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Robust adaptive formation control of underactuated autonomous surface vessels based on MLP and DOB

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Abstract

This paper investigates the leader–follower formation problem of multiple underactuated autonomous surface vessels in the presence of model uncertainties and environmental disturbances. Specially, the formation is defined in the body-fixed coordinates of the leader vessel and velocities of the leader are unavailable to followers. A novel robust adaptive formation control scheme based on the minimal learning parameter (MLP) algorithm and the disturbance observer (DOB) is presented. To address related formation configurations and unknown velocities of the leader, adaptive programming of the virtual vessel is introduced. By the neural networks (NNs) technique, the DOB is constructed and the formation controller is developed with different MLP-based adaptive laws. Under the proposed controller, it is shown that the desired formation can be achieved only with the position and yaw angle of the leader. And formation errors are guaranteed to be semiglobal uniformly ultimately bounded. Compared with existing results, the NNs-based DOB can compensate disturbances effectively with less model information. Meanwhile, the formation controller and the DOB can share the same set of NNs with smaller computational effort, where only two parameters need to be learned online for each of them. Simulations and comparison results are provided to illustrate the effectiveness of theoretical results.

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References

  1. Liu, Z., Zhang, Y., Yu, X., Yuan, C.: Unmanned surface vehicles: an overview of developments and challenges. Annu. Rev. Control 41, 71–93 (2016)

    Article  Google Scholar 

  2. Chen, Y.Q., Wang, Z.: Formation control: a review and a new consideration. In: Intelligent Robots and Systems, 2005.(IROS 2005). 2005 IEEE/RSJ International Conference on, pp. 3181–3186. IEEE (2005)

  3. Fu, M., Yu, L., Li, M., Tuo, Y., Ni, C.: Synchronization control of multiple surface vessels without velocity measurements. In: Mechatronics and Automation (ICMA), 2015 IEEE International Conference on, pp. 643–648. IEEE (2015)

  4. Wu, D., Ren, F., Qiao, L., Zhang, W.: Active disturbance rejection controller design for dynamically positioned vessels based on adaptive hybrid biogeography-based optimization and differential evolution. ISA Transactions (2017)

  5. Xiang, X., Yu, C., Lapierre, L., Zhang, J., Zhang, Q.: Survey on fuzzy-logic-based guidance and control of marine surface vehicles and underwater vehicles. Int. J. Fuzzy Syst. pp. 1–15 (2017)

  6. Xiang, X., Lapierre, L., Jouvencel, B.: Guidance based collision avoidance of coordinated nonholonomic autonomous vehicles. In: Intelligent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on, pp. 6064–6069. IEEE (2010)

  7. Balch, T., Arkin, R.C.: Behavior-based formation control for multirobot teams. IEEE Trans. Robot. Autom. 14(6), 926–939 (1998)

    Article  Google Scholar 

  8. Beard, R.W., Lawton, J., Hadaegh, F.Y.: A coordination architecture for spacecraft formation control. IEEE Trans. Control Syst. Technol. 9(6), 777–790 (2001)

    Article  Google Scholar 

  9. Consolini, L., Morbidi, F., Prattichizzo, D., Tosques, M.: Leader-follower formation control of nonholonomic mobile robots with input constraints. Automatica 44(5), 1343–1349 (2008)

    Article  MathSciNet  Google Scholar 

  10. Xiao, H., Li, Z., Chen, C.P.: Formation control of leader-follower mobile robots’ systems using model predictive control based on neural-dynamic optimization. IEEE Trans. Ind. Electron. 63(9), 5752–5762 (2016)

    Article  Google Scholar 

  11. Wang, Y., Yan, W., Li, J.: Passivity-based formation control of autonomous underwater vehicles. IET Control Theory Appl. 6(4), 518–525 (2012)

    Article  MathSciNet  Google Scholar 

  12. Peng, Z., Wang, J., Wang, D.: Distributed maneuvering of autonomous surface vehicles based on neurodynamic optimization and fuzzy approximation. IEEE Trans. Control Syst. Technol. PP(99), 1–8 (2017)

    Google Scholar 

  13. Dong, X., Li, Q., Ren, Z., Zhong, Y.: Formation-containment control for high-order linear time-invariant multi-agent systems with time delays. J. Frankl. Inst. 352(9), 3564–3584 (2015)

    Article  MathSciNet  Google Scholar 

  14. Peng, Z., Wang, J., Wang, D.: Distributed containment maneuvering of multiple marine vessels via neurodynamics-based output feedback. IEEE Trans. Ind. Electron. 64(5), 3831–3839 (2017)

