# Improving the Efficiency of Modern Warehouses Using Smart Battery Placement
## 4 Experimental Results  
To empirically assess the effectiveness of the proposed AP-based battery placement algorithm, we undertook a systematic comparison against a randomized placement approach. This evaluation aimed to determine how much our AP-driven approach can reduce the average distance a UGV must travel to reach its designated battery station within its cluster. For our experimentation, we ran 100 individual trials. In each trial, a new, randomized traffic pattern was generated for the warehouse environment. We then normalized the traffic data for every cell in the warehouse, transforming the highest traffic cell to represent a value of 100 and proportionally scaling down other cells. This normalized traffic value can be interpreted as the probability of a UGV landing on a particular cell and subsequently requiring a battery recharge. This ensures that our evaluations are grounded on realistic and varied traffic patterns, reflecting the diverse navigational behaviors UGVs may exhibit in actual warehouse settings. Subsequently, for each trial, we calculated two key metrics:  
* Average distance using the AP algorithm: this represents the mean distance a UGV, based on its position, would need to travel to reach a battery station positioned via our AP-based approach. * Average distance using random placement: analogously, this represents the same mean distance, but with batteries placed randomly within the defined clusters. By comparing these distances, we aimed to quantify the improvement gained by using the AP algorithm over a simplistic random placement. Table 1 shows the results of the 10 synthetic experiments we conducted. While distance optimization remains a paramount consideration in our evaluations, an equally critical metric is the energy consumption of UGVs during their transit to the battery stations. Reducing the distance traveled is beneficial, but understanding the energy implications of this travel offers a holistic insight into operational efficiency. It is not just about how far a UGV travels, but also how it travels: considering straight paths versus turns and idle times due to obstructions or other UGVs is also important. As such, to complement our distance metrics and to provide a comprehensive evaluation framework, we delved into an energy consumption model tailored for UGVs operating within the warehouse environment. This model factors in the distinct energy expenditures associated with different movement patterns and behaviors of the UGVs, allowing us to paint a clearer  
Figure 3: (**a**) Visualizes the generated sub-areas using the proposed AP-based algorithm. (**b**) Visualizes the selection of battery placement within each of the generated clusters using the scoring formula (Equation (2)). Cells used for battery placement are marked using “\(\times\)” notation. picture of the tangible benefits of our AP-based battery placement algorithm in terms of both distance and energy. Let  
\(e_{s}=\) energy consumed by the UGV when traveling straight for one cell. \(e_{t}=\) energy consumed by the UGV when making a turn. \(e_{i}=\) idle energy cost per unit time. \(n_{s}=\) number of cells the UGV needs to travel straight. \(n_{t}=\) number of cells the UGV needs to turn. \(t_{i}=\) time the UGV remains idle, waiting for the path to clear. Then, the energy consumption \(E\) for a UGV to reach the battery from its current position is given by  
\[E=e_{s}\times n_{s}+e_{t}\times n_{t}+e_{i}\times t_{i} \tag{3}\]  
This formula effectively captures the total energy expenditure based on the UGV's motion and idle time. It sums the energy used when the UGV travels straight, turns, and idles. It is pivotal to emphasize that the exact energy calculations, especially values for \(e_{s}\), \(e_{t}\), and \(e_{i}\), can vary and depend largely on the specifications of the robot. During the experimental evaluation, compared with the random battery placement, the proposed model managed to achieve up to 50% less distance traveled by the robots.