Abstract
A model predictive control (MPC) method with linear extended state observer (LESO) is presented to address the problems of the input constraints, uncertain parameters and external disturbances for path following of under-actuated surface ships without velocity measurements. The line of sight (LOS) guidance algorithm is employed to convert the path following into the heading control flexibly. The proper reference paths at waypoints are formulated by a variable acceptable radius approach. The matters of the heading control, input constraints including rudder amplitude and rate limit are addressed by virtue of MPC method employing the Norrbin model as the internal model. The LESO is introduced to estimate the uncertain parameters and external disturbances for the improvement of the internal model accuracy and the controller robustness. Moreover, the nonlinear observer and LESO are used to approximate the surge velocity, sway velocity and yaw rate, respectively. The effectiveness of the proposed control law is demonstrated via the compared simulations.
Similar content being viewed by others
References
Padideh R, Khoshnam S, Abbas C (2016) Output feedback look-ahead position control of electrically driven fast surface vessels. Automatika 57(4):968–981
Wang XF, Li TS, Zou ZJ et al (2010) Nonlinear model predictive controller design for path following of underactuated ships. J Ship Mech 14(3):217–227
Fossen TI, Breivik M, Skjetne R (2003) Line-of-sight path following of underactuated marine craft. In: Proceedings of the 6th IFAC Conf. Manoevring Control Marine Craft, Girona, Spain, pp 244–249.
Nagai T, Watanabe R (2016) Applying position prediction model for path following of ship on curved path. In: Proceedings of the IEEE Region 10 Conference, pp 22–25.
Lúcia M, Fossen TI, Soares CG (2007) Path following control system for a tanker ship model. Ocean Eng 34(14):2074–2085
Lekkas AM, Fossen TI (2012) A time-varying lookahead distance guidance law for path following. In: Proceedings of the 9th IFAC Conf. Manoeuvring Control Marine Craft, Arenzano, Italy, pp 398–403.
Pavlov A, Nordahl H, Breivik M (2009) MPC-based optimal path following for underactuated vessels. In: Proceedings of the 8th IFAC Int. Conf. Manoeuvring Control Marine Craft, Guaruja, Brazil, pp 340–345.
Oh SR, Sun J (2009) Path following of underactuated marine surface vessels using line-of-sight based model predictive control. Ocean Eng 37(2):289–295
Lekkas AM, Fossen TI (2014) Integral LOS path following for curved paths based on a monotone cubic hermite spline parametrization. IEEE Trans Control Syst Technol 22(6):2287–2301
Huang, HY, Fan YS (2018) Path following control for under-actuated surface vessel with disturbance. In: Proceedings of the 30th Chinese Control and Decision Conference. Institute of Electrical and Electronics Engineers. Shenyang, China, pp 3265–3269.
Liu L, Wang D, Peng ZH, et al (2018) Cooperative path following ring-networked under-actuated autonomous surface vehicles: algorithms and experimental results. IEEE Trans Cybernet, https://www.ieee.org/publications_standards/publications/rights/index.html
Yu YL, Guo C, Yu HM (2018) Finite-time predictor line-of-sight–based adaptive neural network path following for unmanned surface vessels with unknown dynamics and input saturation. Int J Adv Robot Syst 15(6):1–14
Ding FG, Ma YQ, Wang YH et al (2015) Robust synchronization control of multiple vessels with state observer. J Harbin Eng Univ 36(6):789–794
Yuanhui W, Haiyan T, Chenglong W (2019) High-gain observer-based line-of-sight guidance for adaptive neural path following control of underactuated marine surface vessels. IEEE Access 7:19258–19265
Zheng Z, Feroskhan M (2017) Path following of a surface vessel with prescribed performance in the presence of input saturation and external disturbances. IEEE/ASME Trans Mechatron 22(6):2564–2575
Vo DD, Pham VA, Nguyen DA (2018) Design an adaptive autopilot for an unmanned surface vessel. In: Proceedings of the 4th International Conference on Green Technology and Sustainable Development. IEEE, Ho Chi Minh City, Vietnam, pp 323–328.
Zenon Z (2018) Robust and adaptive ship path-following control system design. In: Proceedings of the 23rd International Conference on Methods and Models in Automation and Robotics. IEEE, Miedzyzdroje, Poland, pp 521–526.
