According to Wikipedia, Bill Ayers (and the so-called "Weathermen") were trying to achieve "the destruction of US imperialism and achieve a classless world: world communism."
Obama hasn't expressed an interest in either of these goals. Some groups (liberal and conservative alike) hold a negative view of U.S. imperialism, and some groups (liberal and conservative alike) claim alternately that Obama is an imperialist or that he is an anti-imperialist. The truth is likely that he holds moderate, centrist views on the subject.
Though it should be added that if by "imperialism" we mean pre-emptive war against countries which pose no threat to the U.S. for financial or strategic gain (what we might call Bush-style imperialism, as can be seen in the Iraq War) then we will almost certainly see less of this sort of thing under President Obama.
Regarding the Weathermen's stated goal of achieving a communist state, no, there is no evidence whatsoever that Obama shares this goal and any suggestion he does is laughable. In fact, there is ample evidence that Obama's policies will promote a much healthier capatalist society than anything we have seen since the 1990's.
It should also be added that your question seems to be implying that Obama, like Ayers, might be a crazy radical who is going to bomb people, and I can only assume you make this connection via right-wing talking points. The suggestion is ridiculous. We could also ask whether Bush or Dick Cheney share the goals of Timothy McVeigh or the recent shooter who burst into a church claiming to "hate liberals." Whatever your opinion of the current Bush administration or the upcoming Obama administration, such questions are of little value.