Space fans could also win some cash while doing so. The winner of the challenge will receive USD 1,000.
"We have this new free-flying robot that we're building," Jason Crusan, director of NASA's Advanced Exploration Systems division, said.
"We don't know what to call it. 'Free-flying robot' sounds kind of boring and not all that exciting, so we're asking you to actually name the robot for us," said Crusan.
The new robot is expected to look like something out of "Star Wars." It could appear as a small, ball-shaped droid that will use fans to move itself around the interior of the ISS.
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The robot is expected to be able to fly itself, or be operated by remote control, the report said.
In order to participate in the NASA challenge, space fans need to register with Topcoder.
Participants will reach a checkpoint where they will receive feedback on their initial designs on October 22, and the challenge ends on October 27. Officials will announce the winners of the competition on November 2.