## 2 Materials and Methods  
### Federated Learning  
FL refers to a machine learning technique that enables the cooperative training of a global machine learning model with local data via individual clients (e.g., mobile or IoT devices) [15]. FL can be classified into three different categories [16; 17; 18]: (1) horizontally federated learning (HFL), consisting of clients sharing a homogeneous feature space with different sample spaces (e.g., patient information in different hospitals); (2) vertically federated learning (VFL), consisting of clients sharing heterogeneous feature spaces with a sample space (e.g., heterogeneous customer in a shopping mall); and (3) federated transfer learning (FTL), consisting of clients with heterogeneous feature spaces with different sample spaces (e.g., wearable healthcare using both personalized local models and a global model). In this way, FL can be classified in terms of the characteristics of feature space and sample space utilization. In this study, HFL is adopted to create individual models based on the same feature space from different sample spaces composed of multiple articulated robots. The individual models are eventually utilized for the generation of a global model (see Section 2.3 for more detail). In general, to train the global model, traditional distributed and parallel machine learning techniques, such as Parallel SGD [19], ADMM [20], and Downpour SGD [21], collect the local data of each client to a central server (or a global server) and train the model at once. However, in the training process of FL, a local model of each client is solely trained using its data, without sharing them with other clients, and the trained model's parameters (e.g., the weights, biases, and gradients of a model) are iteratively aggregated into the global model to enhance the overall performance of global and local models [22]. FL, which shares characteristics with distributed systems, utilizes distributed data to enhance the performance of a model on a task. Therefore, early FL-based approaches can be regarded as extensions of distributed computation, while recent advances in privacy preservation within distributed systems have further reinforced this connection. The CodedPrivateML protocol [23] consists of quantization, encoding, polynomial approximation and gradient computation, and decoding the gradient and model update process, which preserves the privacy of the data and model information while enabling an efficient parallelized training process for distributed workers. However, distributed processing connects multiple client computers in distributed locations to a centralized control server via a communication protocol to complete a task, while each computer completes a different task [24]. As a result, while distributed processing focuses on accelerating processing, FL aims to improve privacy and collaborative machine learning capabilities, even with non-independent and identically distributed (non-IID) data. In FL, a global model is trained according to two approaches of the Federated Stochastic Gradient Descent (FedSGD) and Federated Averaging (FedAVG) algorithms [25]. Bothalgorithms use three hyperparameters: (1) the fraction of clients (C) participating in each round (i.e., one client update model parameter to the server) among all clients (\(0\leq C\leq 1\)); (2) the mini-batch size of local data (\(B\)) used for training in each epoch; and (3) the number of epochs (\(E\)) to train locally for each round. The FedSGD algorithm is built upon the stochastic gradient descent (SGD) algorithm, which is an effective optimization technique that iteratively minimizes the cost or loss function using a minibatch of data. To be more specific, each client trains its local model using the gradient descent method from its full local dataset. Once each client completes the training process, the central server collects the parameter of the trained client model, updates a global model with the collected model parameters, and deploys the updated global model to the clients.