## 5 Discussion  
The braking system has become a vital safety feature in modern vehicles, significantly aiding in the reduction of rear-end collisions. Braking control algorithms primarily face two critical challenges: determining when to apply the brakes and optimizing the braking force. The timing of brake engagement is crucial; if the system responds too late, a collision may occur, while premature activation can cause unnecessary discomfort for passengers and potentially trigger rear-end collisions from following vehicles. Researchers are increasingly focused on integrating drivers' risk perception into braking systems, recognizing that understanding a driver's situational awareness can enhance decision-making processes. The relationship between the time to collision and driver behavior is critical. Drivers perceive their distance to the vehicle ahead based on the TTC. By incorporating this perception into braking control algorithms, the system can be fine-tuned to align more closely with human intuition, resulting in smoother and more effective braking maneuvers. A key consideration in automatic braking control is the balance between safety and comfort. While maximizing safety is essential, sudden and harsh braking can lead to discomfort and panic among passengers. Therefore, automatic braking control systems  
Figure 12: CCRb scenario test results (\(v_{\text{F}}=50\) km/h, \(v_{\text{L}}=50\) km/h, and \(a_{\text{L}}=-6\) m/s\({}^{2}\)). must be designed to ensure that braking actions are gradual and proportional to the perceived risk. Existing research primarily employs time-to-collision models and safe distance models or builds upon them to enhance the control algorithms. While these algorithms can effectively prevent collisions, sudden braking can significantly impact passenger comfort. Although leveraging the braking behavior of professional drivers is an effective way to improve vehicle safety and occupant comfort, modeling and validating such behavior is a complex process. This study adopts a different control approach by transforming the automatic braking collision avoidance problem into a trajectory planning problem, offering a new perspective for braking control. The advantage of this control method lies in its ability to consider constraints both before and after braking, allowing for effective collision avoidance while simultaneously enhancing passenger comfort. The analysis reveals that, under the same initial speed, the braking distance required by the seventh-order polynomial braking algorithm is the longest, being 1.25 times that of the fifth-order polynomial and 1.78 times that of maximum-deceleration braking. Nevertheless, the seventh-order polynomial significantly improves the braking comfort, with the peak jerk reduced by approximately 50% compared to the fifth-order polynomial. For example, when braking at an initial speed of 90 km/h on a road surface with a friction coefficient of 0.9, the seventh-order polynomial requires a braking distance of 61.7 m, a braking time of 5.76 s, and a maximum jerk of 0.61 g/s. In contrast, the fifth-order polynomial requires a braking distance of 49.4 m, a braking time of 4.93 s, and a maximum jerk of 1.23 g/s. The simulation results from both the point mass model and the CarSim dynamic model confirm the effectiveness of the seventh-order polynomial braking algorithm. Thus, when a sufficient braking distance is available, a comfort-oriented control algorithm, such as the proposed seventh-order polynomial braking algorithm, can be employed, rather than relying on abrupt braking at close range. The proposed algorithm is not limited to emergency braking but is applicable to all braking scenarios. It offers valuable insights into scenarios where a vehicle gradually approaches an obstacle from a distance. However, it is worth noting that, in emergency situations where obstacles appear suddenly at close range, the seventh-order polynomial may not be the optimal choice.