What is the exact functional relationship between the 'look-ahead distance' in a path-tracking controller and the vehicle's lateral stability during high-speed cornering?

The look-ahead distance is the physical distance along a reference path that a controller monitors to calculate steering commands. In path-tracking, the controller essentially simulates a driver looking a certain distance ahead to determine how sharply to turn. At high speeds, this distance acts as a critical filter for steering responsiveness and vehicle stability. A short look-ahead distance forces the vehicle to track the path ag....