2.1

Mathematical abstraction and modeling of ship autonomous navigation environment

The autonomous navigation environment of a ship includes static environment and dynamic environment. The static environment refers to the natural navigation environment composed of infrastructure, wind, waves and current, and obstacles to navigation, etc. The modeling can be completed by three-dimensional model construction method². Dynamic environment refers to the dynamic environment modeling with real-time real perceptual information data based on the static environment modeling by using multi-source sensing devices such as vision, AIS and radar to integrate the external traffic environment perception data^{3, 4}. Figure 1 shows the overall architecture of modeling the autonomous navigation environment of ships:

Figure 1.

Overall architecture of virtual simulation modeling of ship autonomous navigation environment.

2.2

Research on ship operation motion model and environmental coupling

Based on the interaction of the hull, propeller and steering gear, a multi-degree of freedom motion response model of the ship was established. Considering the shallow water effect and the hysteresis of the drive response, the multi-degree of freedom motion response characteristics of the ship under different state parameters were studied, and the ship steering model suitable for the dynamic collision avoidance process was constructed. Considering the environmental disturbance such as wind, wave and current, the mathematical model of disturbance force is established and introduced into the ship maneuvering response equation, the change law of ship motion response under the disturbance is analyzed, and the parameters of the model are modified⁵. The overall structure of the ship maneuvering response model is as follows in Figure 2:

Figure 2.

Overall architecture of ship manipulation response model construction.

The second-order nonlinear response model of ship maneuvering motion is shown as follows:

where T1, T2 and T3 are time constants, K is the rudder angle gain coefficient, γ is the yaw angular velocity, α is the coefficient of nonlinear term, δ is the steering angle, and δ_γ is the rudder angle required for initial direct navigation. Establish the observation equation as follows:

Thus, the identification model is transformed into a Second-Order Vector response model. Based on the response structure of numerical simulation and the measured ship data, the extended Kalman filter method is used to optimally estimate the system state x_k, and then identify the elements in λ to solve the response model parameters T1, T2, T3, K, α and·δ_γ. The correlation and regression between the ship state and environmental parameters and the above response model parameters are analyzed, and the correction method of maneuvering response model under the coupling influence of ship itself and environmental factors is established; Finally, the corresponding working conditions are selected, and the ship motion simulation is carried out based on the identified response model, which is compared with the numerical simulation and measured data to verify the generalization ability of the identification model⁶.

3.1

Research on autonomous collision avoidance algorithm based on reinforcement learning and deep supervised learning

Based on the investigation of captain’s experience, the key information needed by large merchant ships sailing in complex waters is preliminarily determined. On this basis, the selection of key information is characterized as the problem of information preprocessing and multi-modal fusion in busy waters⁷. It is planned to use principal component analysis and Transformer structure combined with attention mechanism to study the multi-modal fusion method of image, sound wave and text, so as to provide a basis for the subsequent research on collision avoidance algorithm⁸. The main structure is shown in Figure 3.

Figure 3.

Navigation data preprocessing module structure.

Then, reinforcement learning combined with artificial potential field method is used to study the autonomous collision avoidance algorithm⁹.

The reward function group ℝ is designed. For the autonomous collision avoidance of large merchant ships, sub-tasks are divided. Each sub-reward function reflects the details of obstacle avoidance tasks, including the following aspects:

R_t is defined as a time reward and punishment function, as follows:

where, r_f is the arrival sign of the ship at the end of navigation. If the ship does not arrive at present, it will be set as 0, and if it arrives, it will be set as 1; t_exp is the expected time required for obstacle avoidance navigation, which is analyzed by human experts in many real ship tests; t₀ is the current sailing time; t_thres is the end threshold of the algorithm to avoid falling into the local optimal solution. This value is set artificially.

R_c: For the function of ship collision hazard, the space collision hazard is defined as follows:

where d₁ represents the shortest safety distance for collision avoidance, and d₂ represents the allowable influence range, which depends on the task.

R_r: For the route deviation reward and punishment function. After consulting the captain and expert experience, set the allowable deviation range of the course under sail. The definition is as follows:

S_bumpur is the area of the overlapping part of the ship area, and S_thres is the artificially set collision risk threshold. There are two types of ship domain models, as shown in Figure 4 below. The left side of Figure 4 below is the simplified collision domain model without considering the international maritime collision avoidance rules, and the right side is the simplified collision domain model considering the international maritime collision avoidance rules. In the research process, two different simplified models will be tested to observe the effect of algorithm decision-making¹⁰.

Figure 4.

Two different simplified models of the ship domain.

The ship domain model can be characterized in the following form:

Ship domains of different shapes can be controlled with different values of k and different Q parameters. The above l sub reward functions together form a one-dimensional reward function matrixℝ, and the calculation formula of the final

reward value R is also given:

where Θ is the weight parameter matrix of reward function, and the shape and size are the same as ℝ.

3.2

Study on trace control of proportional calculus based on neural network

Track control is the executive part of the collision avoidance algorithm, and its effect will be fed back to the algorithm¹¹. Therefore, it is necessary to pay attention to the fast response and accuracy of the track control algorithm to implement the collision avoidance decision accurately and reduce the noise error¹². By changing environmental factors such as wind, waves and flow in the simulation environment, the neural network can realize dynamic control of the three parameters controlled by calculus, as shown in Figure 5.

Figure 5.

Dynamic PID parameter control method based on Transformer and MLP.