Want the easy way or the accurate way?
Go to
this site which has all the info needed. Under
field drawings, the third sheet of the Field Assembly file (PDFs) gives you most of the dimensions, just not the exact dimension you want. You'll have to get the dimensions of the defense base, which is in the Field Component file (also a PDF file). It's in there, but you'll have to wade thru a lot of sheets to get all the dimensions. Deduct all those and you'll have the dimension you want.
The easy way is to take that Field Assembly file, plot the third page to a plotter full sheet size (it's to 1:32 scale), and measure the distance. If you lack a plotter that size (they are 24 x 36 inch sheets), you could always drop that third sheet into AutoCAD, bring it to full size, then measure it. (This is actually how I did it, double checking with the given dimensions.) Yeah, the sheet says "Do Not Scale" but if you need it down to the fraction of an inch (or even inches), you're probably not going to have a good autonomous code. Don't forget, are you deducting for the length of the robot? Are you going to place the robot (as you say) *exact* same position each time? Is the battery the same power level each time (less battery power the motors will act differently). Oh, the fun you will have!
Even easier is to use a light sensor to detect the difference between carpet and the ramp.