Trajectory Tracking Control of Azimuth Stern Drive Tugs Based on GRU-MPC

doi:10.16183/j.cnki.jsjtu.2024.146

Abstract

Abstract:

To address the trajectory tracking control problem of azimuth stern drive tug, a three-degree-of-freedom motion data-driven model of the tug is developed by using gated recurrent unit (GRU) neural network, and a model predictive control (MPC) trajectory tracking controller is designed based on the GRU model to overcome the limitations of the traditional control methods that rely on the precise system mechanism model. This controller regulates the tug speed and heading by adjusting the left and right rudder angles without changing the tug propeller speed. Simulation experiments are conducted to validate the effectiveness of the proposed scheme, showing that the model achieves satisfactory accuracy even under noise interference. Furthermore, by comparing the control performance under different prediction step sizes, the influences of these parameters on the control effect and solution time are explored. Due to the increase in the complexity of the optimization solution, when the prediction horizon increases, the control accuracy improves, but the solution time also rises. This study provides new ideas for the precise trajectory tracking control of tugs, and offers valuable references for the control of similar nonlinear systems.

Key words: azimuth stern drive tug control, model predictive control (MPC), gated recurrent unit (GRU) neural network, trajectory tracking control, data-driven model

CLC Number:

U664.82

LI Shijie, LIU Taixu, LIU Jialun, DONG Zhilin, XU Chengqi. Trajectory Tracking Control of Azimuth Stern Drive Tugs Based on GRU-MPC[J]. Journal of Shanghai Jiao Tong University, 2026, 60(3): 418-426.

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参数	取值
质量/kg	187.6
排水, Δ/m³	0.187 6
型深,D/m	0.248 5
船宽,B/m	0.695 2
船长,L/m	2.152
m₁₁/kg	216.472 7
m₂₂/kg	183.490 6
m₃₃/kg	0.063 2
d₁₁/(kg·s^-1)	44.187 8
d₂₂/(kg·s^-1)	152.938 0
d₃₃/(kg·s^-1)	0.262 9

参数	e_RMSE	R²
u	0.000 5 m/s	0.956 0
v	0.008 2 m/s	0.940 2
r	0.252 5 (°)/s	0.928 4

N_p	e_RMSE/m	平均求解时间/s
1	9.49	0.03
3	3.79	0.32
5	3.51	1.15