Fig 1

Diagram of a USV path following control"

Fig 2

Coordinate system of a USV"

Fig 3

Diagram of guidance module for a RL-based controller"

Fig 4

LOS guidance based on the look-ahead distance"

Fig 5

Diagram of a straight LOS guidance vector field"

Fig 6

Diagram of a curved LOS guidance vector field"

Fig 7

Flowchart for generating a random path"

Fig 8

Detailed implementation of the random straight-line path and random curve path"

Fig 9

Instance diagram of random path dataset"

Fig 10

Dataset of 28 standard paths"

Fig 11

Composition and interaction of modules under a step function in a customized Gym environment"

Table 1

Constraints and ranges for variables in state and action spaces"

Fig 12

Diagram of the policy network structure."

Fig 13

Training curve of the LSTM-DPPO"

Fig 14

Trajectory of a typical polygonal path following with LSTM-DPPO"

Fig 15

Trajectory of a typical curve path following with LSTM-DPPO"

Fig 16

History of the heading angle and cross-track errors during the typical polygonal path following experiments with various training epochs"

Fig 17

History of the heading angle and cross-track errors during the typical curved path following experiments with various training epochs"

Fig 18

Trajectories of following the typical polygonal path with four control methods"

Fig 19

Trajectories of following the typical curved path with four control methods"

Fig 20

History of the heading angle and cross-track errors during the typical polygonal path following experiments with four control methods"

Table 2

Comparison results of the RMS for H.A.E. and C.T.E. during the path following validation"

Fig 21

History of the heading angle and cross-track errors during the typical curved path following experiments with four control methods"

Table 3

Comparison results of the RMS for H.A.E. and C.T.E. in the varis scale of data set"