Citation:  H. L. Wei and Y. Shi, “MPCbased motion planning and control enables smarter and safer autonomous marine vehicles: Perspectives and a tutorial survey,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 1, pp. 1–17, Jan. 2023. doi: 10.1109/JAS.2022.106016 
[1] 
E. Zereik, M. Bibuli, N. Mišković, P. Ridao, and A. Pascoal, “Challenges and future trends in marine robotics,” Annual Reviews in Control, vol. 46, pp. 350–368, 2018. doi: 10.1016/j.arcontrol.2018.10.002

[2] 
Y. Shi, C. Shen, H. Fang, and H. Li, “Advanced control in marine mechatronic systems: A survey,” IEEE/ASME Trans. Mechatronics, vol. 22, no. 3, pp. 1121–1131, 2017. doi: 10.1109/TMECH.2017.2660528

[3] 
M. Robotics, “The Otter unmanned surface vehicle,” https://www.maritimerobotics.com/otter, 2022, accessed: 20220506.

[4] 
K. Maritime, “The Hugin AUV,” https://www.kongsberg.com/maritime/products/marinerobotics/autonomousunderwatervehicles/AUVhugin/, 2022, accessed: 20220506.

[5] 
B. Robotics, “The BlueROV2,” https://bluerobotics.com/store/rov/bluerov2/, 2022, accessed: 20220506.

[6] 
I.L. G. Borlaug, K. Y. Pettersen, and J. T. Gravdahl, “Tracking control of an articulated intervention autonomous underwater vehicle in 6DOF using generalized supertwisting: Theory and experiments,” IEEE Trans. Control Systems Technology, vol. 29, no. 1, pp. 353–369, 2020.

[7] 
T. I. Fossen, Handbook of Marine Craft Hydrodynamics and Motion Control. John Wiley & Sons, 2011.

[8] 
Z. Liu, Y. Zhang, X. Yu, and C. Yuan, “Unmanned surface vehicles: An overview of developments and challenges,” Annual Reviews in Control, vol. 41, pp. 71–93, 2016. doi: 10.1016/j.arcontrol.2016.04.018

[9] 
J. B. Rawlings, D. Q. Mayne, and M. Diehl, Model Predictive Control: Theory, Computation, and Design. Madison: Nob Hill Publishing, 2017.

[10] 
Y. Shi and K. Zhang, “Advanced model predictive control framework for autonomous intelligent mechatronic systems: A tutorial overview and perspectives,” Annual Reviews in Control, vol. 52, pp. 170–196, 2021. doi: 10.1016/j.arcontrol.2021.10.008

[11] 
P. Bouffard, A. Aswani, and C. Tomlin, “Learningbased model predictive control on a quadrotor: Onboard implementation and experimental results,” in Proc. IEEE Int. Conf. Robotics and Automation, 2012, pp. 279–284.

[12] 
W. B. Dunbar and D. S. Caveney, “Distributed receding horizon control of vehicle platoons: Stability and string stability,” IEEE Trans. Automatic Control, vol. 57, no. 3, pp. 620–633, 2011.

[13] 
G. Roberts, “Trends in marine control systems,” Annual Reviews in Control, vol. 32, no. 2, pp. 263–269, 2008. doi: 10.1016/j.arcontrol.2008.08.002

[14] 
J. E. Manley, “Unmanned surface vehicles, 15 years of development,” in Proc. IEEE OCEANS, 2008, pp. 1–4.

[15] 
A. J. Sørensen, “A survey of dynamic positioning control systems,” Annual Reviews in Control, vol. 35, no. 1, pp. 123–136, 2011. doi: 10.1016/j.arcontrol.2011.03.008

[16] 
S. Campbell, W. Naeem, and G. W. Irwin, “A review on improving the autonomy of unmanned surface vehicles through intelligent collision avoidance manoeuvres,” Annual Reviews in Control, vol. 36, no. 2, pp. 267–283, 2012. doi: 10.1016/j.arcontrol.2012.09.008

[17] 
J. Melo and A. Matos, “Survey on advances on terrain based navigation for autonomous underwater vehicles,” Ocean Engineering, vol. 139, pp. 250–264, 2017. doi: 10.1016/j.oceaneng.2017.04.047

[18] 
A. Sahoo, S. K. Dwivedy, and P. Robi, “Advancements in the field of autonomous underwater vehicle,” Ocean Engineering, vol. 181, pp. 145–160, 2019. doi: 10.1016/j.oceaneng.2019.04.011

[19] 
Y. Huang, L. Chen, P. Chen, R. R. Negenborn, and P. Van Gelder, “Ship collision avoidance methods: Stateoftheart,” Safety Science, vol. 121, pp. 451–473, 2020. doi: 10.1016/j.ssci.2019.09.018

[20] 
C. Zhou, S. Gu, Y. Wen, Z. Du, C. Xiao, L. Huang, and M. Zhu, “The review unmanned surface vehicle path planning: Based on multimodality constraint,” Ocean Engineering, vol. 200, p. 107043, 2020.

[21] 
L. Chen, R. Negenborn, Y. Huang, and H. Hopman, “A survey on cooperative control for waterborne transport,” IEEE Intelligent Transportation Systems Magazine, vol. 13, no. 2, pp. 71–90, 2020.

