Give science a little more credit :) The n-body problem is hard, but it's more like "we don't know if this same asteroid will hit the Earth 20 years from now" hard than "this asteroid could shift course at any moment!" hard.
From an earlier press release on this asteroid, from a 2010 pass:
[The radar imaging] reveals 2005 YU55 as a spherical object about 400 meters (1,300 feet) in size.
Not only can the radar provide data on an asteroid's dimensions, but also on its exact location in space. Using Arecibo's high-precision radar astrometry capability, scientists were able to reduce orbit uncertainties for YU55 by 50 percent.
"At one time we had classified 2005 YU55 as a potential threat," said Steve Chesley, a scientist at JPL's Near-Earth Object Program Office. "Prior to the Arecibo radar passes on April 19 thru 21 [2010], we had eliminated almost all upcoming Earth flybys as possibilities of impact. But there were a few that had a low remaining probability of impact. After incorporating the data from Arecibo, we were able to rule impacts out entirely for the next 100 years."
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So, they do know this one will be well-behaved for 100 years.
I work at NASA, supporting the person who wrote the codes that is now used for planetary dynamics simulation, like this. It is an extraordinarily complex problem, and a specialized academic discipline in its own right.
n-body dynamics is a complicated, chaotic system. Getting any precision at all over any reasonable period of time is a feat of itself.
Not entirely trivial. Because it is chaotic, it's not terribly well behaved. People who try to integrate the solar system forward in time have to put some effort into accuracy, and ultimately accuracy is limited by our limited knowledge of the initial state of the system.
[The radar imaging] reveals 2005 YU55 as a spherical object about 400 meters (1,300 feet) in size.
Not only can the radar provide data on an asteroid's dimensions, but also on its exact location in space. Using Arecibo's high-precision radar astrometry capability, scientists were able to reduce orbit uncertainties for YU55 by 50 percent.
"At one time we had classified 2005 YU55 as a potential threat," said Steve Chesley, a scientist at JPL's Near-Earth Object Program Office. "Prior to the Arecibo radar passes on April 19 thru 21 [2010], we had eliminated almost all upcoming Earth flybys as possibilities of impact. But there were a few that had a low remaining probability of impact. After incorporating the data from Arecibo, we were able to rule impacts out entirely for the next 100 years."
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So, they do know this one will be well-behaved for 100 years.