МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ГАЛЬМІВНОГО ШЛЯХУ АВТОМОБІЛЯ В КОНТЕКСТІ АВТОМАТИЗОВАНИХ СИСТЕМ АКТИВНОЇ БЕЗПЕКИ

The article presents a comprehensive mathematical model for estimating vehicle braking distance in the context of automated active safety systems such as ABS (Anti-lock Braking System), AEB (Autonomous Emergency Braking), and ADAS (Advanced Driver Assistance Systems). The proposed model considers the braking process as a two-phase phenomenon, consisting of the initial system or driver response delay and the mechanical deceleration phase. Key variables, including vehicle speed, road surface condition, tire-to-road friction coefficient, road slope angle, and the dynamic response of electronic braking systems, are incorporated into the analytical expressions. Special emphasis is placed on the integration of real-time parameters that influence braking behavior under varying environmental conditions. Simulation results for different road scenarios—dry, wet, and icy surfaces, as well as uphill and downhill inclines—demonstrate how even moderate changes in input parameters can result in significant deviations in braking performance. Additionally, the study investigates surface transition effects, such as moving from ice to asphalt, which are critical for adaptive safety algorithms. The influence of ABS is evaluated in terms of its contribution to improved friction utilization and vehicle stability under low-adhesion conditions. Graphical interpretations of braking distance dependencies are provided to illustrate the nonlinear relationship between safety factors and braking efficiency. The study confirms that integrated models combining AEB and ABS are most effective in minimizing braking distance and improving vehicle controllability. The proposed model may be used in the development of predictive algorithms for intelligent braking systems, virtual vehicle testing platforms, and embedded safety modules in autonomous vehicles..