Qiu BB, Wang GF, Fan YS et al (2019) Adaptive sliding mode trajectory tracking control for unmanned surface vehicle with modeling uncertainties and input saturation. Appl Sci 9(1240):1–18
Dong ZP, Liu T, Wan L et al (2015) Straight-path tracking control of underactuated USV based on Takagi-Sugeno fuzzy neural network. Chin J Sci Instrum 36(4):863–870
Zhang GQ, Zhang XK, Guan W (2014) Concise robust adaptive pathfollowing control for underactuated ships. J Harbin Eng Univ 35(9):1053–1059
Liu Y, Bu RX, Gao XR (2018) Ship trajectory tracking control system design based on sliding model control algorithm. Polish Maritime Res 25(3):26–34
Bu RX, Liu ZJ, Hu JQ (2007) Berthing controller of underactuated ship with nonlinear sliding mode. J Traffic Transport Eng 7(4):24–29
Shen ZP, Dai CS (2017) Iterative sliding mode control based on reinforced learning and used for path tracking of under-actuated ship. J Harbin Eng Univ 38(5):697–704
Shen ZP, Dai CS, Zhang N (2017) Trajectory tracking control of underactuated ship based on adaptive iterative sliding mode. J Traffic Transport Eng 17(6):125–134
Mu DD, Wang GF, Fan YS et al (2018) Adaptive trajectory tracking control for under-actuated unmanned surface vehicle subject to unknown dynamics and time-varing disturbances. Appl Sci 8(547):1–16
Shen ZP, Jing FS (2019) Neuron adaptive iterative sliding-mode control for path tracking of underactuated ship. J Harbin Eng Univ 40(3):489–500
Han JQ (2009) From PID to active disturbance rejection control. IEEE Trans Industr Electron 56(3):900–906
Li RH, Cao JH, Li TS (2018) Active disturbance rejection control design and parameters configuration for ship steering with wave disturbance. Control Theory Appl 35(11):1601–1609
Li RH, Li TS, Bu RX et al (2013) Active disturbance rejection with sliding mode control based course and path following for under-actuated ships. Math Problems Eng 1(1):1–9
Huang H, Li DW, Lin ZL et al (2011) An improved robust model predictive control design in the presence of actuator saturation. Automatica 47:861–864
Li GS, Zhang J, Liu ZL, et al (2016) Predictive control for straight path following of under-actuated surface vessels with roll constraints. In: Proceedings of the 28th Chinese Control and Decision Conference. IEEE, pp 583–588.
Liu CG, Chu XM, Wang L et al (2015) Trajectory tracking controller for underactuated surface vessels based on model predictive control. J Shanghai Jiao Tong Univ 49(12):1842–1854
Zheng H, Negenborn RR, Lodewijks G (2014) Trajectory tracking of autonomous vessels using model predictive control. In: Proceedings of the 19th world congress, IFAC, Cape Town, South Africa, pp 24–29.
Wu J, Peng H, Ohtsu K et al (2012) Ship’s tracking control based on nonlinear time series model. Appl Ocean Res 36:1–11
Zhang W, Zou ZJ, Deng DH (2017) A study on prediction of ship maneuvering in regular waves. Ocean Eng 137:367–381
Al Seyab RK, Cao Yi (2008) Differential recurrent neural network based predictive control. Comput Chem Eng 32(7):1533–1545
Fabio Augusto DAA, Anthony RH, Luciano NDL et al (2019) Autonomous unmanned aerial vehicles in search and rescue missions using real-time cooperative model predictive control. Sensors 19(19):1–22
Marjanovic O, Lennox B (2004) Infinite horizon model predictive control with no terminal constraint. Comput Chem Eng 28:2601–2610
Gao ZQ (2003) Scaling and bandwidth-parameterization based controller tuning. In: Proceedings of the American Control Conference. Denver, Colo, USA, pp 4989–4996.
Wang JQ, Zou ZJ, Wang T (2019) Path following of a surface ship sailing in restricted waters under wind effect using robust H-infinity guaranteed cost control. Int J Naval Architect Ocean Eng 11(1):606–623
Qian XB, Yin Y, Shen HL et al (2016) Simulation system for testing ship dynamic positioning control algorithm. J Syst Simul 28(9):2028–2034
Funding
This work was supported in part by Major Projects of Guangdong Education Department for Foundation Research and Applied Research (2019KZDZX1035), the National Natural Science Foundation of China (Nos. 51979045, 51939001, 61976033), and program for scientific research start-up funds of Guangdong Ocean University.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Li, Z., Li, R. & Bu, R. Path following of under-actuated ships based on model predictive control with state observer. J Mar Sci Technol 26, 408–418 (2021). https://doi.org/10.1007/s00773-020-00746-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00773-020-00746-1