## 4 Approach
### Iterative Sampling in the Neighborhood
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & **RRT** & **IK** & **SP-1** & **SP-2** & **HSPP-t** & **HSPP-pt** \\ \hline C1S1G1 & N/A & N/A & N/A & N/A & 7.66 \(\pm\) 4.61 & 11.93 \(\pm\) 5.46 \\ C1S1G2 & N/A & N/A & N/A & N/A & 8.25 \(\pm\) 5.20 & 12.54 \(\pm\) 6.89 \\ C1S2G1 & N/A & N/A & N/A & N/A & 7.48 \(\pm\) 4.47 & 13.42 \(\pm\) 7.51 \\ C1S2G2 & N/A & N/A & N/A & N/A & 8.88 \(\pm\) 6.19 & 11.58 \(\pm\) 6.23 \\ C2S1G3 & N/A & N/A & N/A & N/A & 20.70 \(\pm\) 12.43 & 13.56 \(\pm\) 5.98 \\ C2S2G3 & N/A & N/A & N/A & N/A & 21.11 \(\pm\) 13.08 & 14.71 \(\pm\) 9.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of average time consumption. Figure 9: Comparison of time consumption in all cases. In Figure 10, the comparison of the generated path length is shown. For HSPP-pt, the generated path length is basically positively correlated with the distance from the start configuration to the goal configuration, while for HSPP-t, in complex cases (CIS2G1, CIS2G2, and C2S2G3), the path length is increased due to the fact that the more complex the action, the greater the likelihood of it being caught in the local oscillations, which could increase the path length or even lead to a planning failure. ## 6 Conclusions and Future Work

This paper proposes HSPP-pt, a hybrid sampling-based algorithm for efficiently finding a collision-free path for mobile manipulators performing pick and place tasks in confined spaces. Traditional methods are not applicable to such scenarios for various reasons. HSPP-pt incorporates an SCG method for computing a collision-free mobile manipulator target configuration based on the end-effector position and rotation constraints. Also, HSPP introduces end-effector paths as reference paths and proposes a path generation method based on sampling in the neighborhood. Although there might be a possibility that the method will fall into a local minima when sampling in the neighborhood, it avoids the complexity of random sampling in high-dimensional spaces and strikes a balance between planning efficiency and the success rate. For future work, we plan to improve the planning methodology of the reference path to further reduce the time consumption, to establish a coordination mechanism to fully exploit the advantages of HSPP-pt and HSPP-t in different scenarios, and, finally, to further optimize the generated paths to improve the path quality. Furthermore, this method is currently only applicable to known static environments. However, there is potential for this method to be extended to dynamic obstacle avoidance with the utilization of rapid environmental perception and modelling. Conceptualization, H.C. and X.Z. ; methodology, H.C. and X.Z. ; software, H.C.; validation, H.C. and Y.Z. ; resources, X.Z. ; data curation, H.C.; writing--original draft preparation, H.C.; writing--review and editing, X.Z. ; visualization, H.C.; supervision, X.Z., Y.Z. and J.Z. ; project administration, J.Z. ; funding acquisition, Y.Z. and J.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by in part by the National Outstanding Youth Science Fund Project of National Natural Science Foundation of China, grant number 52025054, and in part by the Major Research Plan of the National Natural Science Foundation of China, grant number 92048301. Not applicable. Figure 10: Comparison of the lengths of the generated paths in all cases. ## Informed Consent Statement: Not applicable. **Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. **Conflicts of Interest:** The authors declare no conflicts of interest. ## References

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