[22] 
X. Zhang, C. Wang, L. Jiang, L. An, and R. Yang, “Collisionavoidance navigation systems for maritime autonomous surface ships: A state of the art survey,” Ocean Engineering, vol. 235, p. 109380, 2021. doi: 10.1016/j.oceaneng.2021.109380

[23] 
N. Gu, D. Wang, Z. Peng, J. Wang, and Q.L. Han, “Advances in lineofsight guidance for path following of autonomous marine vehicles: An overview,” IEEE Trans. Systems,Man,and Cybernetics: Systems, 2022. DOI: 10.1109/TSMC.2022.3162862

[24] 
N. Gu, D. Wang, Z. Peng, J. Wang, and Q.L. Han, “Disturbance observers and extended state observers for marine vehicles: A survey,” Control Engineering Practice, vol. 123, p. 105158, 2022. doi: 10.1016/j.conengprac.2022.105158

[25] 
Z. Zhou, J. Liu, and J. Yu, “A survey of underwater multirobot systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 1, pp. 1–18, 2022. doi: 10.1109/JAS.2021.1004269

[26] 
Ü. Öztürk, M. Akdağ, and T. Ayabakan, “A review of path planning algorithms in maritime autonomous surface ships: Navigation safety perspective,” Ocean Engineering, vol. 251, p. 111010, 2022. doi: 10.1016/j.oceaneng.2022.111010

[27] 
T. I. Fossen, Marine Control Systems: Guidance, Navigation and Control of Ships, Rigs and Underwater Vehicles. Marine Cybernetics, 2002.

[28] 
K. D. Do, Z.P. Jiang, and J. Pan, “Underactuated ship global tracking under relaxed conditions,” IEEE Trans. Automatic Control, vol. 47, no. 9, pp. 1529–1536, 2002. doi: 10.1109/TAC.2002.802755

[29] 
Z. Zeng, K. Sammut, L. Lian, F. He, A. Lammas, and Y. Tang, “A comparison of optimization techniques for AUV path planning in environments with ocean currents,” Robotics and Autonomous Systems, vol. 82, pp. 61–72, 2016. doi: 10.1016/j.robot.2016.03.011

[30] 
C. V. Caldwell, D. D. Dunlap, and E. G. Collins, “Motion planning for an autonomous underwater vehicle via sampling based model predictive control,” in Proc. OCEANS MTS/IEEE SEATTLE, 2010, pp. 1–6.

[31] 
V. T. Huynh, M. Dunbabin, and R. N. Smith, “Predictive motion planning for AUVs subject to strong timevarying currents and forecasting uncertainties,” in Proc. IEEE Int. Conf. Robotics and Automation, 2015, pp. 1144–1151.

[32] 
X. Zhao, J. Gao, and W. Yan, “A receding horizon motion planner for underwater vehicle manipulator systems,” in Proc. OCEANS MTS/IEEE Charleston, 2018, pp. 1–7.

[33] 
C. Shen, Y. Shi, and B. Buckham, “Integrated path planning and tracking control of an AUV: A unified receding horizon optimization approach,” IEEE/ASME Trans. Mechatronics, vol. 22, no. 3, pp. 1163–1173, 2017. doi: 10.1109/TMECH.2016.2612689

[34] 
M. Lutz and T. Meurer, “Optimal trajectory planning and model predictive control of underactuated marine surface vessels using a flatnessbased approach,” in Proc. IEEE American Control Conf., 2021, pp. 4667–4673.

[35] 
A. Bemporad, A. Oliveri, T. Poggi, and M. Storace, “Ultrafast stabilizing model predictive control via canonical piecewise affine approximations,” IEEE Trans. Automatic Control, vol. 56, no. 12, pp. 2883–2897, 2011. doi: 10.1109/TAC.2011.2141410

[36] 
H. Li and Y. Shi, “Eventtriggered robust model predictive control of continuoustime nonlinear systems,” Automatica, vol. 50, no. 5, pp. 1507–1513, 2014. doi: 10.1016/j.automatica.2014.03.015

[37] 
C. Liu, H. Li, and Y. Shi, “A unitary distributed subgradient method for multiagent optimization with different coupling sources,” Automatica, vol. 114, p. 108834, 2020. doi: 10.1016/j.automatica.2020.108834

[38] 
M. Akdağ, P. Solnør, and T. A. Johansen, “Collaborative collision avoidance for maritime autonomous surface ships: A review,” Ocean Engineering, vol. 250, p. 110920, 2022. doi: 10.1016/j.oceaneng.2022.110920

[39] 
T. A. Johansen, T. Perez, and A. Cristofaro, “Ship collision avoidance and COLREGS compliance using simulationbased control behavior selection with predictive hazard assessment,” IEEE Trans. Intelligent Transportation Systems, vol. 17, no. 12, pp. 3407–3422, 2016. doi: 10.1109/TITS.2016.2551780

[40] 
B.O. H. Eriksen, M. Breivik, E. F. Wilthil, A. L. Flåten, and E. F. Brekke, “The branchingcourse model predictive control algorithm for maritime collision avoidance,” Journal of Field Robotics, vol. 36, no. 7, pp. 1222–1249, 2019. doi: 10.1002/rob.21900

[41] 
D. K. M. Kufoalor, T. A. Johansen, E. F. Brekke, A. Hepsø, and K. Trnka, “Autonomous maritime collision avoidance: Field verification of autonomous surface vehicle behavior in challenging scenarios,” Journal of Field Robotics, vol. 37, no. 3, pp. 387–403, 2020. doi: 10.1002/rob.21919

[42] 
J. de Vries, E. Trevisan, J. van der Toorn, T. Das, B. Brito, and J. AlonsoMora, “Regulations aware motion planning for autonomous surface vessels in urban canals,” in Proc. Int. Conf. Robotics and Automation, 2022, pp. 3291–3297.

[43] 
S. Siriya, M. Bui, A. Shriraman, M. Chen, and Y. Pu, “Safetyguaranteed realtime trajectory planning for underwater vehicles in planeprogressive waves,” in Proc. 59th IEEE Conf. Decision and Control, 2020, pp. 5249–5254.

