Can I do research at the university without acceptance to the university
I believe that this is usually up to the faculty member that is running the research project. A couple of my friends in grad school contributed to our research group prior to their actual grad-school application, so that the faculty would know them better when the application came around.

(My area of research is compilers, different specialty, but still in the Computer Science/Computer Engineering department.)

When/if you do contact faculty members, try to have some concrete ideas and thoughts (and mention that you are looking for experience only for future grad-school applications, not a paid position.) Professors get bombarded with emails about grad students wanting TA/grader/RA positions every day, so you won't get a second thought if you send something generic. If you're very new to robotics, then instead of a concrete research topic, you could say something concrete about your experience and send your resume.

Contributing to a project, especially if it leads to a paper (but even if it doesn't) will definitely improve your grad-school application. It's a good strategy!