    Article  Google Scholar 

  15. Fahimi, F.: Sliding-mode formation control for underactuated surface vessels. IEEE Trans. Robot. 23(3), 617–622 (2007)

    Article  MathSciNet  Google Scholar 

  16. Xiang, X., Lapierre, L., Jouvencel, B.: Guidance based collision free and obstacle avoidance of autonomous vehicles under formation constraints. IFAC Proc. Vol. 43(16), 599–604 (2010)

    Article  Google Scholar 

  17. Shojaei, K.: Leader-follower formation control of underactuated autonomous marine surface vehicles with limited torque. Ocean Eng. 105, 196–205 (2015)

    Article  Google Scholar 

  18. Xiao, B., Yang, X., Huo, X.: A novel disturbance estimation scheme for formation control of ocean surface vessels. IEEE Trans. Ind. Electron. 64(6), 4994–5003 (2017)

    Article  Google Scholar 

  19. Oh, K.K., Park, M.C., Ahn, H.S.: A survey of multi-agent formation control. Automatica 53, 424–440 (2015)

    Article  MathSciNet  Google Scholar 

  20. Ge, X., Han, Q.L.: Distributed formation control of networked multi-agent systems using a dynamic event-triggered communication mechanism. IEEE Trans. Ind. Electron. (2017)

  21. Xue, D., Yao, J., Chen, G., Yu, Y.L.: Formation control of networked multi-agent systems. IET Control Theory Appl. 4(10), 2168–2176 (2010)

    Article  MathSciNet  Google Scholar 

  22. Dong, W., Farrell, J.: Formation control of multiple underactuated surface vessels. IET Control Theory Appl. 2(12), 1077–1085 (2008)

    Article  MathSciNet  Google Scholar 

  23. Peng, Z., Wang, D., Li, T., Wu, Z.: Leaderless and leader-follower cooperative control of multiple marine surface vehicles with unknown dynamics. Nonlinear Dyn. 74(1–2), 95–106 (2013)

    Article  MathSciNet  Google Scholar 

  24. Dong, W.: Cooperative control of underactuated surface vessels. IET Control Theory Appl. 4(9), 1569–1580 (2010)

    Article  MathSciNet  Google Scholar 

  25. Peng, Z., Wang, D., Chen, Z., Hu, X., Lan, W.: Adaptive dynamic surface control for formations of autonomous surface vehicles with uncertain dynamics. IEEE Trans. Control Syst. Technol. 21(2), 513–520 (2013)

    Article  Google Scholar 

  26. Jin, X.: Fault tolerant finite-time leader-follower formation control for autonomous surface vessels with LOS range and angle constraints. Automatica 68, 228–236 (2016)

    Article  MathSciNet  Google Scholar 

  27. Li, J., Lee, P.M., Jun, B.H., Lim, Y.K.: Point-to-point navigation of underactuated ships. Automatica 44(12), 3201–3205 (2008)

    Article  MathSciNet  Google Scholar 

  28. Sun, Z., Zhang, G., Lu, Y., Zhang, W.: Leader-follower formation control of underactuated surface vehicles based on sliding mode control and parameter estimation. ISA Transactions (2017)

  29. Radke, A., Gao, Z.: A survey of state and disturbance observers for practitioners. In: American Control Conference, pp. 6–pp. IEEE (2006)

  30. Chen, W.H., Yang, J., Guo, L., Li, S.: Disturbance-observer-based control and related methods: an overview. IEEE Trans. Ind. Electron. 63(2), 1083–1095 (2016)

    Article  Google Scholar 

  31. Do, K.D.: Practical control of underactuated ships. Ocean Eng. 37(13), 1111–1119 (2010)

    Article  Google Scholar 

  32. Yang, Y., Du, J., Liu, H., Guo, C., Abraham, A.: A trajectory tracking robust controller of surface vessels with disturbance uncertainties. IEEE Trans. Control Syst. Technol. 22(4), 1511–1518 (2014)

    Article  Google Scholar 

  33. Du, J., Hu, X., Krstić, M., Sun, Y.: Robust dynamic positioning of ships with disturbances under input saturation. Automatica 73, 207–214 (2016)

    Article  MathSciNet  Google Scholar 

  34. Cui, R., Ge, S.S., How, B.V.E., Choo, Y.S.: Leader-follower formation control of underactuated autonomous underwater vehicles. Ocean Eng. 37(17), 1491–1502 (2010)

    Article  Google Scholar 

  35. He, W., Yin, Z., Sun, C.: Adaptive neural network control of a marine vessel with constraints using the asymmetric barrier Lyapunov function. IEEE Trans. Cybern. 47(7), 1641–1651 (2017)