[44] 
S. HeshmatiAlamdari, A. Nikou, and D. Dimarogonas, “Robust trajectory tracking control for underactuated autonomous underwater vehicles in uncertain environments,” IEEE Trans. Automation Science and Engineering, vol. 18, no. 3, pp. 1288–1301, 2021. doi: 10.1109/TASE.2020.3001183

[45] 
X. Sun, G. Wang, and Y. Fan, “Collision avoidance guidance and control scheme for vector propulsion unmanned surface vehicle with disturbance,” Applied Ocean Research, vol. 115, p. 102799, 2021.

[46] 
L. Ferranti, R. R. Negenborn, T. Keviczky, and J. AlonsoMora, “Coordination of multiple vessels via distributed nonlinear model predictive control,” in Proc. IEEE European Control Conf., 2018, pp. 2523–2528.

[47] 
S. Xie, V. Garofano, X. Chu, and R. R. Negenborn, “Model predictive ship collision avoidance based on Qlearning beetle swarm antenna search and neural networks,” Ocean Engineering, vol. 193, p. 106609, 2019.

[48] 
I. Prodan, E. I. Grøtli, L. Lefèvre, et al., “Safe navigation in a coastal environment of multiple surface vehicles under uncertainties: A combined use of potential field constructions and NMPC,” Ocean Engineering, vol. 216, p. 107706, 2020. doi: 10.1016/j.oceaneng.2020.107706

[49] 
S. Zhang, Y. Yang, S. Siriya, and Y. Pu, “Trajectory planning for multiple autonomous underwater vehicles with safety guarantees,” arXiv preprint arXiv: 2011.13505, 2020.

[50] 
S. Blindheim, S. Gros, and T. A. Johansen, “Riskbased model predictive control for autonomous ship emergency management,” IFACPapersOnLine, vol. 53, no. 2, pp. 14524–14531, 2020. doi: 10.1016/j.ifacol.2020.12.1456

[51] 
A. Wahl and E.D. Gilles, “Trackkeeping on waterways using model predictive control,” IFAC Proceedings Volumes, vol. 31, no. 30, pp. 149–154, 1998. doi: 10.1016/S14746670(17)38432X

[52] 
T. Perez, C.Y. Tzeng, and G. C. Goodwin, “Model predictive rudder roll stabilization control for ships,” IFAC Proceedings Volumes, vol. 33, no. 21, pp. 45–50, 2000. doi: 10.1016/S14746670(17)370490

[53] 
Z. Li and J. Sun, “Disturbance compensating model predictive control with application to ship heading control,” IEEE Trans. Control Systems Technology, vol. 20, no. 1, pp. 257–265, 2011.

[54] 
A. Veksler, T. A. Johansen, F. Borrelli, and B. Realfsen, “Dynamic positioning with model predictive control,” IEEE Trans. Control Systems Technology, vol. 24, no. 4, pp. 1340–1353, 2016. doi: 10.1109/TCST.2015.2497280

[55] 
D. C. Fernández and G. A. Hollinger, “Model predictive control for underwater robots in ocean waves,” IEEE Robotics and Automation Letters, vol. 2, no. 1, pp. 88–95, 2016.

[56] 
K. L. Walker, R. Gabl, S. Aracri, Y. Cao, A. A. Stokes, A. Kiprakis, and F. GiorgioSerchi, “Experimental validation of wave induced disturbances for predictive station keeping of a remotely operated vehicle,” IEEE Robotics and Automation Letters, vol. 6, no. 3, pp. 5421–5428, 2021. doi: 10.1109/LRA.2021.3075662

[57] 
C. Shen, Y. Shi, and B. Buckham, “Lyapunovbased model predictive control for dynamic positioning of autonomous underwater vehicles,” in Proc. IEEE Int. Conf. Unmanned Systems, 2017, pp. 588–593.

[58] 
H. Li and W. Yan, “Model predictive stabilization of constrained underactuated autonomous underwater vehicles with guaranteed feasibility and stability,” IEEE/ASME Trans. Mechatronics, vol. 22, no. 3, pp. 1185–1194, 2017. doi: 10.1109/TMECH.2016.2587288

[59] 
K. Y. Pettersen and O. Egeland, “Timevarying exponential stabilization of the position and attitude of an underactuated autonomous underwater vehicle,” IEEE Trans. Automatic Control, vol. 44, no. 1, pp. 112–115, 1999. doi: 10.1109/9.739086

[60] 
A. A. do Nascimento, H. R. Feyzmahdavian, M. Johansson, W. GarciaGabin, and K. Tervo, “Tubebased model predictive control for dynamic positioning of marine vessels,” IFACPapersOnLine, vol. 52, no. 21, pp. 33–38, 2019. doi: 10.1016/j.ifacol.2019.12.279

[61] 
H. Zheng, J. Wu, W. Wu, and Y. Zhang, “Robust dynamic positioning of autonomous surface vessels with tubebased model predictive control,” Ocean Engineering, vol. 199, p. 106820, 2020.

[62] 
H. Yang, F. Deng, Y. He, D. Jiao, and Z. Han, “Robust nonlinear model predictive control for reference tracking of dynamic positioning ships based on nonlinear disturbance observer,” Ocean Engineering, vol. 215, p. 107885, 2020.

[63] 
Z. Li, J. Sun, and S. Oh, “Path following for marine surface vessels with rudder and roll constraints: An MPC approach,” in Proc. IEEE American Control Conf., 2009, pp. 3611–3616.

[64] 
R. Ghaemi, S. Oh, and J. Sun, “Path following of a model ship using model predictive control with experimental verification,” in Proc. IEEE American Control Conf., 2010, pp. 5236–5241.

