## 3 Materials and Methods
### Multi-Scale Positioning for Waypoint Navigation
In addition to the above two data sets, we also introduced a simulation environment for feasibility testing in the experiment. The collection environment of the experiment is the gazebo simulation environment under the Linux system, which is similar to the environment of the High-dimensional space map and is constructed to eliminate the environmental impact of the entity. We set up the digital manipulator and manually control it to move, so as to realize the parameter recording of the steering gear. This data set contains ten independent environments, and each combination of scenes and obstacles collects ten steering gear parameters and gait sequences, which provides reliable support for qualitative analysis and feasibility analysis. We should notice that these data are dynamic. In addition, we added randomly generated obstacle detection in the test session of the experiment as a way to verify the effectiveness of HDPP in dynamic planning. ### Methods for Experiment

The proposed HDPP is compared with the baseline methods of multi-DOF path planning. The experiment-related algorithms and improvement details are shown below:

**HDPP. ** As the backbone of this algorithm, we adopted U-Net [40] with the VGG-16 [41] backbone network, the last layer of which is activated by Relu (Rectified Linear Unit) constrain the guiding graph. For the multi-scale feature module, we use the feature pyramid to analyze the receptive field and use the Chebyshev distance as a heuristic function suitable for the eight-neighborhood grid world. In addition, in order to achieve high-precision and high-dimensional planning, we introduce a patch optimization and selection module. In this module, we use MSE (mean-square error) loss to filter the Top K (in this paper, K = 10) patches, and introduce the disappear parameter to control the number of patches to adjust the detection accuracy and calculations. The relationship between the quantity. We also introduce gradient balance in the network structure to prevent overfitting. **Baseline. ** In order to evaluate the superiority of HDPP in high-dimensional space motion planning, we adopted the typical path planner and the following data-driven planner as benchmark competitors. These competitors have the same guarantee of planning success in design as we do. We have extended the author's online implementation. * Tangent Bug Algorithms [42]. This is a real-time path planning algorithm for detecting surrounding obstacles, also a variant of Bug1 and Bug2. Tangent Bug is different from the previous two algorithms. Only when the distance from the obstacle is 0, the characteristics of the obstacle are found to be different. The variable R is defined. As long as there is an obstacle within the distance R, it will be detected. Next, take the \begin{table}
\begin{tabular}{l l l} \hline \hline
**Degree of Freedom** & **Original** & **Removing Redundancy** \\ \hline
2-DOF Four-legged car & 37 & 14 \\
3-DOF Robotic arm & 59 & 31 \\
6-DOF Robotic arm & 93 & 56 \\
10-DOF Robotic arm & 152 & 72 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: HDPP waypoint effect in high-dimensional space. robot as a single point to detect whether there is an obstacle on the line between the current position and the target point, and respond to it. We adjusted the R parameters of Tangent Bug, introduced \(\upmu\) parameters, and calculated R according to the robot's motion environment. Compared with the traditional method, this method has certain advantages in the real-time obstacle avoidance scene of the robotic arm. We hope to introduce this algorithm to compare the effect of HDPP at the obstacle avoidance level. * SAIL (Summation-based incremental learning). High search efficiency is achieved by learning heuristic functions from demonstrations. Distinct from HDPP, SAIL uses hand-designed features to introduce prior information into the algorithm, such as the nodes of each target and nearest obstacle. We adjusted SAIL to adapt to the detection and planning of high-dimensional space and evaluated the effect of SAIL on the data set.