pp. 200-212, 2014. [DOI:10.1016/j.matcom.2012.02.011]
43. [43] Y. Su and C. Zheng, "Robust finite-time output feedback control of perturbed double integrator," Automatica, vol. 60, no. 1, pp. 86-91, 2015. [DOI:10.1016/j.automatica.2015.07.008]
44. [44] H. Liu, T. Zhang, and X. Tian, "Continuous output-feedback finite-time control for a class of second-order nonlinear systems with disturbances," International Journal of Robust and Nonlinear Control, vol. 26, no. 2, pp. 218-234, 2016. [DOI:10.1002/rnc.3305]
45. [45] S. P. Bhat and D. S. Bernstein, "Geometric homogeneity with applications to finite-time stability," Mathematics of Control, Signals and Systems, vol. 17, no. 2, pp. 101-127, 2005. [DOI:10.1007/s00498-005-0151-x]
46. [46] Q. Lan, S. Li, J. Yang, and L. Guo, "Finite-time control for soft landing on an asteroid based on line-of-sight angle," Journal of the Franklin Institute, vol. 351, no. 1, pp. 383-398, 2014. [DOI:10.1016/j.jfranklin.2013.08.012]
47. [47] S. Yu and X. Long, "Finite-time consensus for second-order multi-agent systems with disturbances by integral sliding mode," Automatica, vol. 54, no. 1, pp. 158-165, 2015. [DOI:10.1016/j.automatica.2015.02.001]
48. [48] Y. Zhang, G. Liu, and B. Luo, "Finite-time cascaded tracking control approach for mobile robots," Information Sciences, vol. 284, no. 1, pp. 31-43, 2014. [DOI:10.1016/j.ins.2014.06.037]
49. [49] S. Mondal and C. Mahanta, "Adaptive second order terminal sliding mode controller for robotic manipulators," Journal of the Franklin Institute, vol. 351, no. 4, pp. 2356-2377, 2014. [DOI:10.1016/j.jfranklin.2013.08.027]
50. [50] K. Lu and Y. Xia, "Adaptive attitude tracking control for rigid spacecraft with finite-time convergence," Automatica, vol. 49, no. 12, pp. 3591-3599, 2013. [DOI:10.1016/j.automatica.2013.09.001]
51. [51] S. Y. Chen and F. J. Lin, "Robust nonsingular terminal sliding mode control for nonlinear magnetic bearing system," IEEE Transactions on Control Systems Technology, vol. 19, no. 3, pp. 636-643, 2011. [DOI:10.1109/TCST.2010.2050484]
52. [52] Y. Chen, Z. Shi, and C. Lin, "Some criteria for the global finite-time synchronization of two Lorenz-Stenflo systems coupled by a new controller," Applied Mathematical Modelling, vol. 38, no. 15, pp. 4078-4085, 2014. [DOI:10.1016/j.apm.2014.02.007]
53. [53] S. Liu and L. Q. Chen, "Second-order terminal sliding mode control for networks synchronization," Nonlinear Dynamics, vol. 79, no. 1, pp. 205-213, 2015. [DOI:10.1007/s11071-014-1657-x]
54. [54] H. Komurcugil, "Adaptive terminal sliding-mode control strategy for DC-DC buck converters," ISA Transactions, vol. 51, no. 6, pp. 673-681, 2012. [DOI:10.1016/j.isatra.2012.07.005]
55. [55] A. Abooee, M. Moravej Khorasani, and M. Haeri "Free-chattering robust finite time tracking for connected double integrator nonlinear systems," submitted to 4th International Conference on Control, Instrumentation, and Automation, Qazvin Islamic Azad University, Qazvin, Iran, January 27-28, 2016. [DOI:10.1109/ICCIAutom.2016.7483178]
56. [56] Y. Feng, X. Yu, and F. Han, "On nonsingular terminal sliding-mode control of nonlinear systems," Automatica, vol. 49, no. 6, pp. 1715-1722, 2013. [DOI:10.1016/j.automatica.2013.01.051]
57. [57] S. Zhankui and K. Sun, "Nonlinear and chaos control of a micro-electro-mechanical system by using second-order fast terminal sliding mode control," Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 9, pp. 2540-2548, 2013. [DOI:10.1016/j.cnsns.2013.01.002]
58. [58] X. Liu and Y. Han, "Finite time control for MIMO nonlinear system based on higher-order sliding mode," ISA Transactions, vol. 53, no. 6, pp. 1838-1846, 2014. [DOI:10.1016/j.isatra.2014.09.002]
59. [59] M. Ghasemi, S. G. Nersesov, and G. Clayton, "Finite-time tracking using sliding mode control," Journal of the Franklin Institute, vol. 351, no. 5, pp. 2966-2990, 2014. [DOI:10.1016/j.jfranklin.2014.02.001]
60. [60] J. Yang, S. Li, J. Su, and X. Yu, "Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances," Automatica, vol. 49, no. 7, pp. 2287-2291, 2013. [DOI:10.1016/j.automatica.2013.03.026]
61. [61] S. E. Parsegov, A. E. Polyakov, and P. S. Shcherbakov, "Fixed-time consensus algorithm for multi-agent systems with integrator dynamics," IFAC Proceedings Volumes, vol. 46, no. 27, pp. 110-115, 2013. [DOI:10.3182/20130925-2-DE-4044.00055]
62. [62] M. Defoort, A. Polyakov, G. Demesure, M. Djemai, and K. Veluvolu, "Leader-follower fixed-time consensus for multi-agent systems with unknown non-linear inherent dynamics," IET Control Theory and Applications, vol. 9, no. 14, pp. 2165-2170, 2015. [DOI:10.1049/iet-cta.2014.1301]
63. [63] A. Polyakov and A. Poznyak, "Lyapunov function design for finite-time convergence analysis: "Twisting" controller for second-order sliding mode realization," Automatica, vol. 45, no. 2, pp. 444-448, 2009. [DOI:10.1016/j.automatica.2008.07.013]
64. [64] G. H. Hardly, J. E. Littlewood, and G. Polya "Inequalities," Cambridge University Press, 1952.
65. [65] B. Geranmehr and S.Rafee Nekoo, "Nonlinear suboptimal control of fully coupled non-affine six-DOF autonomous underwater vehicle using the state-dependent Riccati equation," Ocean Engineering, vol. 96, no. 1, pp. 248-257, 2015. [DOI:10.1016/j.oceaneng.2014.12.032]
66. [66] T. I. Fossen, "Marine control systems: guidance, navigation and control of ships, rigs and underwater vehicles," Marine Cybernetics, Trondheim, Norway, 2002.
67. [67] T. I. Fossen, "Guidance and control of ocean vehicles," John Wiley and Sons Ltd, England, 1994.

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