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Professor Alexandre Bayen joined the Department of Civil and Environmental Engineering faculty in January 2005. (Peg Skorpinski photo)

Air traffic controllers have a tough job. Busy airspaces can be logistical nightmares, requiring fast planning to help planes depart and arrive on schedule without crashing into each other. Still, accidents do occasionally occur, like in 2002 when a Russian passenger jet and an American cargo plane collided over southern Germany killing 71 people. UC Berkeley civil engineer Alexandre Bayen is applying mathematics to the problem of congested airspaces. His work could improve the safety of the skyways while enabling airports to run like clockwork.

"The long term vision is a bit like what you might see in Star Wars films when streams of aircraft in the sky are crisscrossing each other beautifully," Bayen says.

The aim is to develop a system that would provide aircraft with the computational smarts to automatically avoid each other. Initially, the system would recognize when an aircraft is acting unsafely and suggest an evasive maneuver. Eventually, Bayen says, a system could potentially take over control from the pilot in an emergency situation.

The first step though is to develop the mathematical algorithms that would be at the heart of an advanced collision avoidance system. To do that, Bayen and his colleagues use formulas to describe the set of all possible positions of the two aircraft relative to each other. By solving the problem for the worst-case scenario, they prepare for the worst and hoping for better.

"We solve it under the assumption that one aircraft will do everything possible to avoid being hit and that the intruder aircraft is trying its hardest to collide," Bayen says. "In real life, hopefully the intruder won't act so badly."

To deal with the complexities of the problem, Bayen employs the mathematics of level sets, a method developed in 1988 at UC Berkeley and UCLA to track and simulate shifting boundaries of dynamic objects and materials. Rather than compute each of the aircraft's possible trajectories, the planes are represented by level sets incorporating an infinite number of trajectories.

This .avi video clip depicts air traffic over a period of ten hours in several sectors covered by the Oakland Air Route Traffic Control Center. Aircraft flying above 33,000 feet are displayed. Aircraft that appear to collide are actually traveling at different altitudes. The visualization was created using Enhanced Traffic Management System data provided by NASA Ames. [Video]

"If you can compute these sets, it gives you a mathematical border," Bayen says. "Outside the border, you're safe. Inside, you're not safe. As soon as an aircraft hits the border of the unsafe set, the pilot will receive an alert that might say, 'Warning! Here is the way to avoid a collision.' We can prove mathematically that if the pilot responds right away, he or she can escape the danger."

In Bayen's laboratory, the researchers are applying the algorithms to air traffic computer simulations developed jointly with NASA Ames. Meanwhile, his former adviser at Stanford University , aeronautics professor and Berkeley alumna Claire Tomlin, is experimenting with hardware implementations based on the algorithms and testing the systems on manned and unmanned aerial vehicles.

Someday, other algorithms that Bayen is developing could aid air traffic controllers at busy airports. Due to safety constraints, the air traffic controllers assign various maneuvers--holding patterns and turns, for example--that ensure a buffer of time between aircraft landings. However, this buffer decreases the efficiency of the airspace.

"It's a very high workload for the humans in charge of that airspace," Bayen says. "So the question is: Can we automatically assign maneuvers so that the aircraft are delivered at an optimal rate? The key is to translate what a human air traffic controller does into a mathematical language."

Do you have a comment or question regarding this research? We want to hear from you...

A preliminary implementation of their optimization algorithms applied to historical air traffic data was promising, Bayen says. Now they're developing techniques they hope could compute optimal maneuver assignments in real-time to crank up an airspace's efficiency, reducing delays and increasing arrival predictability. These suggestions could then appear as advisories on air traffic controllers' display screens.

"Everybody agrees automation should become more important in air traffic control, but there's no global consensus of what should and should not be automated," Bayen says. "Decisions about deploying new automation technologies involve many different scientific, social, and political factors. Our main goal is to overcome the scientific challenges which prevent these decisions from being made."

Alexandre Bayen's home page

Bayen Research Projects

"A Force Field for No-Fly Zones" by David Pescovitz (Lab Notes, June/July 2003)

"Ultimate Auto-Pilot" by David Pescovitz (Lab Notes, October 2003)

"Boundaries Unbounded: Level Sets" by David Pescovitz (ScienceMatters@Berkeley, Vol. 1 Issue 3)

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