[65] 
S.R. Oh and J. Sun, “Path following of underactuated marine surface vessels using lineofsight based model predictive control,” Ocean Engineering, vol. 37, no. 2–3, pp. 289–295, 2010. doi: 10.1016/j.oceaneng.2009.10.004

[66] 
T. Faulwasser and R. Findeisen, “Constrained output pathfollowing for nonlinear systems using predictive control,” IFAC Proceedings Volumes, vol. 43, no. 14, pp. 753–758, 2010. doi: 10.3182/201009013IT2016.00122

[67] 
T. Faulwasser and R. Findeisen, “Nonlinear model predictive control for constrained output path following,” IEEE Trans. Automatic Control, vol. 61, no. 4, pp. 1026–1039, 2016. doi: 10.1109/TAC.2015.2466911

[68] 
N. Kapetanović, M. Bibuli, N. Mišković, and M. Caccia, “Realtime model predictive line following control for underactuated marine vehicles,” IFACPapersOnLine, vol. 50, no. 1, pp. 12374–12379, 2017. doi: 10.1016/j.ifacol.2017.08.2501

[69] 
C. Shen, Y. Shi, and B. Buckham, “Pathfollowing control of an AUV: A multiobjective model predictive control approach,” IEEE Trans. Control Systems Technology, vol. 27, no. 3, pp. 1334–1342, 2018.

[70] 
J. Zhang, T. Sun, and Z. Liu, “Robust model predictive control for pathfollowing of underactuated surface vessels with roll constraints,” Ocean Engineering, vol. 143, pp. 125–132, 2017. doi: 10.1016/j.oceaneng.2017.07.057

[71] 
C. Liu, D. Wang, Y. Zhang, and X. Meng, “Model predictive control for path following and roll stabilization of marine vessels based on neurodynamic optimization,” Ocean Engineering, vol. 217, p. 107524, 2020.

[72] 
S. Helling and T. Meurer, “A culling procedure for collision avoidance model predictive control with application to ship autopilot models,” IFACPapersOnLine, vol. 54, no. 16, pp. 43–50, 2021. doi: 10.1016/j.ifacol.2021.10.071

[73] 
S. Helling, C. Roduner, and T. Meurer, “On the dual implementation of collisionavoidance constraints in pathfollowing MPC for underactuated surface vessels,” in Proc. IEEE American Control Conf., 2021, pp. 3366–3371.

[74] 
C. Liu, H. Zheng, R. Negenborn, X. Chu, and S. Xie, “Adaptive predictive path following control based on least squares support vector machines for underactuated autonomous vessels,” Asian Journal of Control, vol. 23, no. 1, pp. 432–448, 2021. doi: 10.1002/asjc.2208

[75] 
A. Pavlov, H. Nordahl, and M. Breivik, “MPCbased optimal path following for underactuated vessels,” IFAC Proceedings Volumes, vol. 42, no. 18, pp. 340–345, 2009. doi: 10.3182/200909163BR3001.0065

[76] 
Z. Yan and J. Wang, “Model predictive control for tracking of underactuated vessels based on recurrent neural networks,” IEEE Journal of Oceanic Engineering, vol. 37, no. 4, pp. 717–726, 2012. doi: 10.1109/JOE.2012.2201797

[77] 
J. Wang, J. Wang, and Q.L. Han, “Neurodynamicsbased model predictive control of continuoustime underactuated mechatronic systems,” IEEE/ASME Trans. Mechatronics, vol. 26, no. 1, pp. 311–322, 2021.

[78] 
Y. Zhang, X. Liu, M. Luo, and C. Yang, “MPCbased 3D trajectory tracking for an autonomous underwater vehicle with constraints in complex ocean environments,” Ocean Engineering, vol. 189, p. 106309, 2019. doi: 10.1016/j.oceaneng.2019.106309

[79] 
W. Gan, D. Zhu, Z. Hu, X. Shi, L. Yang, and Y. Chen, “Model predictive adaptive constraint tracking control for underwater vehicles,” IEEE Trans. Industrial Electronics, vol. 67, no. 9, pp. 7829–7840, 2020. doi: 10.1109/TIE.2019.2941132

[80] 
Z. Yan, P. Gong, W. Zhang, and W. Wu, “Model predictive control of autonomous underwater vehicles for trajectory tracking with external disturbances,” Ocean Engineering, vol. 217, p. 107884, 2020. doi: 10.1016/j.oceaneng.2020.107884

[81] 
B. J. Guerreiro, C. Silvestre, R. Cunha, and A. Pascoal, “Trajectory tracking nonlinear model predictive control for autonomous surface craft,” IEEE Trans. Control Systems Technology, vol. 22, no. 6, pp. 2160–2175, 2014. doi: 10.1109/TCST.2014.2303805

[82] 
C. Shen, B. Buckham, and Y. Shi, “Modified C/GMRES algorithm for fast nonlinear model predictive tracking control of AUVs,” IEEE Trans. Control Systems Technology, vol. 25, no. 5, pp. 1896–1904, 2017. doi: 10.1109/TCST.2016.2628803

[83] 
C. Shen and Y. Shi, “Distributed implementation of nonlinear model predictive control for AUV trajectory tracking,” Automatica, vol. 115, p. 108863, 2020.

