# The Sense of Agency in Human-Machine Interaction Systems
## 3 Measurement of the SoA
### How to Measure the SoA in Continuous Tasks within HMI Systems  
Measuring the SoA has always been a key issue. However, evaluating the SoA in continuous tasks presents problems for both explicit and implicit measurements. Explicit measurement is easily affected by the subjective judgment of the operator and experimental conditions. Even worse, this method interrupts the operator because they need to report their subjective evaluation of the SoA. Sensory attenuation and intentional binding are designed for single discontinuous tasks and need to introduce interference items, which is inconvenient for continuous tasks. EEG signal measurement is capable of handling continuous and complex measurement tasks, but it is easily interfered with by the environment and varies significantly among operators, so the collection of EEG signals has stringent requirements for the experimental environment, EEG equipment, and the operator. So, it is unrealistic for continuous tasks, especially when the operator's movement has to be restricted. On the other hand, in most studies, physiological signals are usually used as dependent variables, and because these features may also be affected by other irrelevant variables. If external variables are not fully controlled, they may not provide high accuracy as proxy indicators [36]. So, how can the SoA in continuous tasks using HMI systems be measured? [PERSON] et al. [36] gave their suggestions. The first approach is to use physiological signals to decode the SoA. The second approach is to use attention as a proxy for the SoA. The third approach is to use control-motivated action to indicate the SoA. These three suggested methods hold significant value. Additionally, these approaches effectively visualize the dynamic changes in SoA over time. As operators gain more experience using HMI systems over time, their familiarity directly impacts the system's SoA. However, it is important to note that these methods may not yield the precise quantification of the SoA. [PERSON] et al. [112; 113] suggested a data-driven approach to infer SoA levels from sensor data, similar to how human affective states are determined. They propose that SoA changes can be modeled like human emotions in Affective Computing, using physiological, facial, vocal, postural, and gestural signals, among others, with subjective self-assessment as the ground truth. [PERSON] and [PERSON]. [114] have shown these bodily signals accurately reflect changes in affective states. [PERSON] et al. [113] utilized a smartphone app to collect participants' Self-Reported Data, Behavioral Logs, Contextual Data, and Goal-Related Metrics, enabling a comprehensive and multidimensional analysis of the SoA. This multi-faceted data collection approach captures both subjective experiences and objective behavioral patterns. While using multidimensional data to analyze the SoA is a valuable research direction, this method still requires active reporting by participants. In HMI systems, the key challenge lies in enabling machines to autonomously predict and analyze the operator's SoA in real time using sensor-derived data. This is crucial for the comprehensive application of the SoA in HMI systems. Potential approaches include the following:  
* Using cameras to recognize the operator's emotions. * Employing eye-tracking and an EEG to analyze changes in the operator's attention. * Analyzing changes in the operator's physical state through electromyography, blood pressure, and other physiological signals. * Utilizing multiple physiological signals to model and numerically analyze the SoA. The integration of these technologies opens new horizons for SoA research in HMI systems. [PERSON] et al. [115] concluded that measures of driver out-of-the-loop can be divided into two main categories: (1) vehicle-based sensors that can assess the degree of the driver's physical control of the vehicle during or immediately after automation and (2) driver-based sensors and measures. Although the study by [PERSON] et al.