RFID is a terrible method to prevent collision. Here is why:
LOCATION: RFID does not detect location. At best you would have to get multiple receivers/readers and try to do triangulation based on RF signal levels, but that is tricky and error prone.
RANGE: RFID is inherently short range. There are versions which are longer range, but these versions actually make triangulating a position more difficult.
SPEED: RFID is SLOW. The "reader" has to transmit an RF signal long enough to charge up a small cap in the tag (for the APRT version). Only then can the tag respond with its ID. The bit rate is also relatively slow. This will reduce the reaction time of your collision avoidance system.
There are versions of RFID that try to improve the range and speed, but these systems are R&D projects and not commercial products. Even if you could get one, there is no guarantee that it would work for your application.
You could try to roll your own RFID solution that would work for your application, but it is more likely that engineering a proper solution (and not trying to force RFID into this application) would give you better results.
If I were doing this project, I would be looking into those cheap radar units that are currently used in cars for collision avoidance. They are mainly used in the rear bumper to detect objects when backing up, but they are being used more and more in cars facing forward for break assist and cruise control stuff.