## 2 Related Works
### Joint Attention in HRI  
Joint attention has been extensively studied as a foundational mechanism in HRI, with researchers exploring its implementation and evaluation across diverse scenarios. Efforts to replicate JA mechanisms in robots often focus on modeling human-like behaviors. [PERSON] et al. [24] proposed a developmental model in which a robot autonomously acquires JA by attending to salient visual stimuli and correlating them with sensorimotor patterns. Using statistical filtering to discard incorrect associations, the robot self-evaluated successful attention episodes without external supervision. Experiments showed that the system replicated infant-like developmental trajectories, highlighting its potential for modeling early social learning and enhancing robotic autonomy. In the same direction, [PERSON] et al. [25] presented a robot model combining JA with social referencing, allowing it to associate emotional valence with objects based on a caregiver's facial expressions and gaze. The robot used a simple sensorimotor architecture to incrementally learn gaze following and emotional tagging of objects. The experimental results confirmed the system's ability to adapt to emotional cues, suggesting that social referencing can enhance the contextual and affective grounding of JA. [PERSON] [26] implemented a developmental architecture on the humanoid robot Cog [27] to model JA through imitation. The system decomposed JA into sequential stages, including mutual gaze, gaze following, and pointing, mirroring infant development. By learning to reproduce head orientation and gaze shifts, the robot engaged in shared attention episodes. This modular approach emphasized imitation as a foundational mechanism for social interaction and showed how layered developmental stages can replicate complex human-like behaviors in robots. [PERSON] and [PERSON] [28] explored JA and turn-taking through imitation games using the Sony (Tokyo, Japan) humanoid robot QRIO [29]. They employed a recurrent neural network with parametric biases to allow the robot to learn cyclic movement patterns from user input. Two experimental setups were tested: one with robot-only adaptation and another with mutual adaptation. The robot synchronized its actions with users, enabling smooth transitions and spontaneous role shifts. The study demonstrated that mutual adaptation supports naturalistic interaction and dynamic modeling of JA and turn-taking. Recent work has explored integrating multiple sensory and behavioral channels into JA. [PERSON] and [PERSON] [30] introduced a multimodal model to estimate the FoA during group interactions. Using data from 92 participants, the model integrated gaze, voice, upper-body motion, and head pose through a Transformer encoder for multimodal fusion, combined with an LSTM module to capture temporal dynamics. Evaluation in multi-user discussions showed accurate tracking of attentional shifts. This work highlights the role of temporal and multimodal integration in advancing JA estimation in complex social contexts. To evaluate the emulated JA mechanism in robots, different studies have been carried out in real-world user scenarios to contribute to understanding the impact on HRI quality. [PERSON] and [PERSON] [31] examined a JA framework comprising RJA, JJA, and ensuring joint attention (EJA) modules. They defined two experimental conditions in which the [PERSON] robot either responded to a user's referential focus or employed behaviors like gaze monitoring to maintain JA. The results showed that RJA improved task performance and social perceptions, while EJA behaviors were seen as more natural and effective. The study highlighted the value of combining RJA, JJA, and EJA for smoother HRI. Likewise,Skantze et al. [19] explored the integration of turn-taking and gaze-following in HRI using a humanoid robot in a map task. The participants followed the robot's instructions to draw a route, while it used consistent gaze shifts to landmarks and prosodic speech cues to manage conversational flow.