## 3 Materials and Methods
### Multi-Scale Positioning for Waypoint Navigation
## 5 Conclusions

In this article, we investigate the problem of exploiting the multi-scale and discriminative information for multi-degree-of-freedom dynamic motion planning in high dimensional space, and our novel approach--HDPP--is proposed. A multi-scale positioning framework with patch-based waypoint refinement is employed to learn high-level features, which contain strongly represented semantic and geometric information, and dynamically fuse them. This mechanism can adaptively locate important waypoints, and then refine the planning results gradually through iteration and eliminate redundancy. In order to narrow the scope of the model and make quick calculations, a patch-based selection and refining scheme is proposed to dynamically capture key regions for path planning by computing gradient accumulation. For the selection of planning feature points, we balance the gradients from different types of waypoints to avoid over-optimizing one of them. The experiments conducted on both in reality and simulation environment demonstrate the effectiveness of the proposed method. However, although our HDPP can achieve more than 95% efficient obstacle avoidance for multi-degree-of-freedom motion targets, there are still some limitations. For example, collisions still exist in high-dimensional path planning due to the anticipation of fast path planning, even though we have focused on collision costs in design. Due to the existence of multiple efficient paths in multi-DOF and multi-dimensional space, it is difficult to evaluate the optimal scheme. These problems will influence the performance of our model. In the future, we want to find an appropriate approach to balance the relationship between planning efficiency and equilibrium collision, which is devastating to robots, and design a set of evaluation rules to standardize the analysis of high-dimensional path planning. In addition, we hope that our work can arouse more people's attention to the safety of high-dimensional spatial motion planning and provide a way to improve the real-time performance of planning. Conceptualization, [PERSON] and J.H. ; methodology, [PERSON]; software, [PERSON]; validation, [PERSON]; formal analysis, [PERSON]; investigation, [PERSON]; resources, [PERSON] and J.H. ; data curation, [PERSON]; writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON] and [PERSON]; visualization, [PERSON]; supervision, [PERSON]; project administration, [PERSON] and [PERSON]; funding acquisition, [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript. This research was funded by National Key Research and Development Program Project (No. 2020 YFB1005900), National Natural Science Foundation of China (No. 61773027 and 62076014), and Industrial Internet Innovation and Development Project (No. 135060009002). \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Stabilizing Gradient** & \(\surd\) & & & & & \(\surd\) \\ \hline Gradient-based Location & & \(\surd\) & & & & \(\surd\) \\ Patch Selection and Refining & & & \(\surd\) & \(\surd\) & \(\surd\) & \\ Eliminate camera distortion & & & & \(\surd\) & & \\ Position correction & & & & & \(\surd\) & \(\surd\) \\ \hline
3-6 Robot & 0.83 & 0.87 & 0.69 & 0.71 & 0.73 & 0.94 \\
2-2 Robot & 0.91 & 0.89 & 0.83 & 0.91 & 0.95 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of HDPP algorithm on three data sets. We have summarized the test results of HDPP on three data sets. Each data set contains three rows of data, the first row is the minimum value, the second row is the maximum value, and the third row is the average. ## References

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