Genetic Algorithms "Naturally Select" Better Satellite Orbits

Purdue University engineers used "genetic algorithms" to design innovative constellations, or collections, of satellites orbiting the Earth. The algorithms are helpful in designing low-cost constellations that save money by placing a small number of satellites around the Earth at relatively low altitudes, said William Crossley, an associate professor at Purdue's School of Aeronautics and Astronautics and a faculty member of the university's Center for Satellite Engineering.

Such low-altitude satellite constellations are expected to bring a boon to mobile computing by making it more possible for people to use wireless communication devices. The constellations also may have military applications because they make it possible to quickly reposition satellite constellations for specific surveillance purposes.

However, the constellations have a key disadvantage. To maintain contact with stations on Earth, the satellites must be in a line of sight with antennas on the planet. Because the constellations contain only a few satellites orbiting at low altitudes, there are times when none of the satellites can be seen by ground stations; they are blocked by the Earth's curvature, temporarily cutting off communications. The conventional method for designing constellations containing three or four satellites in low-altitude orbits results in the satellites being out of touch with Earth for about four orbital periods out of each day. Each period represents a single orbit around the Earth, which takes about 90 minutes. During those four orbits, a base on Earth would not have a line of sight to any of the satellites, making communication to or from the Earth base impossible.

The Purdue-designed constellation, however, reduced the blackout time to three orbital periods, keeping the satellites in touch 90 minutes longer. The design is now being considered for defense-related satellites. A research paper about the findings is in the July-September issue of the Journal of Astronautical Sciences, published by the American Astronautical Society.

Genetic algorithms, or computer instructions, adapt Charles Darwin's evolutionary model, interchanging design elements in hundreds of thousands of different combinations. Only the best-performing combinations are permitted to survive, and those combinations "reproduce" further, progressively yielding better and better results. The most profound impact of such algorithms is that they sometimes find solutions that researchers would ordinarily have missed. An added bonus is that they run continuously, overnight and for days at a time, sometimes working faster than would have been humanly possible.

"The genetic algorithm can provide a good starting point," Crossley said. "Once the genetic algorithm has generated a solution, fine tuning or refinement needs to be done to obtain the best final solution."

The genetic algorithm developed by Crossley and former graduate student Edwin Williams has been used to design a constellation of satellites for a possible defense mission, and research collaborators at The Aerospace Corporation in El Segundo, Calif., are currently using the approach to investigate other possible constellation designs.

"For small numbers of satellites, at low altitude, we find constellations that outperform significantly the ones that you would find using the traditional approach," Crossley said.

If money is no object, then satellites can be kept in constant communication with Earth by placing constellations of three satellites in orbit 20,000 miles above Earth. Because they are high above Earth, each satellite can see a large portion of the surface. But the satellites are more expensive to design and build because they must withstand higher radiation than lower-altitude satellites, they require larger on-board power supplies to send and receive signals, and placing them in the proper orbits requires a larger launch vehicle and takes more time.

In comparison, the lower altitude satellites are placed in orbits only a few hundred miles above Earth.

Genetic algorithms are helpful in designing lower-cost constellations by sorting through the multitude of possible configurations and coming up with a design that minimizes the amount of time that the satellites are out of touch with links on the ground. The genetic algorithm designed at Purdue naturally selected the best-performing constellations by interchanging variables such as how far apart the satellites are from each other, the heading of the satellites as they cross the equator, and how high they are above the Earth's surface.

The results were unexpected. Normally, in constellations containing small numbers of satellites, the satellites are spaced at equal distances from each other as they track across the globe's equator. But in the best-performing constellations discovered by the genetic algorithm, the satellites were not spaced at equal distances.

"For example, the constellations might have two satellites spaced very far apart, and the third one will be very close to the second one," Crossley said, noting that engineers with years of aerospace experience were surprised by the higher performance offered by the unconventional design.

Williams, who earned a master of science degree in December 1999, currently works for the Pratt & Whitney Division of United Technologies Corp., in East Hartford, Conn.