[84] 
D. M. de la Peña and P. D. Christofides, “Lyapunovbased model predictive control of nonlinear systems subject to data losses,” IEEE Trans. Automatic Control, vol. 53, no. 9, pp. 2076–2089, 2008. doi: 10.1109/TAC.2008.929401

[85] 
D. Q. Mayne, “Model predictive control: Recent developments and future promise,” Automatica, vol. 50, no. 12, pp. 2967–2986, 2014. doi: 10.1016/j.automatica.2014.10.128

[86] 
S. HeshmatiAlamdari, G. C. Karras, P. Marantos, and K. J. Kyriakopoulos, “A robust predictive control approach for underwater robotic vehicles,” IEEE Trans. Control Systems Technology, vol. 28, no. 6, pp. 2352–2363, 2020. doi: 10.1109/TCST.2019.2939248

[87] 
M. Abdelaal, M. Fränzle, and A. Hahn, “Nonlinear model predictive control for trajectory tracking and collision avoidance of underactuated vessels with disturbances,” Ocean Engineering, vol. 160, pp. 168–180, 2018. doi: 10.1016/j.oceaneng.2018.04.026

[88] 
Y. Dai, S. Yu, Y. Yan, and X. Yu, “An EKFbased fast tube mpc scheme for moving target tracking of a redundant underwater vehiclemanipulator system,” IEEE/ASME Trans. Mechatronics, vol. 24, no. 6, pp. 2803–2814, 2019. doi: 10.1109/TMECH.2019.2943007

[89] 
Y. Dai, S. Yu, and Y. Yan, “An adaptive EKFFMPC for the trajectory tracking of UVMs,” IEEE Journal of Oceanic Engineering, vol. 45, no. 3, pp. 699–713, 2020. doi: 10.1109/JOE.2019.2899689

[90] 
S. Kong, J. Sun, C. Qiu, Z. Wu, and J. Yu, “Extended state observerbased controller with model predictive governor for 3D trajectory tracking of underactuated underwater vehicles,” IEEE Trans. Industrial Informatics, vol. 17, no. 9, pp. 6114–6124, 2021. doi: 10.1109/TII.2020.3036665

[91] 
C. Long, X. Qin, Y. Bian, and M. Hu, “Trajectory tracking control of ROVs considering external disturbances and measurement noises using ESKFbased MPC,” Ocean Engineering, vol. 241, p. 109991, 2021.

[92] 
Y. Cui, L. Peng, and H. Li, “Filtered probabilistic model predictive controlbased reinforcement learning for unmanned surface vehicles,” IEEE Trans. Industrial Informatics, vol. 18, no. 10, pp. 6950–6961, 2022. doi: 10.1109/TII.2022.3142323

[93] 
A. B. Martinsen, A. M. Lekkas, and S. Gros, “Reinforcement learningbased NMPC for tracking control of ASVs: Theory and experiments,” Control Engineering Practice, vol. 120, p. 105024, 2022. doi: 10.1016/j.conengprac.2021.105024

[94] 
W. Wang, N. Hagemann, C. Ratti, and D. Rus, “Adaptive nonlinear model predictive control for autonomous surface vessels with largely varying payload,” in Proc. IEEE Int. Conf. Robotics and Automation, 2021, pp. 7337–7343.

[95] 
H. Zhang, D. Zhu, C. Liu, and Z. Hu, “Tracking faulttolerant control based on model predictive control for human occupied vehicle in threedimensional underwater workspace,” Ocean Engineering, vol. 249, p. 110845, 2022. doi: 10.1016/j.oceaneng.2022.110845

[96] 
H. Liang, H. Li, and D. Xu, “Nonlinear model predictive trajectory tracking control of underactuated marine vehicles: Theory and experiment,” IEEE Trans. Industrial Electronics, vol. 68, no. 5, pp. 4238–4248, 2021. doi: 10.1109/TIE.2020.2987284

[97] 
W. Wang, L. A. Mateos, S. Park, P. Leoni, B. Gheneti, F. Duarte, C. Ratti, and D. Rus, “Design, modeling, and nonlinear model predictive tracking control of a novel autonomous surface vehicle,” in Proc. IEEE Int. Conf. Robotics and Automation, 2018, pp. 6189–6196.

[98] 
W. Wang, T. Shan, P. Leoni, D. FernándezGutiérrez, D. Meyers, C. Ratti, and D. Rus, “Roboat II: A novel autonomous surface vessel for urban environments,” in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, 2020, pp. 1740–1747.

[99] 
R. M. Saback, A. G. S. Conceicao, T. L. M. Santos, J. Albiez, and M. Reis, “Nonlinear model predictive control applied to an autonomous underwater vehicle,” IEEE Journal of Oceanic Engineering, vol. 45, no. 3, pp. 799–812, 2019.

[100] 
J. Wang, Z. Wu, M. Tan, and J. Yu, “Model predictive controlbased depth control in gliding motion of a gliding robotic dolphin,” IEEE Trans. Systems,Man,and Cybernetics: Systems, vol. 51, no. 9, pp. 5466–5477, 2021. doi: 10.1109/TSMC.2019.2956531

[101] 
E. Yang and D. Gu, “Nonlinear formationkeeping and mooring control of multiple autonomous underwater vehicles,” IEEE/ASME Trans. Mechatronics, vol. 12, no. 2, pp. 164–178, 2007. doi: 10.1109/TMECH.2007.892826

[102] 
R. Cui, S. S. Ge, B. V. E. How, and Y. S. Choo, “Leaderfollower formation control of underactuated autonomous underwater vehicles,” Ocean Engineering, vol. 37, no. 17–18, pp. 1491–1502, 2010. doi: 10.1016/j.oceaneng.2010.07.006

[103] 
Y.L. Wang and Q.L. Han, “Networkbased modelling and dynamic output feedback control for unmanned marine vehicles in network environments,” Automatica, vol. 91, pp. 43–53, 2018. doi: 10.1016/j.automatica.2018.01.026

[104] 
Y.L. Wang, Q.L. Han, M.R. Fei, and C. Peng, “Networkbased TS fuzzy dynamic positioning controller design for unmanned marine vehicles,” IEEE Trans. Cybernetics, vol. 48, no. 9, pp. 2750–2763, 2018. doi: 10.1109/TCYB.2018.2829730

[105] 
H. Li and Y. Shi, Robust Receding Horizon Control for Networked and Distributed Nonlinear Systems. Springer, 2017.

