Fault reset by push button

What type of interfacing is done between PLC and robot? Is it hard-wired or any communication protocol is defined like EthernetIP or Profinet?

Get your fault reset push button input to PLC first and then (if robot and plc IOs are properly mapped) program this PLC input to robot UI 05(Reset) in peripheral inputs of robot. Check the status of UI05 input by pressing the fault reset PB.

You say the "PLC rack in the controller". That sentence doesn't make very much sense. The robot controller is not a PLC. It may or may not have a rack of I/O cards. A PLC would be a separate device unrelated to the robot, that may or may not have its own I/O cards.

So which is it? Do you have a 3rd party PLC with a rack of I/O cards or do you have Fanuc I/O cards?

Well if your DI's are already mapped, then all you have to do is look at the mapping for that DI and copy the same mapping to UI[5], i.e., make UI[5] the same rack/slot/start point as the DI that you want it to match.

On the DI screen push config and it will show you the configuration for the inputs.
Then in the UI screen set the config to the same as the DI for the input you need.

Example

Rest Push button is DI1

Rack Slot Start PT
DI 1-16 89 1 1

Then you would set the UI as follows

UI 1-4 0 0 0
UI 5-5 89 1 1

Here is another example with DI15 being the reset button.

Yes, UI 1,2,3 & 8 all need to be on in order to allow the robot to run when UI signals are enabled. You can read about this in the manual by searching for UOP Input Signals.