## 3 Materials and Methods
### Multi-Scale Positioning for Waypoint Navigation
\begin{table}
\begin{tabular}{l c c c} \hline \hline \multicolumn{4}{c}{**High-Dimensional Space Map Dataset**} \\ \hline Methods & OPT\({}^{\star}\) & ACC\({}^{\star}\) & TS\({}^{\star}\) \\ Dijkstra’s Algorithm & 0 & 0.71 & 0.49 \\ A\({}^{\star}\)—_A-star algorithm_ & 0.13 & 0.93 & 0.58 \\ D\({}^{\star}\) Lite & 0.59 & 0.77 & 0.38 \\ RRT—_Rapidly-exploring Random Trees_ & 0.04 & 0.89 & 0.74 \\ RRT\({}^{\star}\) & 0.16 & 0.87 & 0.81 \\ Bug Algorithms & 0.48 & 0.83 & 0.78 \\ Monte Carlo & 0.60 & 0.43 & 0.24 \\ DQN & 0.75 & 0.62 & 0.43 \\ Tangent Bug Algorithms & 0.56 & 0.89 & 0.81 \\ SAIL & 0.63 & 0.92 & 0.91 \\ Cuckoo Search Algorithm. & 0.48 & 0.93 & 0.94 \\ HDPP & 0.72 & 0.91 & 0.97 \\ \multicolumn{4}{c}{**Motion planning Dataset**} \\ Methods & OPT\({}^{\star}\) & ACC\({}^{\star}\) & TS\({}^{\star}\) \\ Dijkstra’s Algorithm & 0 & 0.63 & 0.51 \\ A\({}^{\star}\)—_A-star algorithm_ & 0.14 & 0.91 & 0.45 \\ D\({}^{\star}\) Lite & 0.58 & 0.74 & 0.49 \\ RRT—_Rapidly-exploring Random Trees_ & 0.10 & 0.92 & 0.63 \\ RRT\({}^{\star}\) & 0.12 & 0.94 & 0.57 \\ Bug Algorithms & 0.52 & 0.79 & 0.61 \\ Monte Carlo & 0.35 & 0.31 & 0.47 \\ DQN & 0.52 & 0.54 & 0.66 \\ Tangent Bug Algorithms & 0.60 & 0.79 & 0.77 \\ SAIL & 0.64 & 0.89 & 0.83 \\ Cuckoo Search Algorithm. & 0.46 & 0.90 & 0.94 \\ HDPP & 0.81 & 0.87 & 0.94 \\ \multicolumn{4}{c}{**Simulation Dataset**} \\ Methods & OPT\({}^{\star}\) & ACC\({}^{\star}\) & TS\({}^{\star}\) \\ Dijkstra’s Algorithm & 0 & 0.60 & 0.55 \\ A\({}^{\star}\)—_A-star algorithm_ & 0.13 & 0.92 & 0.64 \\ D\({}^{\star}\) Lite & 0.69 & 0.78 & 0.43 \\ RRT—_Rapidly-exploring Random Trees_ & 0.11 & 0.89 & 0.79 \\ RRT* & 0.21 & 0.90 & 0.72 \\ Bug Algorithms & 0.48 & 0.84 & 0.78 \\ Monte Carlo & 0.65 & 0.60 & 0.57 \\ DQN & 0.87 & 0.84 & 0.68 \\ Tangent Bug Algorithms & 0.56 & 0.91 & 0.86 \\ SAIL & 0.62 & 0.91 & 0.93 \\ Cuckoo Search Algorithm. & 0.46 & 0.95 & 0.98 \\ HDPP & 0.83 & 0.93 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison on 6 DOF (degree-of-freedom) robotic arm. We conducted 50 tests on sports in 10 scenarios. We use the three metrics mentioned in Section 4.3. to quantify performance. much attention to the safety issues in robot motion. In order to make a fair comparison with these works, we follow their experimental settings and generate no more than 70% of the waypoints based on the search algorithm for our HDPP. Despite the addition of such constraints, the experimental results show that the proposed HDPP works well in anti-collision, and the scale of waypoints and the number of gait updates are not too different. At the same time, we also test the hypothesis that reinforcement learning is less efficient in calculating rewards under time constraints in high-dimensional path planning. Table 3 shows the performance of HDPP algorithm on three data sets. As shown in Tables 2 and 3, on the basis of ensuring the robustness of planning, our HDPP has greatly improved in the two links of waypoint optimization and safety. It can obtain stable waypoint planning results in a short time and minimize the probability of collision with obstacles, which is crucial in the actual robot path planning. **Qualitative Results. ** Figure 4 shows the selected path planning results of the qualitative experiment on six-degree-of-freedom robotic arm. We visualized the path planning for different algorithms. Specifically, the higher guidance cost was allocated to the entire obstacle area that caused the dead end, and it was drawn on the map in green form, and the bypass that was not searched and traversed to the target was not planned to pass through. The map is displayed in gray. Figure 4 depicts how methods including HDPP adaptively perform searches for targets in the same map. **The Result of Optimization and Gradient Balance**. We set up experiments to explore the effects of patch optimization and gradient balance modules on model training. In this section, we selected the initial high-dimensional spatial motion scene for testing.