[106] 
H. Wei, Q. Sun, J. Chen, and Y. Shi, “Robust distributed model predictive platooning control for heterogeneous autonomous surface vehicles,” Control Engineering Practice, vol. 107, p. 104655, 2021. doi: 10.1016/j.conengprac.2020.104655

[107] 
H. Zheng, R. R. Negenborn, and G. Lodewijks, “Fast ADMM for distributed model predictive control of cooperative waterborne AGVs,” IEEE Trans. Control Systems Technology, vol. 25, no. 4, pp. 1406–1413, 2016.

[108] 
H. Zheng, R. R. Negenborn, and G. Lodewijks, “Robust distributed predictive control of waterborne AGVsA cooperative and costeffective approach,” IEEE Trans. Cybernetics, vol. 48, no. 8, pp. 2449–2461, 2017.

[109] 
L. Chen, H. Hopman, and R. R. Negenborn, “Distributed model predictive control for vessel train formations of cooperative multivessel systems,” Transportation Research Part C: Emerging Technologies, vol. 92, pp. 101–118, 2018. doi: 10.1016/j.trc.2018.04.013

[110] 
L. Chen, H. Hopman, and R. R. Negenborn, “Distributed model predictive control for cooperative floating object transport with multivessel systems,” Ocean Engineering, vol. 191, p. 106515, 2019. doi: 10.1016/j.oceaneng.2019.106515

[111] 
L. Chen, Y. Huang, H. Zheng, H. Hopman, and R. Negenborn, “Cooperative multivessel systems in urban waterway networks,” IEEE Trans. Intelligent Transportation Systems, vol. 21, no. 8, pp. 3294–3307, 2020. doi: 10.1109/TITS.2019.2925536

[112] 
H. Li, P. Xie, and W. Yan, “Receding horizon formation tracking control of constrained underactuated autonomous underwater vehicles,” IEEE Trans. Industrial Electronics, vol. 64, no. 6, pp. 5004–5013, 2017. doi: 10.1109/TIE.2016.2589921

[113] 
F. Fahimi, “Nonlinear model predictive formation control for groups of autonomous surface vessels,” Int. Journal of Control, vol. 80, no. 8, pp. 1248–1259, 2007. doi: 10.1080/00207170701280911

[114] 
H. Wei, C. Shen, and Y. Shi, “Distributed Lyapunovbased model predictive formation tracking control for autonomous underwater vehicles subject to disturbances,” IEEE Trans. Systems,Man,and Cybernetics: Systems, vol. 51, no. 8, pp. 5198–5208, 2021. doi: 10.1109/TSMC.2019.2946127

[115] 
S. L. de Oliveira Kothare and M. Morari, “Contractive model predictive control for constrained nonlinear systems,” IEEE Trans. Automatic Control, vol. 45, no. 6, pp. 1053–1071, 2000. doi: 10.1109/9.863592

[116] 
C. Shen, Y. Shi, and B. Buckham, “Trajectory tracking control of an autonomous underwater vehicle using Lyapunovbased model predictive control,” IEEE Trans. Industrial Electronics, vol. 65, no. 7, pp. 5796–5805, 2018. doi: 10.1109/TIE.2017.2779442

[117] 
G. Lv, Z. Peng, H. Wang, L. Liu, D. Wang, and T. Li, “Extendedstateobserverbased distributed model predictive formation control of underactuated unmanned surface vehicles with collision avoidance,” Ocean Engineering, vol. 238, p. 109587, 2021.

[118] 
N. T. Hung, A. M. Pascoal, and T. A. Johansen, “Cooperative path following of constrained autonomous vehicles with model predictive control and eventtriggered communications,” Int. Journal of Robust and Nonlinear Control, vol. 30, no. 7, pp. 2644–2670, 2020. doi: 10.1002/rnc.4896

[119] 
Y. Yang, Y. Wang, C. Manzie, and Y. Pu, “Realtime distributed MPC for multiple underwater vehicles with limited communication datarates,” in Proc. IEEE American Control Conf., 2021, pp. 3314–3319.

[120] 
G. Lv, Z. Peng, L. Liu, and J. Wang, “Barriercertified distributed model predictive control of underactuated autonomous surface vehicles via neurodynamic optimization,” IEEE Trans. Systems,Man,and Cybernetics: Systems, pp. 1–13, 2022.

[121] 
M. van Pampus, A. Haseltalab, V. Garofano, V. Reppa, Y. Deinema, and R. Negenborn, “Distributed leaderfollower formation control for autonomous vessels based on model predictive control,” in Proc. IEEE European Control Conf., 2021, pp. 2380–2387.

[122] 
S. Krupínski, G. Allibert, M.D. Hua, and T. Hamel, “An inertialaided homographybased visual servo control approach for (almost) fully actuated autonomous underwater vehicles,” IEEE Trans. Robotics, vol. 33, no. 5, pp. 1041–1060, 2017. doi: 10.1109/TRO.2017.2700010

[123] 
K. Zhang, Y. Shi, and H. Sheng, “Robust nonlinear model predictive control based visual servoing of quadrotor UAVs,” IEEE/ASME Trans. Mechatronics, vol. 26, no. 2, pp. 700–708, 2021. doi: 10.1109/TMECH.2021.3053267

[124] 
S. HeshmatiAlamdari, A. Eqtami, G. C. Karras, D. V. Dimarogonas, and K. J. Kyriakopoulos, “A selftriggered visual servoing model predictive control scheme for underactuated underwater robotic vehicles,” in Proc. IEEE Int. Conf. Robotics and Automation, 2014, pp. 3826–3831.

