## 1 Introduction  
Path planning is a basic task of computer vision and robot kinematics. It is necessary to predict the target position and gait at the same time. With the great development of deep learning, path planning is successfully integrated into more and more real-world application systems, such as autonomous driving, human-machine collaboration, and remote control [1; 2]. Among them, motion planning in high-dimensional space becomes a hot topic, which is a key for realizing the slogan of \"machine serving society\" (for example, palletizing in delivery warehouses, underwater exploration, aerial cruise) [3; 4]. However, today's high-dimensional spatial planning can only accomplish simple motions in specific environments with few obstacles, and this planning process is lengthy. Hence, it is necessary to explore an efficient path planning approach, especially for high-dimensional space, to fill the gap, which is a prominent and interdisciplinary research area. However, it is a challenging task to deal with high-dimensional data for path planning. Firstly, most current works are rarely studied in high-dimensional environments, and the vulnerability of general path detectors has been revealed by planning in more complex environments [5; 6]. For example, although the Walk To algorithm [7] can be directly used in any dimension, it is completely unable to deal with obstacles and other situations. Bugs [8] need to rotate clockwise (or counterclockwise) around the obstacle, and it is difficult to define the direction in high-dimensional space. The ant colony algorithm [9] will bring about slow convergence, easy to over-fitting problems. Other search-based or sampling-based methods, such as RRT and A*, can predict waypoints in high-dimensional space but cannot be executed in the real world due to the huge scale of time cost for even analyzing a single dimension. The existing, more mature robotic arm planning algorithms mostly rely on sensors [10]. They iteratively update the planned waypoints by continuously scanning obstacles through devices such as laser and radar, which has a high cost but low efficiency. Secondly, path planning methods based on research [11; 12] can be used just in simple known scenes but tend to crash in unknown environments. The paths generated by these methods are so limited that such a priori detection is unpredictable for emergent factors, which is devastating for robots. Some training-based waypoint detection models (such as gray-level co-occurrence matrices [13]) are not efficient enough to generate the best waypoints and are likely to cause overfitting. Thirdly, although today's high-dimensional path planning of robots has made some progress in targets such as drones [14], there is still a certain risk of collision. To date, not much research has been conducted on employing the balance between planning speed and obstacle avoidance accuracy. Therefore, we conclude that a stable and efficient high-dimensional space path planning approach can be designed from the following aspects by analyzing the situations mentioned above: regional obstacle detection planning to determine the current dynamic sequence is a dynamic process; a screening mechanism for waypoints to ensure safety and efficiency; operations to reduce the number of iterations and computing time. In light of this, we launched an exploration of HDPP. A novel multi-scale positioning and waypoint refinement approach--HDPP--is proposed for high-dimensional dynamic path planning. Specifically, it is obvious that for complex space planning, the less waypoints of the image that are detected while the path planning effect does not degenerate [15], the better. In order to separate viable areas in the sensory field from obstacles as quickly as possible, a multi-scale model is proposed to dynamically refine and learn adaptively assigned feature maps at different scales with multiple predictions. Secondly, we empirically observe that the importance of different areas in the receptive field varies greatly for high-dimensional navigation.