## 1 Introduction  
Automatic emergency braking (AEB) systems are vital components of modern automotive safety technology, designed to reduce or prevent collisions and ensure the safety of both occupants and pedestrians [1; 2; 3; 4]. With the rising incidence of traffic accidents, especially those caused by driver distraction and fatigue, AEB systems have become essential in intelligent vehicles. Many manufacturers now equip their models with AEB systems, applicable to both passenger cars and heavy commercial vehicles [5; 6; 7; 8; 9; 10; 11]. As advancements in autonomous driving technology progress, the importance and scope of AEB systems are broadening, establishing them as foundational elements for the achievement of fully automated driving. AEB systems utilize sensors and cameras to continuously monitor the environment and identify potential collision risks. Upon detecting a potential collision, the system automatically applies the brakes to mitigate or prevent the accident. A major advantage of AEB systems is their ability to intervene before the driver can react, significantly enhancing the safety on the road. Additionally, the precise timing of activation, combined with the coordinated control of passive safety systems, can further enhance the vehicle's overall safety performance [12; 13]. While the use of automatic emergency braking can reduce traffic accidents, many drivers do not fully understand the conditions that trigger this system. Reference [12] examined drivers' ability to recognize the triggering conditions of AEB. The recognition of the condition was influenced by either information gathering or personal interest in cars. Additionally, a novel methodology was devised to predict how people's heads move in self-driving cars during emergency stops [13]. It used a computer model of a person to simulate how their head moved in car crashes with different seatbelt types. Early research on control methods for AEB systems primarily focused on time-to-collision (TTC) models [14; 15; 16; 17; 18; 19; 20]. These models assess the risk of collision between vehicles and other objects--such as other vehicles, pedestrians, or obstacles--by calculating the relative distance and velocity to predict the time until a collision occurs under the current conditions. A smaller TTC means a higher risk of a crash, while a larger TTC means a lower risk. However, at close distances, the TTC model can have significant errors; thus, using the inverse of the TTC can provide a more accurate risk assessment in these situations. Reference [14] presented a theory on how drivers use visual cues to control braking, highlighting that drivers depend on information related to the time to collision rather than on distance, speed, or acceleration data. Reference [15] showed that drivers' fear of crashing is influenced by how close they are to the car in front and how quickly they are closing the gap. Reference [16] conducted a comparative analysis of evaluation indices for the assessment of drivers' risk perception of rear-end collisions. Reference [17] presented findings from driving simulator experiments indicating that drivers' perceptions of the lead vehicle's closure rate are characterized by 1/TTC, irrespective of constant velocity or deceleration conditions. Reference [18] proposed a novel deceleration method for collision avoidance, incorporating a revised driver reaction time parameter. Reference [19] showed how to quickly calculate the risk of a crash using only camera images from a car. Reference [20] modeled the AEB control strategy using a hierarchical control approach. The upper controller established a time-to-collision model for the vehicle's braking deceleration decision, determining the collision time threshold while considering comfort. The lower controller controlled the car's speed by adjusting the gas and brakes, following instructions from the upper controller. The design of control systems based on safety distance models is another crucial approach for AEB systems [21; 22; 23; 24].