[125] 
J. Gao, A. A. Proctor, Y. Shi, and C. Bradley, “Hierarchical model predictive imagebased visual servoing of underwater vehicles with adaptive neural network dynamic control,” IEEE Trans. Cybernetics, vol. 46, no. 10, pp. 2323–2334, 2016. doi: 10.1109/TCYB.2015.2475376

[126] 
J. Gao, X. Liang, Y. Chen, L. Zhang, and S. Jia, “Hierarchical imagebased visual servoing of underwater vehicle manipulator systems based on model predictive control and active disturbance rejection control,” Ocean Engineering, vol. 229, p. 108814, 2021. doi: 10.1016/j.oceaneng.2021.108814

[127] 
A. Haseltalab and R. R. Negenborn, “Model predictive maneuvering control and energy management for allelectric autonomous ships,” Applied Energy, vol. 251, p. 113308, 2019. doi: 10.1016/j.apenergy.2019.113308

[128] 
N. Yang, D. Chang, M. JohnsonRoberson, and J. Sun, “Energyoptimal control for autonomous underwater vehicles using economic model predictive control,” IEEE Trans. Control Systems Technology, 2022. DOI: 10.1109/TCST.2022.3143366

[129] 
K. Wang, J. Li, X. Yan, L. Huang, X. Jiang, Y. Yuan, R. Ma, and R. R. Negenborn, “A novel bilevel distributed dynamic optimization method of ship fleets energy consumption,” Ocean Engineering, vol. 197, p. 106802, 2020. doi: 10.1016/j.oceaneng.2019.106802

[130] 
G. Bracco, M. Canale, and V. Cerone, “Optimizing energy production of an inertial sea wave energy converter via model predictive control,” Control Engineering Practice, vol. 96, p. 104299, 2020. doi: 10.1016/j.conengprac.2020.104299

[131] 
A. Bourgois, “Safe & collaborative autonomous underwater docking,” Ph.D. dissertation, ENSTA BretagneÉcole nationale supérieure de techniques avancées Bretagne, 2021.

[132] 
G. Bitar, A. B. Martinsen, A. M. Lekkas, and M. Breivik, “Trajectory planning and control for automatic docking of ASVs with fullscale experiments,” IFACPapersOnLine, vol. 53, no. 2, pp. 14488–14494, 2020. doi: 10.1016/j.ifacol.2020.12.1451

[133] 
M. C. Nielsen, T. A. Johansen, and M. Blanke, “Cooperative rendezvous and docking for underwater robots using model predictive control and dual decomposition,” in Proc. IEEE European Control Conf., 2018, pp. 14–19.

[134] 
D. M. Rachman, A. Maki, Y. Miyauchi, and N. Umeda, “Warmstarted semionline trajectory planner for ship’s automatic docking (berthing),” Ocean Engineering, vol. 252, p. 111127, 2022.

[135] 
N. Van Eck and L. Waltman, “Software survey: VOSviewer, a computer program for bibliometric mapping,” Scientometrics, vol. 84, no. 2, pp. 523–538, 2010. doi: 10.1007/s1119200901463

[136] 
L. Ljung, “Perspectives on system identification,” Annual Reviews in Control, vol. 34, no. 1, pp. 1–12, 2010. doi: 10.1016/j.arcontrol.2009.12.001

[137] 
C. De Persis and P. Tesi, “Formulas for datadriven control: Stabilization, optimality, and robustness,” IEEE Trans. Automatic Control, vol. 65, no. 3, pp. 909–924, 2020. doi: 10.1109/TAC.2019.2959924

[138] 
H. J. Van Waarde, J. Eising, H. L. Trentelman, and M. K. Camlibel, “Data informativity: A new perspective on datadriven analysis and control,” IEEE Trans. Automatic Control, vol. 65, no. 11, pp. 4753–4768, 2020. doi: 10.1109/TAC.2020.2966717

[139] 
J. Berberich, J. Köhler, M. A. Müller, and F. Allgöwer, “Datadriven model predictive control with stability and robustness guarantees,” IEEE Trans. Automatic Control, vol. 66, no. 4, pp. 1702–1717, 2021. doi: 10.1109/TAC.2020.3000182

[140] 
J. Coulson, J. Lygeros, and F. Dorfler, “Distributionally robust chance constrained dataenabled predictive control,” IEEE Trans. Automatic Control, 2021.

[141] 
E. Elokda, J. Coulson, P. N. Beuchat, J. Lygeros, and F. Dörfler, “Dataenabled predictive control for quadcopters,” Int. Journal of Robust and Nonlinear Control, vol. 31, no. 18, pp. 8916–8936, 2021. doi: 10.1002/rnc.5686

[142] 
P. Tøndel, T. A. Johansen, and A. Bemporad, “An algorithm for multiparametric quadratic programming and explicit MPC solutions,” Automatica, vol. 39, no. 3, pp. 489–497, 2003. doi: 10.1016/S00051098(02)002509

[143] 
A. Alessio and A. Bemporad, “A survey on explicit model predictive control,” ser. Lecture Notes in Control and Information Sciences. Berlin, Heidelberg: Springer, 2009, vol. 384, pp. 345–369.

