## 2 Materials and Methods
### Federated Learning for Articulated Robot Control
#### 2.3.1 FL Module
According to the experimental results in Table 4, the proposed object detection model requires fewer epochs to train than that of YOLO-LITE, which focuses solely on lightweight models. This is due to the presence of the batch normalization layer, which contributes to a reduction in the number of required epochs. Furthermore, Faster R-CNN and SSD, which require fewer epochs, have 33.2 billion and 34.9 billion FLOPs and 42.5 million and 35.6 million parameters, respectively, while the proposed model requires only 1.8 billion FLOPs and 3.5 million parameters. Therefore, the total GPU usage of the proposed model is 18.2%, indicating that the proposed model can be applied even to low-end computing devices. To make it possible to train an object detection model by performing FL on low-end hardware devices, the proposed object detection model shows viable performance in terms of FLOPs, the number of parameters, and GPU usage, making it suitable for use on low-end hardware devices. ### Robot Control Performance

To evaluate the efficiency of the proposed robot control module, which derives joint parameters for picking tasks, the experiments were conducted over 30 iterations under the given condition (see Section 3.1). Figures 9 and 10 present the results of the average picking task completion time (\(T_{a,i}\)) and average hardware resource share percentage (\(R_{a,i}\)) for the four articulated robots over 30 replications. Figure 10: Average hardware resource share percentage of articulated robots over 30 iterations. Figure 9: Average task completion time of articulated robots over 30 iterations. In Figure 9, although the case with two articulated robots showed the best average picking task completion time of 79.87 s, there are no statistical differences between the four cases at a significance level of 0.05. Theoretically, all the cases are supposed to provide a similar picking task completion time because each robot performs its own picking task independently. In other words, each articulated robot only utilizes its trained client model to perform the inference process on to picking object and conducts the picking task. Therefore, during the picking task, there is no communication between the server and clients. The result actually implies that the variation in picking task completion time between the four cases is caused by factors inherent to the articulated robots themselves. That is why, at a significance level of 0.05, there are no statistical differences between the four cases. In Figure 10, the case with two articulated robots shows the lowest average hardware resource share percentage, at 20.25%. However, similarly to the results for the average picking task completion time shown in Figure 9, the variation in average hardware resource share percentage between the four cases is caused by factors inherent to the articulated robots themselves, so at a significance level of 0.05, there are no statistical differences between the four cases. From the results in Figures 9 and 10, we can conclude that the proposed framework is appropriately designed to perform identical picking tasks via multiple articulated robots. ### Federated Learning Performance

In the FL module, experiments were conducted to compare the learning performance of relevant machine learning models based on the relevant FL hyperparameters, i.e., \(C\), \(B\), \(E\), rounds, and other performance metrics, i.e., \(T_{f}\), \(R_{f}\), and \(N_{f}\), as described in Table 5. In particular, the number of communication rounds was set to 1000 by default, and the modeling completion time was measured when the model reached an object recognition accuracy of 80% in terms of communication rounds. In Table 5, since FedSGD trains all their local models using the gradient descent method from their full local dataset at once, there is only one case in terms of hyperparameters of \(C=1\), \(B=\infty\), \(E=1\).