## 2 Materials and Methods
### Federated Learning for Articulated Robot Control
#### 2.3.1 FL Module
\begin{table}
\begin{tabular}{c c} \hline \hline
**Metric** & **Description** \\ \hline \(T_{f}\) & Training completion time (s) for participating clients in FL module at each round. \\ \(R_{f}\) & Average hardware resource share percentage (\%) of memory and CPU in FL module at each round. \\ \(N_{f}\) & Total network traffic (download and upload; Mb) per client in FL module at each round. \\ \(T_{a,i}\) & Average picking task completion time (s) for \(i\)th articulated robot over 30 iterations. \\ \(R_{a,i}\) & Average hardware resource share percentage (\%) of memory and CPU of \(i\)th articulated robot control module performing picking task over 30 iterations. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance metrics of the FL module and the articulated robot control module. Figure 8: Specification of the experiment environment. In each task, each articulated robot performs the pick-and-place motion to move a 2 cm \(\times\) 2 cm \(\times\) 2 cm cubic part of the class specified for each articulated robot a minimum of 1 cm and a maximum of about 8.5 cm. Also, to avoid overheating the actuators in each motion, i.e., positioning the actuators to satisfy each of the derived joint parameters, a time step of 0.1 s/\({}^{\circ}\) was used when setting the joint parameters. The experiments were conducted on four clients (i.e., articulated robots) and one central server (Intel Xeon(r) Silver 4210 Processor, NVIDIA RTX Quadro 4000, and Ubuntu 20.04). Table 2 details the hardware specification (i.e., a system on chip (SoC), CPU, GPU, memory, network, and power) of clients related to the joint learning process and the joint parameter derivation task of the articulated robot, while Table 3 details the specification of the articulated robots (i.e., small torque, operating speed, dead bandwidth and frequency of the actuators, and supplied power) that can be highly correlated with the performance of pick-and-place tasks. ### Object Detection Model Performance

First, the performance of the object detection model, which plays an important role in the picking task using the proposed federated learning-based framework, was evaluated. Notice that the proposed object detection model was successfully implemented on low-specification hardware equipment. The experiments were conducted on the GPU-equipped machines described in Section 3.1. This allowed for the testing of not only YOLO-LITE and our proposed model, which were developed on low-end machines, but also standard CNN models such as Faster R-CNN and SDD. In this instance, Faster R-CNN sets ResNet-50 as a backbone, with a 1x learning schedule, and SSD uses VGG16 [42; 46; 47] as a backbone. The experimental results, based on an 80% accuracy rate with a batch size of 64, a learning rate of 0.001, and a weight decay of 0.1, are presented in Table 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Epochs** & **FLOPs** & **\#Param** & **GPU Usage (\%)** \\ \hline Proposed model & 36 & 1.8 B & 3.5 M & 18.2\% \\ Faster R-CNN 1  & 15 & 33.2 B & 42.5 M & 87.5\% \\ SSD 2  & 11 & 34.9 B & 35.6 M & 78.3\% \\ YOLO-LITE & 47 & 1.6 B & 2.2 M & 14.7\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Training process results of proposed model compared to standard CNN models. \begin{table}
\begin{tabular}{c c} \hline \hline
**Category** & **Specification** \\ \hline SoC & Broadcom BCM2711 SoC \\ CPU & 1.5 GHz ARM Cortex-A72 MP4 \\ GPU & Broadcom VideoCore VI MP2 500 MHz \\ Memory & 8 GB LPDDR4 with 2 GB swap memory \\ Network & 802.11b/g/n/ac Dual-Band \\ Power & 5 V, 3 A \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hardware specification of the clients. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **Specification** \\ \hline \multirow{4}{*}{Actuator} & Small torque & 9.4 kg/cm (4.8 V) \\  & Operating speed & 0.17 s per 60\({}^{\circ}\) \\  & Dead bandwidth & 5 \(\mu\)s \\  & Frequency & 50 Hz \\  & Power & 5 V, 3 A \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hardware specification of the articulated robots.