[144] 
H. Wei, K. Zhang, and Y. Shi, “Distributed minmax MPC for dynamically coupled nonlinear systems: A selftriggered approach,” IFACPapersOnLine, vol. 53, no. 2, pp. 6037–6042, 2020. doi: 10.1016/j.ifacol.2020.12.1671

[145] 
H. Wei, K. Zhang, and Y. Shi, “Selftriggered minmax DMPC for asynchronous multiagent systems with communication delays,” IEEE Trans. Industrial Informatics, vol. 18, no. 10, pp. 6809–6817, 2022. doi: 10.1109/TII.2021.3127197

[146] 
S. Richter, C. N. Jones, and M. Morari, “Computational complexity certification for realtime MPC with input constraints based on the fast gradient method,” IEEE Trans. Automatic Control, vol. 57, no. 6, pp. 1391–1403, 2011.

[147] 
M. N. Zeilinger, D. M. Raimondo, A. Domahidi, M. Morari, and C. N. Jones, “On realtime robust model predictive control,” Automatica, vol. 50, no. 3, pp. 683–694, 2014. doi: 10.1016/j.automatica.2013.11.019

[148] 
Z. Du, R. R. Negenborn, and V. Reppa, “Colregscompliant collision avoidance for physically coupled multivessel systems with distributed MPC,” Ocean Engineering, vol. 260, p. 111917, 2022.

[149] 
Z. Jia, H. Lu, S. Li, and W. Zhang, “Distributed dynamic rendezvous control of the AUVUSV joint system with practical disturbance compensations using model predictive control,” Ocean Engineering, vol. 258, p. 111268, 2022.

[150] 
H. Esen, M. Adachi, D. Bernardini, A. Bemporad, D. Rost, and J. Knodel, “Control as a service (CaaS) cloudbased software architecture for automotive control applications,” in Proc. 2nd Int. Workshop Swarm at the Edge of the Cloud, 2015, pp. 13–18.

[151] 
Q. Sun and Y. Shi, “Model predictive control as a secure service for cyberphysical systems: A cloudedge framework,” IEEE Internet of Things Journal, 2021. DOI: 10.1109/JIOT.2021.3091981

[152] 
H. Ishii, Y. Wang, and S. Feng, “An overview on multiagent consensus under adversarial attacks,” Annual Reviews in Control, vol. 53, pp. 252–272, 2022. doi: 10.1016/j.arcontrol.2022.01.004

[153] 
D. Zhang, G. Feng, Y. Shi, and D. Srinivasan, “Physical safety and cyber security analysis of multiagent systems: A survey of recent advances,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 319–333, 2021. doi: 10.1109/JAS.2021.1003820

[154] 
J. Chen and Y. Shi, “Stochastic model predictive control framework for resilient cyberphysical systems: Review and perspectives,” Philosophical Transactions of the Royal Society A, vol. 379, no. 2207, p. 20200371, 2021. doi: 10.1098/rsta.2020.0371

[155] 
Q. Sun, K. Zhang, and Y. Shi, “Resilient model predictive control of cyberphysical systems under DoS attacks,” IEEE Trans. Industrial Informatics, vol. 16, no. 7, pp. 4920–4927, 2020. doi: 10.1109/TII.2019.2963294

[156] 
Q. Sun, J. Chen, and Y. Shi, “Eventtriggered robust mpc of nonlinear cyberphysical systems against DoS attacks,” Science China Information Sciences, vol. 65, no. 1, pp. 1–17, 2022.

[157] 
I. R. Bertaska and K. D. von Ellenrieder, “Experimental evaluation of supervisory switching control for unmanned surface vehicles,” IEEE Journal of Oceanic Engineering, vol. 44, no. 1, pp. 7–28, 2018.

[158] 
A. A. R. Newaz, T. Alam, G. M. Reis, L. Bobadilla, and R. N. Smith, “Longterm autonomy for AUVs operating under uncertainties in dynamic marine environments,” IEEE Robotics and Automation Letters, vol. 6, no. 4, pp. 6313–6320, 2021. doi: 10.1109/LRA.2021.3091697

[159] 
A. Babić, G. Vasiljević, and N. Mišković, “Vehicleintheloop framework for testing longterm autonomy in a heterogeneous marine robot swarm,” IEEE Robotics and Automation Letters, vol. 5, no. 3, pp. 4439–4446, 2020. doi: 10.1109/LRA.2020.3000426

[160] 
L. Zhang, S. Zhuang, and R. D. Braatz, “Switched model predictive control of switched linear systems: Feasibility, stability and robustness,” Automatica, vol. 67, pp. 8–21, 2016. doi: 10.1016/j.automatica.2016.01.010

[161] 
K. Zhang and Y. Shi, “Adaptive model predictive control for a class of constrained linear systems with parametric uncertainties,” Automatica, vol. 117, p. 108974, 2020.

[162] 
R. Scattolini, “Architectures for distributed and hierarchical model predictive control–A review,” Journal of Process Control, vol. 19, no. 5, pp. 723–731, 2009. doi: 10.1016/j.jprocont.2009.02.003

[163] 
P. D. Christofides, R. Scattolini, D. M. de la Pena, and J. Liu, “Distributed model predictive control: A tutorial review and future research directions,” Computers &Chemical Engineering, vol. 51, pp. 21–41, 2013.

[164] 
R. R. Negenborn and J. M. Maestre, “Distributed model predictive control: An overview and roadmap of future research opportunities,” IEEE Control Systems Magazine, vol. 34, no. 4, pp. 87–97, 2014. doi: 10.1109/MCS.2014.2320397

[165] 
T. Yang, X. Yi, J. Wu, Y. Yuan, D. Wu, Z. Meng, Y. Hong, H. Wang, Z. Lin, and K. H. Johansson, “A survey of distributed optimization,” Annual Reviews in Control, vol. 47, pp. 278–305, 2019. doi: 10.1016/j.arcontrol.2019.05.006
