Optimizing Collision Warnings: A Shift from Time to Collide to Time to Brake

In automotive safety systems, Time to Collide (TTC) is traditionally used to trigger warnings in auto-emergency braking systems. However, TTC can lead to premature or inaccurate warnings as it is calculated based on the relative speed and distance between the ego and an obstacle. TTC does not consider the vehicle's braking dynamics, such as brake prefill lag which varies across different vehicles, maximum deceleration, and the effectiveness of braking systems and assumes constant speed which may not always be realistic. We propose Time to Brake (TTB) as a more effective parameter for driver warnings. TTB directly relates to the action a driver needs to take—braking. It provides a clear indication of when braking should begin to avoid a collision, whereas TTC only tells us about the possibility of a collision. To calculate TTB we utilize the brake profile, which incorporates both deceleration and system jerk for improved accuracy. The proposed warning time is the sum of variable brake prefill lag, average driver reaction time, and TTB. TTB is calculated for two distinct scenarios due to differing constraints using Newtonian equations of motion. The comoving and oncoming scenario involve both ego and object colliding at the same location, but in the former, the relative velocity is zero, and in the latter the ego’s velocity is zero at the point of collision. This approach enhances driver response and safety by providing timely and relevant warnings. Tailored for specific braking dynamics, TTB improves the effectiveness of automotive safety systems.