A sample run of Horn’s simulator (complete with brake lights). The system starts out in a stable state, but backups begin about 30 seconds in, even though all the cars are executing algorithms typical of current adaptive-cruise-control systems. Horn’s algorithm is switched on at the one-minute mark.
Everybody’s experienced it: a miserable backup on the freeway, which you think must be caused by an accident or construction until it thins out at some point for no apparent reason.
Such “traffic flow instabilities” have been studied since the 1930s, but although there are a half-dozen ways to model them mathematically, little has been done to prevent them.
Berthold Horn, a professor of computer science and engineering, has developed a new algorithm for alleviating traffic flow instabilities. He believes that it could be implemented with a modified version of the adaptive cruise-control systems available in many high-end cars.
Traffic flow instabilities arise, Horn explains, because variations in velocity are magnified as they pass through a lane of traffic. “Suppose that you introduce a perturbation by just braking really hard for a moment,” he says. “That will propagate upstream and increase in amplitude as it goes away from you.”
A car with adaptive cruise control uses sensors to monitor the speed and distance of the car in front of it. When traffic gets backed up, the car automatically slows, returning to its programmed speed when possible.
A car equipped with Horn’s system would, counterintuitively, also monitor the car behind it. Staying roughly halfway between the cars in front and behind means a car won’t have to slow down as sharply if the one in front brakes—and makes the car less likely to pass disruptions “upstream.”
Horn found that this approach could be modeled using something called the damped-wave equation, which describes how oscillations, such as waves propagating through a heavy fluid, die out over distance. Once he had a mathematical description of his dynamic system, he used techniques standard in control theory to demonstrate that his algorithm could stabilize the string of moving vehicles.
Of course, Horn’s algorithm works only if a large percentage of cars are using it. And the laser range finders and radar systems used in existing adaptive cruise-control systems are relatively expensive.
But digital cameras are cheap, and many cars already use them to monitor drivers’ blind spots. Horn’s chief area of research is computer vision, and his group has previously published work on extracting information about distance and velocity from a single camera.
“Strangely,” he says, “while it’s difficult for a monocular camera to get distance accurately without additional information, and it’s difficult to get velocity accurately without additional information, the ratio can be had.” Horn is investigating whether his algorithm could use only that ratio, rather than absolute information about speed and distance.