Is there any general problem in using precise positioning (centimeter-accurate GNSS RTK system meant) for autonomous car guidance given I have a predefined path the car should follow? I mean, autonomous cars were the topic #1 at CES 2016 yet no such simple system seems to have been introduced to date... Of course the "path planning" is only a part of the "autonomous package" and other problems need to be solved (collision prevention etc.) but I really wonder whether something simple like RTK guidance could be used.
An RTK system relies on very little amount of live correction data (about 1 kB/s) and mobile networks are really ubiquitous today so I can not really see a technical problem in such solution given there are enough RTK base stations around.
This question is only about using precise positioning to follow a predefined track in obstacle-free environment. I am not asking about other systems that need to be implemented in an autonomous car like collision prevention etc. (such systems may employ LIDAR or a stereo camera). Surely a collision prevention is a must for an autonomous system but I consider a theoretical case only.
An updated question may be: Is precise satellite positioning accurate enough to guide/navigate a full-scale passenger car in an obstacle-free outdoor environment in the speed of about 100 km/h given I have a precise-enough path prerecorded that is to follow?
Some answers below already say yes, this is a solved problem. It would be nice to have the answers elaborated in more detail regarding the existing solutions (accuracy, possible problems etc.). One of the solutions may probably be the open source APM autopilot which work for rovers too (example by Emlid) but that does not seem to use RTK so the accuracy may be rather low.