## 3 Materials and Methods
### Multi-Scale Positioning for Waypoint Navigation
In order to stabilize the calibration and cope with different robot vision sensor installation conditions, we use the following method to perform coordinate mapping:

\[x_{k+1}=x_{k}+\sum_{i=1}^{N}\omega_{i}\cdot\mu\cdot sign(\
abla_{x},J_{i}(x_{k},y)) \tag{8}\]

\[X^{\prime\prime}=drawContours(X,k^{(..)}) \tag{1}\]0

\[X^{\prime\prime}=drawContours(X,k^{(..)}) \tag{1}\]1

where \(x_{k}\) is Optimized image in kth iteration, \(J(\alpha)\) is the loss function we use to optimize \(i\)-th image, where L is the Mean Square Error (MSE), \(\alpha_{i}\) is the confidence score of \(i\)-th bounding box. And \(\mu\) is the updated step, the weight \(\omega_{i}\) is the parameter of balancing gradients. ## 4 Experiment

In this section, we first describe the experimental datasets. Next, due to space limitations, we have carried out detailed methods settings in the second section. In the third section, we introduce the implementation details to provide scientific and detailed evaluation indicators for the experiment. In the experimental link, we first conducted an extensive experiment to evaluate HDPP's planning of moving objects in different high-dimensional spaces and horizontally compared it with other algorithms. At the same time, in order to explore the impact of HDPP on search optimality and efficiency trade-off, we also conducted a qualitative analysis, namely how HDPP effectively finds the optimal gait sequence optimization problem. ### Datasets

We adopted the following path-planning datasets include self-constructed and public with obstacle annotations to collect planning demonstrations. * High-dimensional Space Map Dataset. This is a data set we created. In the scene, we manually control the robotic arm to calibrate the position of the steering gear and perform image acquisition at a fixed frame rate. This data set is based on pelletizing application scenarios, with a total of ten environments. Each environment contains 6 different specifications of obstacles (3 \(\times\) 2, there are 3 shapes of obstacles, and each shape has 2 sizes). A single environment group consists of 600 training images, 100 verification images, and 100 test images. Obstacles of the same type are placed in different layouts. At the same time, we use robots with different degrees of freedom (as shown in Table 1) to complete the entire experiment in a reasonable time. We follow the original settings to independently train and evaluate each environment group. In addition, in order to increase the amount of data and provide a basis for more robust ablation experiments, we have performed data enhancement operations. We cropped multiple random blocks with a size of 64 \(\times\) 64 from each map and randomly generated them in the dataset scene. We use 30 of the 10 scene maps to generate 1600 training and 300 validation maps randomly. At the same time, we also constructed 200 data for testing through mapping, so as to ensure that there is no overfitting caused by the occurrence of shared maps. The entire data set contains more than 6000 sets of data for robust detection, 1900 sets of data for modular detection, and more than 2000 sets of collected data for safety collision detection. We hope to achieve the purpose offeasibility experiment and robustness detection through this original high-dimensional spatial data set. * Motion Planning Dataset [39]. This data set was selected by us as the data for qualitative experiments. The MP dataset is a collection of eight grid world environments with unique obstacle shapes created by [PERSON] et al. Each environment group is composed of 800 training maps, 100 verification maps and 100 test maps, and obstacles of the same type are placed in different layouts. We resize the data set to the same size scene specification of the High-dimensional Space Map Dataset to provide data support for the feasibility of the experiment. The entire data set contains a total of 8000 sets of data. We hope to use this data set to provide a sufficient and objective test for the experimental conclusions.