Relaxed joint mode?

So I have a robot which forms our cartons by picking up the blanks off a pallet, dropping them into a squaring table, picking the blank back up and pushing it down through a former.

The issue we run into most often with the process is when the robot goes to pick-up the blanks. Essentially the end of arm tool which was designed is a rectangular frame with four suctions cups on the bottom. One of the suction cups has a vacuum sensor which lets the robot know when a blank has been picked up and the robot will go through the next motion after that. However, sometimes the stacks do not come in perfectly level and we have to shim corners to avoid the robot from crashing because one side of the end of arm tool hits the blanks stack more than the other causing a collision detect.

I was curious if there was a way I could put one of the joints into a "relaxed" mode so that it would turn with outside pressure. So basically if one side of the end of arm tool hits first, instead of detecting a collision it would see that this joint is getting pressure and turn with the pressure. If anyone has heard of a way to do this any information would be appreciated.

Thanks.

Controller is R-30iB, mechanical unit is an M-710iC/50. Does the handling tool manual give instructions on how to use this function and is it available for purchase or download?

Thank you Sergei, you've been very helpful.

The robot also palletizes the finished product. The cartons only get up to maybe 50 lbs filled and 4 foot in length. However, to do both these functions a wide range of motion is required, which is why I assume they specified this robot.