## 4 Simulation Experiment and Results
### Case 1: Simple Scenario
#### 4.2.2 Discussion  
From the simulation of the simple scenario, it can be seen that the PH-RPM proposed in this paper can achieve better results in terms of computational efficiency and path computation results in this scenario. In terms of computational efficiency, the PH-RPM method takes only 1.884 s for path planning under the simple scenario, which is slightly longer than the time taken by the PRM, but it is still the second most efficient algorithm. The time cost of A* is related to the search range; the span from the starting point to the target point is smaller in the simple scenario, so A* has a smaller search range and consumes less time. RRT* is characterized by a reconnection step that tries to change existing connections to find a better path and, therefore, consumes more time. The initial value input to the RPM uses a random strategy, and poor quality of the initial values can lead to the method taking more time. The. PH-RPM uses a probabilistic roadmap and heuristic rules for the initial solution construction, and kinematic characteristics are taken into account in the computation process, so the computation time is slightly longer compared to the PRM. Compared with the RPM, we can find that the initial solution generation strategy proposed in this paper can effectively reduce the computation time of the pseudospectral method.  
Combining the path lengths, passing times, path diagrams, and speed and angle variations, it can be seen that the paths planned by the PH-RPM method proposed in this paper have the shortest passable paths and take less time. Usually, in path planning problems, we consider the path planned by the A* algorithm to be the theoretical optimal path because the A* algorithm will consider the object as a point using a grid map for planning. But in the simple scenario shown in Figure 8, since the A* algorithm uses an eight-direction move strategy, which considers that each move needs to pass through the center of the grid, the calculated path may not be the shortest path when the number of grids passed is small. Moreover, since the paths generated by the A*, RRT*, and PRM methods do not consider kinematic constraints, their paths are not directly applicable to PMCU pushing. Although the RPM takes kinematic constraints into account, the algorithm is not fully applicable to this problem as it satisfies path constraints only at collocation points, resulting in collisions of the computed paths between neighboring collocation points.  
Compared with the RPM, the velocity and orientation angle changes of the PH-RPM in the PMCU pushing process in the simple scenario are more in line with the actual movement, and the velocity and angle change rates are within a reasonable range. And the  
Figure 9: Variation of velocity and orientation angle in the simple scenario. (**A**) Variation of velocity. (**B**) Variation of orientation angle.  
angle will be fine-tuned when approaching certain key obstacle nodes to avoid them. In the actual PMCU pushing process of cruise ship production, similar to the simple scenario, the current state and speed will be adjusted in advance according to the simulation results at critical path nodes before encountering obstacles, avoiding the wide range of state adjustments after the cabin is close to the obstacles.  
In summary, compared with other path-planning algorithms, the PH-RPM algorithm can plan shorter motion paths with no collisions while considering kinematic constraints in the simple scenario.