# Improving the Efficiency of Modern Warehouses Using Smart Battery Placement
## 3 The Proposed System  
### Environment Definition  
At the heart of our proposed system lies the meticulous and precise representation of a modern warehouse environment. Understanding the spatial configuration of a warehouse is pivotal for the seamless movement and optimal functioning of UGVs. In order to computationally model and interpret the expansive nature of a warehouse, we utilized a grid-based representation. Each cell within the grid corresponds to the Cartesian coordinates of an actual warehouse, effectively transmuting the physical space into a digital grid. This systematic digital mirroring allows for more efficient algorithmic traversals and path calculations for the UGVs.  
Within this gridded representation, the shelves, which are fundamental structures housing products, are meticulously arranged in rows. These shelves serve as both landmarks and destinations for the UGVs. Notably, the structural design of these shelves is not uniform; their heights vary considerably. Some shelves are so high that they are inaccessible to certain UGVs due to their design constraints. This height variation introduces an additional layer of complexity in task allocation, as UGVs have to be delegated tasks based on both their capability to navigate and their ability to access specific shelf heights. Figure 1 depicts a grid representing a modern warehouse environment.  
Figure 1: (a) A 20 \(\times\) 20 modern warehouse environment where white cells indicate accessible areas for UGVs inside the warehouse and green cells indicate the shelves. Red cells indicate the two exits (and delivery areas) of the warehouse. During operation, robots navigate to pick up the product and bring it to one of the exits. (b) depicts a blue robot (blue dot) navigating its way to pick up a product (blue cell) and then bring it to the closest exit.  
A delivery task, in its essence, is a sequence of moves that a UGV undertakes to fulfill an order. Initiated from its resting or starting point, a UGV embarks on a journey that sees it navigate through the matrix-defined warehouse. It weaves its way toward the designated shelf, secures the desired product, and then proceeds to transport this product to a predetermined exit within the warehouse. Given the design constraints and to maintain simplicity in their movement patterns, UGVs are programmed to move in straight lines, which means their navigation is strictly confined to vertical and horizontal trajectories. This movement constraint ensures predictability in their paths and facilitates easier coordination between multiple UGVs.  
As we delve deeper into the intricacies of task allocation and path generation for UGVs within our digitally represented warehouse environment, it is crucial to mention that the underlying algorithmic framework for these processes is largely based on our previously proposed methodology detailed in paper [15]. Given its prior establishment and comprehensive detailing in that publication, an exhaustive discussion of the algorithm's nuances, mechanics, and applications is beyond the purview of this current work. The cornerstone of this manuscript and its primary contribution to the existing body of research is the innovative approach to battery placement within warehouse environments. By synergizing energy management with optimized logistics, our focus here was to underscore the significance of strategic battery placement and its overarching impact on the efficiency and throughput of modern warehousing operations.