## 4 Simulation Experiment and Results
### Case 2: Complex Scenario
#### 4.3.2 Discussion  
In terms of computational efficiency, the results of the complex scenario are similar to the results of the simple scenario, with the PRM having the shortest computation time and PH-RPM being in second place, taking less time than the RPM. This is due to the effect produced by the introduction of the initial value strategy proposed in this paper. The computation time consumed by the A* algorithm becomes the longest due to the increase in the search range required for the complex scenario. RRT* is more efficient in searching in the complex scenario compared to A*, but still not comparable to the PRM and the PH-RPM with efficient probabilistic roadmap construction strategies.  
Combining the path lengths, passing times, path diagrams, and speed and angle variations, the results in the complex scenario are different from the results in the simple scenario; the A* algorithm has the shortest path in the complex scenario. This is because the number of grids explored by the A* algorithm in the complex scenario is large enough so that the path length is minimized, but it cannot be applied to the PMCU pushing path planning directly because the shape constraints and kinematic constraints of the PMCU are not considered. Although the traditional RPM algorithm for complex scenario planning successfully solves and obtains the result of \(t_{f}=136.35\) s, \(L=54.77\) m, the planned path passes through multiple obstacles, and no valid solution is obtained at all. As for the path planned by the PH-RPM, the path of the whole process of cabin motion is collision-free so that the path planning can be realized under the condition that the outer contour of the cabin does not collide with the obstacles and the obtained motion time is \(t_{f}=239.78\) s, which is in the acceptable range. The path length is shorter compared with the RRT* and PRM algorithms. However, there is a 13.9% gap in path length compared to the A* algorithm. This part of the gap is due to the way the A* algorithm searches for a path. This is because A* will only search and judge the eight adjacent grids of the current node, which means that the path of the A* algorithm will be infinitely close to the obstacles when they exist nearby. It's also more indicative of the advantage in length of the paths planned by A* considering the object as a point. Therefore, the path of A* is usually regarded as the theoretical shortest path without considering the outer contour and kinematic constraints. The path planned by the PH-RPM proposed in this paper ensures the outer contour of the PMCU does not collide with obstacles because of the constraints imposed by the path constraints of the optimal control model. The gap in path length is acceptable compared to the path planned by A*. For production applications, it is more important to get a path to pass through obstacles than to get the shortest path. RRT* and PRM can plan paths, but the optimality and practicality of the planned paths are not high, and they do not take kinematic constraints into account either. Therefore, they cannot be used as PMCU path planning as well. The path planned by PH-RPM can be considered as the optimal path under the complex scenario, which satisfies the kinematic constraints.  
In summary, the PH-RPM algorithm in this paper can be used to solve the PMCU pushing path planning problem in the complex scenario, and the algorithm has stronger applicability to complex scenarios compared with the traditional RPM algorithm. Compared with other path planning algorithms, it can realize the planning of accessible paths in complex scenarios with careful consideration of kinematic constraints, and the planned paths have shorter path lengths.