The robot consists ideally of some die-hard sensors positioned as far away as possible and as close as necessary - which are retractable mechanically in case of software failure by left behind elements. Then there is the actual tooling, which is basically just a remote controlled shell. A complicated setup, to say the least.
Imagine a Anemone with some little remote camera fishes on a tentacle, controlling a robotic crab on the longest tentacle of them all.
Is there a material that is transparent at optical frequencies but opaque at higher energies?
(Married to person who used to ship Californium-252)
This is what was done at Chernobyl in admittedly much more dire situation. A quantity of Japanese remote-controlled robots were urgently imported back then as well, and failed in the same manner.
Not this mess, or even that one, really. The "bio-robots", so called by their masters, were mainly collecting debris from the reactor explosion for containment; they were not trying to deal with the core slag sunk into the basement of the building, which at that time was still thermally very hot as well as being ferociously active. Even to approach that would have been immediately lethal.
Given the cited dose rate, the same is true at Fukushima - an acute dose of 10Sv is very likely lethal on its own, and at 650Sv/h you get more than that every minute. Anyone you send into that is going to be unable to work within seconds, and dead inside a couple of minutes tops.
We should also distinguish between site cleanup (which is certainly impossible) and secure containment (which is possible and was done before). The idea is not to chip away bits of highly radioactive substance, but find a safe way around it to isolate the world from further contamination. Apparently, not everyone is convinced Japan has a plan there.
https://en.wikipedia.org/wiki/Enewetak_Atoll
https://www.nytimes.com/2017/01/28/us/troops-radioactive-isl...