    Article  Google Scholar 

  36. Xu, B., Shou, Y.: Composite learning control of mimo systems with applications. IEEE Trans. Ind. Electron. 65(8), 6414–6424 (2018)

    Article  Google Scholar 

  37. Du, J., Hu, X., Liu, H., Chen, C.P.: Adaptive robust output feedback control for a marine dynamic positioning system based on a high-gain observer. IEEE Trans. Neural Netw. Learn. Syst. 26(11), 2775–2786 (2015)

    Article  MathSciNet  Google Scholar 

  38. Xu, B., Sun, F.: Composite intelligent learning control of strict-feedback systems with disturbance. IEEE Trans. Cybern. 48(2), 730–741 (2018)

    Article  Google Scholar 

  39. Zhang, G., Zhang, X.: Concise robust adaptive path-following control of underactuated ships using DSC and MLP. IEEE J. Ocean. Eng. 39(4), 685–694 (2014)

    Article  MathSciNet  Google Scholar 

  40. Cui, R., Ge, S.S., How, B.V.E., Choo, Y.S.: Leader-follower formation control of underactuated AUVs with leader position measurement. In: Robotics and Automation, 2009. ICRA’09. IEEE International Conference on, pp. 979–984. IEEE (2009)

  41. Li, T., Wang, D., Feng, G., Tong, S.: A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems. IEEE Trans. Syst. Man Cybern. Part B 40(3), 915–927 (2010)

    Article  Google Scholar 

  42. Reyhanoglu, M.: Exponential stabilization of an underactuated autonomous surface vessel. Automatica 33(12), 2249–2254 (1997)

    Article  MathSciNet  Google Scholar 

  43. Dong, W., Guo, Y.: Global time-varying stabilization of underactuated surface vessel. IEEE Trans. Autom. Control 50(6), 859–864 (2005)

    Article  MathSciNet  Google Scholar 

  44. Chen, M., Ge, S.S., Ren, B.: Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica 47(3), 452–465 (2011)

    Article  MathSciNet  Google Scholar 

  45. Chen, M., Ge, S.S.: Adaptive neural output feedback control of uncertain nonlinear systems with unknown hysteresis using disturbance observer. IEEE Trans. Ind. Electron. 62(12), 7706–7716 (2015)

    Article  MathSciNet  Google Scholar 

  46. Shahvali, M., Askari, J.: Adaptive neural dynamic surface control of MIMO stochastic nonlinear systems with unknown control directions. Int. J. Adapt. Control Signal Process. 31(1), 97–121 (2017)

    Article  MathSciNet  Google Scholar 

  47. Shahvali, M., Shojaei, K.: Distributed adaptive neural control of nonlinear multi-agent systems with unknown control directions. Nonlinear Dyn. 83(4), 2213–2228 (2016)

    Article  MathSciNet  Google Scholar 

  48. Shahvali, M., Shojaei, K.: Distributed control of networked uncertain Euler–Lagrange systems in the presence of stochastic disturbances: a prescribed performance approach. Nonlinear Dyn. 90(1), 697–715 (2017)

    Article  MathSciNet  Google Scholar 

  49. Skjetne, R., Fossen, T.I., Kokotović, P.V.: Adaptive maneuvering, with experiments, for a model ship in a marine control laboratory. Automatica 41(2), 289–298 (2005)

    Article  MathSciNet  Google Scholar 

  50. Jiang, Z.P.: Global tracking control of underactuated ships by Lyapunov’s direct method. Automatica 38(2), 301–309 (2002)

    Article  Google Scholar 

  51. Breivik, M., Hovstein, V.E., Fossen, T.I.: Ship formation control: a guided leader-follower approach. IFAC Proc. Vol. 41(2), 16008–16014 (2008)

    Article  Google Scholar 

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Acknowledgements

This paper is partly supported by National Natural Science Foundation of China (61473183, U1509211), National Postdoctoral Program for Innovative Talents of China (BX201600103) and Chinese Postdoctoral Science Foundation (2016M601600). The authors would like to thank anonymous reviewers for their constructive suggestions and comments.

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  1. Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Yu Lu, Guoqing Zhang, Zhijian Sun & Weidong Zhang

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  1. Yu Lu
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Correspondence to Weidong Zhang.

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Lu, Y., Zhang, G., Sun, Z. et al. Robust adaptive formation control of underactuated autonomous surface vessels based on MLP and DOB. Nonlinear Dyn 94, 503–519 (2018). https://doi.org/10.1007/s11071-018-4374-z

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