The "radiation" from a reactor core mostly consists of highly energetic particles and gamma rays. It's not going to directly interfere with anything in the radio spectrum, or induce significant voltages on cables.
Radiation causes huge headaches in space because there's no way to pull it out or send in a replacement, and comms have seconds - minutes of lag. These don't apply to Earth based robots, even in super hazardous environments like this.
I wonder how many robots will become part of the contaminated decommissioning waste. Perhaps they will develop robots to disassemble and store the damaged and contaminated robots, filling a function like decomposers in nature.
Is it unlikely that a human would be able to work on the robots to repair them due to the levels of radiation?
See: https://www.bbc.co.uk/news/technology-20678838
"Most nuclear robots operate on power provided by a trailing umbilical. This means there are no batteries to change and no refuelling issues to contend with."
It's reasonably rare to have full or even semi-autonomous in nuclear due to the risks involved of something going wrong, or the thing just dying. Easier just to remote control down a cable.
See also https://www.emeraldinsight.com/doi/full/10.1108/014399112112... for an interesting overview of robots used at Fukushima.
Note that these robots probably aren't usiu the latest 14nm process so they have a natural immunity to bit flips.