## 2 Materials and Methods
### Federated Learning for Articulated Robot Control
#### 2.3.1 FL Module  
As mentioned in Section 2.1, the FL module trains local models, makes inferences to plan picking tasks, and updates the global model to enhance the performance of overall clients in different locations with non-IID data. To this end, there are three modes in the FL module: (1) the train/aggregate mode, which trains the local model to update the global model with local data and aggregates the global model with local model parameters; (2) the deploy mode, which initializes the global model at round 0 and deploys the aggregated  
Figure 1: Overview of the proposed FL framework for articulated robot control: (**a**) picking process; (**b**) FL process. global model to overall clients; (3) and the inference mode, which infrees a task object with the deployed local model to plan the picking task of the articulated robot. The proposed FL module is designed to conduct cost-efficient training and inference operations under low-end computing resources without GPU. Object detection, which involves the identification of the location and class of objects within an image, has gained significant attention from both academics and industry due to its wide range of applications. In general, a Convolutional Neural Network (CNN)-based model, such as Region-based CNN (RCNN) [40], You-Only-Look-Once (YOLO) [41], Single Shot Detector (SSD) [42], and Residual Neural Network (ResNet), is used for object detection [43]. The proposed model adopts the network architecture shown in Figure 2 for cost-effective object recognition. The Convolution-Batch Normalization-ReLu-6 (ConvBNR) layer is composed of a convolution layer, a batch normalization layer, and an activation function of ReLu-6, which contributes to reducing the complexity of multiple layers of the existing CNN-based algorithms into one layer. In particular, the ReLu-6 activation function [44] is selected due to its practicality in mobile and embedded applications requiring reasonable precision in computationally limited environments. Algorithm 1 shows the process for training and updating a global model in the train/aggregate and deploy operating modes. ```
1 Initialize initial global model parameter \(\omega_{0}\)
2 Deploy model parameter \(\omega_{0}\) across overall clients
3 while global model performance does not achieve the set performance
4 for round \(t\)
5 Sample clients set \(S_{t}\)
6 for client \(k\) in set \(S_{t}\)
7 Train local model of client \(k\)
8 Send updated model parameter \(\omega_{t-1}^{k}\) to server
9 Aggregate process with received model parameter set \(\sum_{k\in S_{t}}\omega_{t-1}^{k}\)
10 Deploy global model parameter \(\omega_{t}\)
11 end for
12 end for

Figure 2: Model network architecture. As depicted in Algorithm 1, each process occurs in the FL module of the clients and the central server. First, to enhance the training model's performance, weight initialization is conducted at round \(0\)\((t=0)\), which is the beginning of the FL process. The ConvBNR layer uses ReLu-6 as an activation function, and He Normal Initialization, or Kaiming Initialization [43], is applied for the weight initialization of the model. Next, the global model parameter is deployed to overall clients via Secure File Transfer Protocol (SFTP) before round \(1\)\((t=1)\) starts. The set of clients participating in the local training process, \(S_{t}\), is randomly sampled from all clients, with its own size determined by the client participation rate per round, \(C,(0\leq C\leq 1)\). To update the weights of the deployed model with each client's local dataset, the train process proceeds in parallel based on the hyperparameters \(E\) (local epoch) and \(B\) (mini-batch size). Finally, each participating client sends the updated model parameters back to the server at the end of the local training process; when all clients in the sampled client set have completed the training process, the parameters of the collected clients are aggregated and used to update the weights of the global model.