Image: Comet-probing Rosetta spacecraft
The Comet-probing Rosetta spacecraft will reach Comet 67P/Churyumov-Gerasimenko in 2014, after a total of three Earth swing-bys and one Mars swing-by.
updated 1/9/2008 1:04:55 PM ET 2008-01-09T18:04:55

Spacecraft could soon take advantage of a sophisticated math algorithm that simulates evolution to find the best paths to distant planets and comets.

Engineers at the University of Missouri tweaked a mathematical approach called "differential evolution" so that it works quickly and efficiently to plot the best course for robotic deep space missions.

"This helps you figure out trajectory, size up the spacecraft, how much fuel is needed, what kind of launch vehicles are needed ... all answers you need to get before going into the mission details," said Craig Kluever, aerospace engineer at the University of Missouri.

The math algorithm treats possible solutions as individuals in a population, choosing a few each time to "mutate" and swap traits, then testing the mutants against the previous solutions. The best solutions win out and survive to the next generation, where the process may repeat again and again.

Applying this approach to calculating spacecraft trajectories is "not new, but it's catching on," said Aaron Olds, a former MU grad student who worked with Kluever. The European Space Agency (ESA) sponsored two studies that compared differential evolution with other methods — one study deemed differential evolution the best, while the other study found its performance just average.

This contradiction in success arose because the ESA researchers used different numbers for population size, rate of mutation and the likelihood of traits crossing over between solutions. Kluever and Olds set out to find the best numbers for calculating spacecraft trajectories.

They fine-tuned the algorithm by testing it in a software program against four space mission scenarios — including the complex 1997 Cassini mission to Saturn that involved swing-bys of Earth, Venus and Jupiter, as well as deep space maneuvers.

"The Cassini results were actually very close to what was actually flown," noted Kluever. "A lot of event times and flybys were right on the same day or just off by one day."

Many of the best solutions for Cassini did not precisely happen during the mission because of real world constraints. For instance, a planned course correction might have been delayed because mission control had problems communicating with the Cassini spacecraft.

Such real world constraints will play a role in any real missions, but the differential evolution algorithm simply ignores them. Kluever and Olds think the approach can best help mission planners who design challenging future missions to distant targets within the solar system.

Olds pointed to recent "missions that require a little more computational power," such as the International Rosetta mission that will chase down a comet and put a lander on the surface by 2014. Rosetta's complex trajectory has already included two swing-bys of Earth and one of Mars, with a final Earth swing-by planned in 2009 before the spacecraft heads for its final destination.

The differential evolution approach could also apply to future missions such as a crewed mission to Mars, which Kluever and Olds used as a scenario to fine-tune the algorithm.

Mission planners currently use a variety of tools, including a "design driven" approach where experienced analysts make a best guess for spacecraft trajectories before making calculations, Olds said. He and Kluever hope that space agencies will continue looking into differential evolution.

"I think it'd be nice if NASA would like to put it in their toolbox," said Kluever. "It's not going to be a replacement, but you can look at a problem from a different angle."

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