A question about time travel

[Umbran]

The wall from the second experiment starting being gray, the robot from the future arrives and paints the wall, maybe blue. Then the scientific group sends other robot to the past, and then the wall is painted red. What happens if the first robot travels to the past to paint the now red wall?

There is no "other robot", as you've described it. Let's be specific.

A wall is built in 1968. It is grey.

At 11:59 AM, August 1st, 1970, a robot appears from the future, and paints it red or blue, randomly. It finishes painting about one hour later, at 1 PM, August 1st, 1970.

At Noon, October 16th, 2020, someone sends a robot back to 11:59 AM, August 1st, 1970, a time when the wall is still grey.

So, there's no real problem here - the robot does not arrive to see a wall it has already painted itself. There is no loop here.