From a kid in the same situation, take it from me. Nobody can talk about your chances. Nobody has the end-all answer. When you read the "Is grad school for me" documents (which can be found hidden on particularly benevolent professors' pages) they all say the same thing: we don't know. So I'll repeat what I've found over the last year of searching:
Accolades aside, the only determining factor in admission to grad school (from what I can tell) is your motivation. If you haven't decided until now that you "might" be interested, then you have some catching up to do. Don't worry, I'm a late-bloomer too, and I'm doing the same catching up.
No one (aside from maybe your adviser) can give you the confidence and reassurance you want. You have to do it for yourself. Of COURSE you are going to apply to CMU, and every other great school. There is no harm in trying, and you'll regret not trying, I'd bet. The best schools have the most resources and connections. They also admit mostly kids from schools they know, recommended by professors they remember. It's just like any job connection: you are best off if you met someone before. Cold applications don't usually work. That said, their admission rate is similar to any other school (10-25% of all applicants). That means most applicants are being scared off before they apply. I'm guessing you feel that already. Remember: From Mor Harchol-Balter's own admission, the most heavily considered factors are:
1) letters of recommendation (which reflect the approval of someone already "in the club"),
2) personal statements (which reflect maturity, confidence, motivation, and competitiveness), and
3) relevant research experience (ie. prior experience).
Finally: Don't be rush to be pretentious. Look at the researchers, not the school. Peruse scientific journals, make use of google, IEEE, and ACM to find the research that is being done. Find a prof with a well-funded lab at any school. Make great use of your adviser's contacts, and other contacts in your school. Do not consider yourself a failure if you don't go to CMU. Most of the researchers of the world didn't go to CMU. In the end, the truth will out, and it is your personal capability, motivation, and resourcefulness that will determine your success, not your alma mater. Remember that the last and longest part of a PhD is individual research. Your worth as a researcher will probably be more heavily judged by the quality of your research, not whether or not you were admitted to CMU. (But still go for it!)
Finally again: Don't go to grad school if you don't have some idea of a topic you want to explore. Grad is not like a continuation of a bachelors, esp. a PhD program. Find a topic, find labs that are exploring that topic, and apply to the school that host those labs. A large part of your time will probably be spent in that project. A PhD is expected to take classes needed to further their research. The general education stuff is over.
Finally Finally Finally: If you want to build robots: Consider that Big Dog was built by a Master of EE. Their project lead has a masters anyway. Don't put all your eggs in a PhD track, unless you want to spend most of your time sitting and thinking. The kids with masters get to do the fun stuff, from what I can tell, because they are expected to apply knowledge. A PhD gets to research and pontificate, a Masters gets to be a master. Look up those robots you find most inspiring, and see who is actually involved. Read their bios, you will probably be very surprised to find that most have a similar story as yours. (or mine, by proxy).
Hope that helps. Feel free to get a hold of me whenever. I'm no expert, and all this is second-hand knowledge, but I'm headed down the same path you are.