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!

It's not necessarily a problem that you're not enrolled in the university - it's possible for researchers to hire non-students in many cases.

However, it would be difficult to get someone to take you on when you don't want to make any commitment (e.g. get an official job). From their point of view: why should they invest time and effort training you and working with you, when you have no formal connection to them and can disappear at any time?

It may also be legally problematic (depending on the country) for them to allow you to work for free, when it's not part of an educational program for your benefit (like a formal internship program for students, or thesis research).

One way to effect this is to enroll as a "special student" taking one or two courses.

That way, you have not been "accepted" by the university for a degree. But it may allow you to "qualify" for an internship by being a student. Also, if you attend classes for even one or two courses, it makes it easier to make connections.