## 6 Conclusions  
This paper is oriented to the PMCU pushing installation process of the cruise ship and mainly solves the path planning problem of the cabin pushing process. Based on the kinematic model of the pushing cabin process, a PH-RPM for solving the path planning under complex space is proposed. The main contributions of this paper can be summarized as follows:  
1. In this paper, the kinematic modeling of the PMCU pushing installation process for cruise ships is carried out, and the continuous-time optimal control model for PMCU pushing path planning is constructed based on the kinematic characteristics.
2. To solve this optimal control problem, we use the Radau pseudospectral method for discretization to a NLP and solution. For the characteristics of the NLP problem sensitive to the initial value, an initialization strategy based on a probabilistic roadmap and heuristic rule is proposed to quickly generate high-quality initial solutions and achieve fast planning of optimal paths.
3. The performance of the PH-RPM proposed in this paper is evaluated through simulation experiments and compared with well-known path planning algorithms, including A*, RRT*, and PRM, while the traditional RPM is also used for comparison. The experimental results show that the PH-RPM generates optimal or sub-optimal passable path lengths compared to other methods. Combining kinematic constraints and outer contour collision constraints, the PH-RPM generates higher-quality paths and can effectively solve the PMCU pushing path planning problem.  
In this paper, the RPM with initial value strategy (PH-RPM) is proposed and used to solve the PMCU pushing path planning problem. The method may also be used for other complex spatial path planning or motion planning problems that require consideration of kinematic constraints, like path planning for robot indoor environments, unmanned vehicles, etc. In addition to this, the RPM can be improved in the collocation points configuration strategy, and higher initial solution generation strategies may exist to further improve the initial value quality. In future research, PMCU pushing dynamic path planning with real-time environmental information and application of AI, such as reinforcement learning on cruise ship construction, will be our main research content. Since there is a temporary construction situation on the deck of the cruise ship, the real-time environmental information is likely to affect the PMCU path planning decisions. This is specifically important, considering that real-time environmental information can lead to a path that is more capable of guiding the production process, which in turn promotes the application of intelligent devices in the cruise ship construction process.  
Conceptualization, J.L. and R.D.; methodology, R.D.; software, R.D.; validation, R.D. and W.H.; formal analysis, R.D.; investigation, R.D. and W.H.; resources, J.L.; data curation, W.H.; writing--original draft preparation, R.D.; writing--review and editing, J.L., R.D. and W.H.; visualization, R.D.; supervision, J.L.; project administration, J.L.; funding acquisition, J.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the ministerial civil ship research project: \"Research on Key Technologies for Design and Construction of Typical Accommodations and Public Areas\" [Grant number 2019331].  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available in article.  
**Acknowledgments:** The authors are responsible for the contents of this publication. In addition, the authors would like to thank lab classmates for their contribution to the writing quality.  
**Conflicts of Interest:** The authors declare no conflict of interest.