# Adaptive Cruise Control Algorithm that keeps a car halfway between front and rear cars will prevent traffic jams

At this month’s IEEE Conference on Intelligent Transport Systems, Berthold Horn, a professor in MIT’s Department of Electrical Engineering and Computer Science, presented a new algorithm for alleviating traffic flow instabilities, which he believes could be implemented by a variation of the adaptive cruise-control systems that are an option on many of today’s high-end cars.

A car with adaptive cruise control uses sensors, such as radar or laser rangefinders, to monitor the speed and distance of the car in front of it. That way, the driver doesn’t have to turn the cruise control off when traffic gets backed up: The car will automatically slow when it needs to and return to its programmed speed when possible.

Counterintuitively, a car equipped with Horn’s system would also use sensor information about the distance and velocity of the car behind it. A car that stays roughly halfway between those in front of it and behind it won’t have to slow down as precipitously if the car in front of it brakes; but it will also be less likely to pass on any unavoidable disruptions to the car behind it. Since the system looks in both directions at once, Horn describes it as “bilateral control.”

Suppressing traffic flow instabilities (8 pages)

Simulations seemed to bear out his intuition, but to publish, he needed mathematical proof. After a few false starts, he found that bilateral control 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 — in particular, the Lyapunov function — to demonstrate that his algorithm could stabilize it.

Horn’s algorithm works, however, only if a large percentage of cars are using it. And laser rangefinders and radar systems are relatively costly pieces of hardware, which is one of the reasons that adaptive cruise control has remained a high-end option.

Digital cameras, on the other hand, have become extremely cheap, and many cars already use them to monitor drivers’ blind spots. “There are several techniques,” Horn says. “One is using binocular stereo, where you have two cameras, and that allows you to get distance as well as relative velocity. The disadvantage of that is, well, two cameras, plus alignment. If they ever get out of alignment, you have to recalibrate them.