); [EMAIL_ADDRESS] (Y.S)  
[PERSON]  
1 The College of Information, Mechanical and Electrical Engineering, Shanghai Normal University, Shanghai 201418, China; [EMAIL_ADDRESS] (S.Z. ); [EMAIL_ADDRESS] (Y.S)  
[PERSON]  
2 Department of Mechanical Engineering, The University of Hong Kong, Hong Kong 99077, China; [EMAIL_ADDRESS]  
[PERSON]  
3 Nanjing Huade Storage Equipment Manufacturing Co., Ltd., Nanjing 211122, China; [EMAIL_ADDRESS] (G.C. ); [EMAIL_ADDRESS] (Y.C)  
[PERSON]  
3 Nanjing Huade Storage Equipment Manufacturing Co., Ltd., Nanjing 211122, China; [EMAIL_ADDRESS] (G.C. ); [EMAIL_ADDRESS] (Y.C)  
[PERSON]  
1 The College of Information, Mechanical and Electrical Engineering, Shanghai Normal University, Shanghai 201418, China; [EMAIL_ADDRESS] (S.Z. ); [EMAIL_ADDRESS] (Y.S)  
[PERSON]  
1 The College of Information, Mechanical and Electrical Engineering, Shanghai Normal University, Shanghai 201418, ChinaChinese supply chain company that provides warehousing solutions for modern smart manufacturing. In an HDS system, the main tracks serve as primary logistics arteries for four-way shuttles, the major transportation equipment, while sub-tracks arranged in arrays serve dual roles as storage locations and auxiliary paths. Supporting components, such as hoisters and conveyors, facilitate cargo loading, vertical movements, and lateral distribution [5]. Coordinated with sophisticated path planning algorithms and scheduling systems, HDS architectures are providing increasing production throughput and operational agility in modern smart manufacturing. Despite their benefits, HDS systems also generate new difficulties, e.g., narrow transportation spaces, intricate device coordination, constrained path options due to blockages, etc., and therefore they impose stringent demands on intelligent and scalable path planning methods [6]. So far, designing an effective path planning algorithm for such a system remains an open challenge in modern warehousing logistics and smart manufacturing. We propose a two-step path planning algorithm in this paper to address this pragmatic challenge. We first introduce a mesh-tree grid map topological representation to analog and simplify the HDS system layouts geometrically. In our representation, the main track is used for cargo transportation from the entrance to the storage area and plays a role as the backbone of a tree, while the sub-tracks are auxiliary paths to guide the shipping cargos into or from the identified storage position, as branches of a tree. In this way, an HDS layout is transferred structurally and geometrically into a mesh-tree grid topological network with categorized shipping paths and storage positions. This representation can significantly reduce computational costs in the subsequent path planning step. Next, we introduce our Lattice-Hopping (LH) algorithm, where 'Lattice' represents the mesh-tree grid structure and 'Hopping' means 'jumping'. Our algorithm always returns an optimal shipping path by leveraging the hierarchical structure of an HDS system with  
Figure 1: The composition of a typical high-density storage system; pictures were taken from Huade Co., Ltd.  
the design of main track priority and jumping mechanism, if such a path exists. During path planning, the search first moves along the main track to the storage area and then reaches the specific position via sub-tracks. This is the'main track priority'. Once obstacles are met, the jumping mechanism is triggered to enforce the path turning around from the obstacles and to reach the destination via another sub-track, if it is accessible. In this way, our method can provide superior performances by avoiding most unnecessary searches and return a shorter average searching time as well as a smaller number of traversed nodes.